NeQST — Publications

Publications: Qudit stabilizer codes for ZN lattice gauge theories with matter

Thu, 26 Feb 2026 00:00:00 +0000

Authors: Luca Spagnoli, Alessandro Roggero, and Nathan Wiebe

Journal reference: arXiv:2602.20661 [quant-ph] — Published February 26, 2026

In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a \(ZN\) gauge theory with prime dimension \(N\) coupled to dynamical matter can be expressed as a qudit stabilizer code. Using the stabilizer formalism we show how to formulate an exact mapping of the encoded \(ZN\) gauge theory onto two different bosonic models, uncovering a logical duality generated by error correction itself. From this perspective, quantum error correction provides a unifying language to expose dual descriptions of lattice gauge theories. In addition, we generalize earlier \(Z2\) constructions on qubits to \(ZN\) on \(N\)-level qudits and demonstrate how universal fault-tolerant gates can be implemented via state injection between compatible qudit codes.

Publications: Improving Quantum Multi-Objective Optimization with Archiving and Substitution

Wed, 11 Feb 2026 00:00:00 +0000

Authors: Linus Ekstrom, Takafumi Hosogi, Xavier Bonet-Monroig, Sebastian Schmitt, Hao Wang, and Thomas Bäck

Journal reference: Presented at The 11th International Conference on Machine Learning, Optimization, and Data Science (LOD) 2025 — Published February 11, 2026

Finding optimal solutions of conflicting objectives is a daily matter in many industrial applications, with multi-objective optimization trying to find the best solutions to them. The advent of quantum computing has led to researchers wondering if the promised exponential advantage can be obtained for these problems by variational quantum multi-objective optimization (QMOO) algorithm. Here, we improve it by introducing a Pareto Archive and dominated solutions substitution, clearly improving in hyper-volume convergence at additional quantum and classical cost. We propose the use of RMNK-landscapes as a unifying testbed for benchmarking QMOO, as it is common in classical multi-objective field. By devising a generic classical-to-quantum mapping of these landscapes, we perform a numerical hyperparameter tuning of QMOO, significantly enhancing its performance. Finally, we compare QMOO against well-known classical solvers for multi-objective tasks, NSGA-II/III, showing comparable results in small instances. Our results demonstrate that QMOO, when carefully tuned for the task at hand, might be advantageous on harder problems than its classical counterparts.

Publications: Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes

Fri, 16 Jan 2026 00:00:00 +0000

Authors: Luca Spagnoli, Alessandro Roggero, and Nathan Wiebe

Journal reference: Quantum 10, 1968 — Published January 16, 2026

Preprint: arXiv:2405.19293 [quant-ph]

We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian \(Z2\) LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.

Publications: Device-independent Shannon entropy certification

Wed, 26 Nov 2025 00:00:00 +0000

Authors: Robert Okuła and Remigiusz Augusiak

Journal reference: New J. Phys. 27 114519 — Published November 26, 2025

Preprint: arXiv:2505.05395 [quant-ph]

Quantum technologies promise information processing and communication technology advancements, including random number generation (RNG). Using Bell inequalities, a user of a quantum RNG hardware can certify that the values provided by an untrusted device are truly random. This problem has been extensively studied for von Neumann and min-entropy as a measure of randomness. However, in this paper, we analyze the feasibility of such verification for Shannon entropy. We investigate how the usability of various Bell inequalities differs depending on the presence of noise. Moreover, we present the benefit of certification for Shannon compared to min-entropy, as well as the tight analytical lower bound for Shannon entropy in randomness certification.

Publications: Entanglement witnesses for stabilizer states and subspaces beyond qubit

Thu, 20 Nov 2025 00:00:00 +0000

Authors: Jakub Szczepaniak, Owidiusz Makuta, and Remigiusz Augusiak

Journal reference: Rep. Prog. Phys. 88 117602 — Published November 20, 2025

Preprint: arXiv:2508.13734 [quant-ph]

Genuine multipartite entanglement (GME) is arguably the most valuable form of entanglement in the multipartite case with application for instance in quantum metrology. In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses. The aim of this paper is to generalize the results of Tóth and Gühne (2005 Phys. Rev. A 72 022340) in order to provide a construction of witnesses of GME tailored to entangled subspaces originating from the multi-qudit stabilizer formalism—a framework well known for its role in quantum error correction, which also provides a very convenient description of a broad class of entangled multipartite states (both pure and mixed). Our construction includes graph states of arbitrary local dimension. We then show that in certain situations, the obtained witnesses detecting GME in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.

Publications: Superresolving collective quantum measurements

Wed, 05 Nov 2025 00:00:00 +0000

Authors: J. O. de Almeida, M. Lewenstein, and M. Skotiniotis

Journal reference: Phys. Rev. A 112, 052605 — Published November 05, 2025

Preprint: arXiv:2110.00986 [quant-ph]

We demonstrate a method for superresolving signals encoded as finite mixtures of bosonic modes using collective measurements that exploit permutation symmetry. Specifically, we use multiple copies of the state 𝜌 of the finite mixture to extract an estimate for the purity of 𝜌 via a spectrum measurement, the weak Schur-sampling measurement. Depending on the outcome, we then further fine-grain the measurement to optimally extract an estimate of the relative intensity between the two incoherent mixtures. Our protocol furnishes simultaneous estimates for both the relative intensity and the separation of incoherent signals saturating the multiparameter Cramér-Rao bound and is robust against misalignment errors. We also provide viable experimental avenues for implementing such collective measurements in different setups.

Publications: Deep Neural Network-assisted improvement of quantum compressed sensing tomography

Mon, 03 Nov 2025 00:00:00 +0000

Authors: Adriano Macarone-Palmieri, Leonardo Zambrano, Maciej Lewenstein, Antonio Acín, and Donato Farina

Journal reference: Phys. Scr. 100 115106 — Published November 03, 2025

Preprint: arXiv:2405.10052 [quant-ph]

Quantum compressed sensing is a fundamental technique for tomographic reconstruction of low-rank density matrices in informationally incomplete scenarios. However, when the available measurement data is insufficient, standard compressed sensing, like other algorithmic estimators such as maximum-likelihood, can yield imprecise or noisy estimates. To mitigate this, we propose a deep neural network-based post-processing to enhance the initial reconstruction. By treating the compressed sensing-estimated quantum state as a noisy input, the network performs a supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate the effectiveness of our method through numerical experiments. Additionally, we explore iterative application of the inference process to further enhance performance, and we analyze the network’s generalization ability by testing its performance on states and noise models not seen during training.

Publications: Inequality constraints in variational quantum circuits with qudits

Fri, 29 Aug 2025 00:00:00 +0000

Authors: Alberto Bottarelli, Sebastian Schmitt, and Philipp Hauke

Journal reference: Phys. Rev. Research 7, 033202 — Published August 29, 2025

Preprint: arXiv:2410.07674 [quant-ph]

Preprint: Zenodo data repository

Quantum optimization is emerging as a prominent candidate for exploiting the capabilities of near-term quantum devices. Many application-relevant optimization tasks require the inclusion of inequality constraints, usually handled by enlarging the Hilbert space through the addition of slack variables. This approach, however, requires significant additional resources especially when considering multiple constraints. Here, we study an alternative direct implementation of these constraints within the quantum approximate optimization algorithm, achieved using qudit-sum gates, and compare it to the slack variable method generalized to qudits. We benchmark these approaches on three paradigmatic optimization problems. We find that the direct implementation of the inequality penalties vastly outperforms the slack variables method, especially when studying real-world inspired problems with many constraints. Within the direct penalty implementation, a linear energy penalty for unfeasible states outperforms other investigated functional forms, such as the canonical quadratic penalty. The proposed approach may thus be an enabling step for approaching realistic industry-scale and fundamental science problems with large numbers of inequality constraints.

Publications: All genuinely entangled stabilizer subspaces are multipartite fully nonlocal

Sat, 23 Aug 2025 00:00:00 +0000

Authors: Owidiusz Makuta and Remigiusz Augusiak

Journal reference: npj Quantum Inf 11, 144 — Published August 23, 2025

Preprint: arXiv:2312.08757 [quant-ph]

Understanding which entangled states give rise to Bell nonlocality and thus are resourceful in the device-independent framework is a long-standing unresolved problem. Here, we establish the equivalence between genuine entanglement and genuine nonlocality for a broad class of multipartite (pure and mixed) states originating from the stabilizer formalism. In fact, we prove that any (mixed) stabilizer state defined on a genuinely entangled subspace is multipartite fully nonlocal, meaning that it gives rise to correlations with no contribution from local hidden variable models of any type. Importantly, we also derive a lower bound on genuine nonlocality content of arbitrary multipartite states, opening the door to its experimental estimation.

Publications: Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model

Wed, 30 Jul 2025 00:00:00 +0000

Authors: Pavel P. Popov, Valentin Kasper, Maciej Lewenstein, Erez Zohar, Paolo Stornati, and Philipp Hauke

Journal reference: Phys. Rev. D 112, 014515 — Published July 30, 2025

Preprint: arXiv:2405.00745 [hep-lat]

Preprint: Zenodo data repository

Gauge-field configurations with nontrivial topology have profound consequences for the physics of Abelian and non-Abelian gauge theories. Over time, arguments have been gathering for the existence of gauge-field configurations with fractional topological charge, called fractons. Ground-state properties of gauge theories can drastically change in presence of fractons in the path integral. However, understanding the origin of such fractons is usually restricted to semiclassical argumentation. Here, we show that fractons persist in strongly correlated many-body systems, using the multiflavor Schwinger model of quantum electrodynamics as a paradigm example. Through detailed numerical tensor-network analysis, we find strong fracton signatures even in highly discretized lattice models, at sizes that are implementable on already existing quantum-simulation devices. Our work sheds light on how the nontrivial topology of gauge theories persists in challenging nonperturbative regimes, and it shows a path forward to probing it in tabletop experiments.

Publications: Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories

Tue, 22 Jul 2025 00:00:00 +0000

Authors: Edoardo Ballini, Julius Mildenberger, Matteo M. Wauters, and Philipp Hauke

Journal reference: Quantum 9, 1802 — Published July 22, 2025

Preprint: arXiv:2412.07844 [quant-ph]

Preprint: Zenodo data repository

Non-Abelian gauge theories underlie our understanding of fundamental forces of modern physics. Simulating them on quantum hardware is an outstanding challenge in the rapidly evolving field of quantum simulation. A key prerequisite is the protection of local gauge symmetries against errors that, if unchecked, would lead to unphysical results. While an extensive toolkit devoted to identifying, mitigating, and ultimately correcting such errors has been developed for Abelian groups, non-commuting symmetry operators complicate the implementation of similar schemes in non-Abelian theories. Here, we discuss two techniques for error mitigation through symmetry verification, tailored for non-Abelian lattice gauge theories implemented in noisy qudit hardware: dynamical post-selection (DPS), based on mid-circuit measurements without active feedback, and post-processed symmetry verification (PSV), which combines measurements of correlations between target observables and gauge transformations. We illustrate both approaches for the discrete non-Abelian group \(D3\) in 2+1 dimensions, explaining their usefulness for current NISQ devices even in the presence of fast fluctuating noise. Our results open new avenues for robust quantum simulation of non-Abelian gauge theories, for further development of error-mitigation techniques, and for measurement-based control methods in qudit platforms.

Publications: String breaking dynamics in Ising chain with local vibrations

Mon, 21 Jul 2025 00:00:00 +0000

Authors: Arindam Mallick, Maciej Lewenstein, Jakub Zakrzewski, and Marcin Płodzie

Journal reference: Phys. Rev. B 112, 024311 — Published July 21, 2025

Preprint: arXiv:2501.00604 [quant-ph]

We consider the dynamics in the one-dimensional quantum Ising model in which each spin coherently interacts with its phononic mode. The model is motivated by quantum simulators based on Rydberg atoms in tweezers or trapped ions. The configuration of two domain walls simulates the particle-antiparticle connecting string. We concentrate on the effect the local vibrations have on the dynamics of this initial state. Our study extends recent investigations of string breaking, traditionally studied within quantum chromodynamics, to quantum many-body systems. Two regimes are identified depending on the strength of the coupling with local vibrations. For weak coupling, the string breaking is slowed down compared to the dynamics in an isolated Ising string. Strong coupling leads to complicated dynamics in which the domain wall character of the excitation is dissolved among many coupled states.

Publications: Many-body quantum resources of graph states

Thu, 17 Jul 2025 00:00:00 +0000

Authors: Marcin Płodzień, Maciej Lewenstein, and Jan Chwedeńczuk

Journal reference: Rep. Prog. Phys. 88 077601 — Published July 17, 2025

Preprint: arXiv:2410.12487 [quant-ph]

Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. An ideal tool for this task would scale well with the size of the system, be easily computable and be easily measurable. In this work, we focus on graph states, which are promising platforms for quantum computation, simulation, and metrology. We consider four topologies: star graph states with edges, Turán graphs, r-ary tree graphs, and square grid cluster states. We provide a method to characterize their quantum content: many-body Bell correlations, non-separability and entanglement strength for an arbitrary number of qubits. We also relate the strength of these correlations to the usefulness of graph states for quantum sensing. Finally, we characterize many-body entanglement in graph states with up to eight qubits in 146 classes that are not equivalent under local transformations or graph isomorphisms. This technique is straightforward and does not require any assumptions about the multi-qubit state; therefore it could be applied wherever precise knowledge of many-body quantum correlations is necessary.

Publications: Efficient Qudit Circuit for Quench Dynamics of \(2+1D\) Quantum Link Electrodynamics

Wed, 16 Jul 2025 00:00:00 +0000

Authors: Rohan Joshi, Michael Meth, Jan C. Louw, Jesse J. Osborne, Kevin Mato, Martin Ringbauer, and Jad C. Halimeh

Journal reference: arXiv:2507.12589 [quant-ph] — Published July 16, 2025

A major challenge in the burgeoning field of quantum simulation for high-energy physics is the realization of scalable \(2+1\)D lattice gauge theories on state-of-the-art quantum hardware, which is an essential step towards the overarching goal of probing \(3+1\)D quantum chromodynamics on a quantum computer. Despite great progress, current experimental implementations of \(2+1\)D lattice gauge theories are mostly restricted to relatively small system sizes and two-level representations of the gauge and electric fields. Here, we propose a resource-efficient method for quantum simulating \(2+1\)D spin-\(S\)\(U(1)\) quantum link lattice gauge theories with dynamical matter using qudit-based quantum processors. By integrating out the matter fields through Gauss's law, we reformulate the quantum link model in a purely spin picture compatible with qudit encoding across arbitrary spatial dimensions, eliminating the need for ancillary qubits and reducing resource overhead. Focusing first on the spin-\(1/2\) case, we construct explicit circuits for the full Hamiltonian and demonstrate through numerical simulations that the first-order Trotterized circuits accurately capture the quench dynamics even in the presence of realistic noise levels. Additionally, we introduce a general method for constructing coupling-term circuits for higher-spin representations \(S > 1/2\). Compared to conventional qubit encodings, our framework significantly reduces the number of quantum resources and gate count. Our approach significantly enhances scalability and fidelity for probing nonequilibrium phenomena in higher-dimensional lattice gauge theories, and is readily amenable to implementation on state-of-the-art qudit platforms.

Publications: Quantum simulation of non-Abelian lattice gauge theories: A variational approach to D8 with dynamical matter

Wed, 02 Jul 2025 00:00:00 +0000

Authors: Emanuele Gaz, Pavel P. Popov, Guy Pardo, Maciej Lewenstein, Philipp Hauke, and Erez Zohar

Journal reference: Phys. Rev. Research 7, 033012 — Published July 02, 2025

Preprint: arXiv:2501.17863 [hep-lat]

Preprint: Zenodo data repository

Quantum simulation of lattice gauge theories (LGTs) provides a powerful framework for understanding nonperturbative phenomena. However, to realize the hope of answering challenging physics questions on near-term devices it is crucial to develop resource-efficient formulations, in particular for non-Abelian LGTs and beyond (1+1) dimensions. In this work, we address this issue by focusing on the difficulty of simulating fermionic degrees of freedom and on mitigating the Hilbert space redundancy, i.e., the presence of exponentially many nonphysical states that do not obey gauge invariance. First, we show a procedure that removes the matter and improves the hardware-resource efficiency. We demonstrate it for the simplest non-Abelian group addressable with this procedure, \(D8\), in the cases of both one and two spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the \(D8\) LGT onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem, and reducing the amount of quantum resources. This approach can serve as a way of simulating LGTs in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.

Publications: Symmetry-Protected Topological Haldane Phase on a Qudit Quantum Processor

Wed, 11 Jun 2025 00:00:00 +0000

Authors: C.L. Edmunds, E. Rico, I. Arrazola, G.K. Brennen, M. Meth, R. Blatt, and M. Ringbauer

Journal reference: PRX Quantum 6, 020349 — Published June 11, 2025

Preprint: arXiv:2408.04702 [quant-ph]

Preprint: Zenodo data repository

Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2.

Publications: Certifying classes of d-outcome measurements with quantum steering

Thu, 29 May 2025 00:00:00 +0000

Authors: Alexandre C. Orthey and Remigiusz Augusiak

Journal reference: New J. Phys. 27 064501 — Published May 29, 2025

Preprint: arXiv:2410.20477 [quant-ph]

Device-independent (DI) certification schemes are based on minimal assumptions about the quantum system under study, which makes the most desirable among certification schemes. However, they are often the most challenging to implement. In order to reduce the implementation cost one can consider semi-DI (SDI) schemes such as those based on quantum steering. Here we provide a construction of a family of steering inequalities which are tailored to large classes of d-outcomes projective measurements being a certain linear combination of the Heisenberg–Weyl operators on the untrusted side and a fixed set of known measurements on the trusted side. We then prove that the maximal quantum violation of those inequalities can be used for certification of those measurements and the maximally entangled state of two qudits. Importantly, in our self-testing proof, we do not assume the shared state to be pure, nor do we assume the measurements to be projective. Before concluding, we also show how robust to noise our self-testing statement is. We believe that our construction broadens the scope of SDI certification, paving the way for more general but still less costly quantum certification protocols.

Publications: Device-Independent Quantum Key Distribution beyond qubits

Tue, 27 May 2025 00:00:00 +0000

Authors: Javier Rivera-Dean, Anna Steffinlongo, Neil Parker-Sánchez, Antonio Acín, and Enky Oudot

Journal reference: New J. Phys. 27 054512 — Published May 27, 2025

Preprint: arXiv:2402.00161 [quant-ph]

Preprint: Github

Device-independent quantum key distribution (DIQKD) aims to generate secret keys between two parties without relying on trust in their employed devices, imposing strict constraints on the experimental conditions needed for successful key generation. In this study, we derive bounds for noise and detection efficiency—two critical parameters for experimental implementations—beyond qubit-based protocols. Our results show that while lower bounds indicate no improvement in noise resilience with increased dimensionality, upper bounds reveal marginal, albeit insignificant, enhancements. Given the experimental challenges associated with the development of qudit-based systems, our findings prompts a debate on their practical utility for DIQKD.

Publications: A Real-World Energy Management Dataset from a Smart Company Building for Optimization and Machine Learning

Sat, 24 May 2025 00:00:00 +0000

Authors: Jens Engel, Andrea Castellani, Patricia Wollstadt, Felix Lanfermann, Thomas Schmitt, Sebastian Schmitt, Lydia Fischer, Steffen Limmer, David Luttropp, Florian Jomrich, René Unger, and Tobias Rodemann

Journal reference: Sci Data 12, 864 — Published May 24, 2025

Preprint: arXiv:2503.11469 [eess.SY]

Preprint: Data repository

We present a large real-world dataset obtained from monitoring a smart company facility over the course of six years, from 2018 to 2023. The dataset includes energy consumption data from various facility areas and components, energy production data from a photovoltaic system and a combined heat and power plant, operational data from heating and cooling systems, and weather data from an on-site weather station. The measurement sensors installed throughout the facility are organized in a hierarchical metering structure with multiple sub-metering levels, which is reflected in the dataset. The dataset contains measurement data from 72 energy meters, 9 heat meters and a weather station. Both raw and processed data at different processing levels, including labeled issues, is available. In this paper, we describe the data acquisition and post-processing employed to create the dataset. The dataset enables the application of a wide range of methods in the domain of energy management, including optimization, modeling, and machine learning to optimize building operations and reduce costs and carbon emissions.

Publications: Quantum algorithms for inverse participation ratio estimation in multiqubit and multiqudit systems

Fri, 16 May 2025 00:00:00 +0000

Authors: Yingjian Liu, Piotr Sierant, Paolo Stornati, Maciej Lewenstein, and Marcin Płodzień

Journal reference: Phys. Rev. A 111, 052614 — Published May 16, 2025

Preprint: arXiv:2405.03338 [quant-ph]

Preprint: Github

Inverse participation ratios (IPRs) and the related participation entropies quantify the spread of a quantum state over a selected basis of the Hilbert space, offering insights into the equilibrium and nonequilibrium properties of the system. In this work, we propose three quantum algorithms to estimate IPRs on multiqubit and multiqudit quantum devices. The first algorithm allows for the estimation of IPRs in the computational basis by single-qubit measurements, while the second one enables measurement of IPR in the eigenbasis of a selected Hamiltonian, without the knowledge about the eigenstates of the system. Next, we provide an algorithm for IPR in the computational basis for a multiqudit system. We discuss resources required by the algorithms and benchmark them by investigating the one-axis twisting protocol, the thermalization in a deformed PXP model, and the ground state of a spin-1 Affleck-Kennedy-Lieb-Tasaki chain in a transverse field.

Publications: Anderson localization induced by structural disorder

Wed, 14 May 2025 00:00:00 +0000

Authors: Sourav Bhattacharjee, Piotr Sierant, Marek Dudyński, Jan Wehr, Jakub Zakrzewski, and Maciej Lewenstein

Journal reference: Phys. Rev. B 111, L180202 — Published May 14, 2025

Preprint: arXiv:2411.10247 [cond-mat.dis-nn]

We examine the onset of Anderson localization in three-dimensional systems with structural disorder in form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of lattice regularities, we show that the Anderson localization transition occurs when the strength of the structural disorder is smoothly increased. Performing finite-size scaling analysis, we show that the transition belongs to the same universality class as regular Anderson localization induced by on-site disorder. Our paper identifies a class of structurally disordered lattice models in which destructive interference of matter waves may inhibit transport and lead to a transition between metallic and localized phases.

Publications: Variational quantum multiobjective optimization

Mon, 12 May 2025 00:00:00 +0000

Authors: Linus Ekstrom, Hao Wang, and Sebastian Schmitt

Journal reference: Phys. Rev. Research 7, 023141 — Published May 12, 2025

Preprint: arXiv:2312.14151 [quant-ph]

Preprint: Github

Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attention in recent years. Currently, most studies have focused on single-objective problems, whereas many real-world applications need to consider multiple, mostly conflicting objectives, such as cost and quality. We present a variational quantum optimization algorithm to solve discrete multiobjective optimization problems on quantum computers. The proposed quantum multiobjective optimization (QMOO) algorithm incorporates all cost Hamiltonians representing the classical objective functions in the quantum circuit and produces a quantum state consisting of Pareto-optimal solutions in superposition. From this state, we retrieve a set of solutions and utilize the widely applied hypervolume indicator to determine its quality as an approximation to the Pareto front. The variational parameters of the QMOO circuit are tuned by maximizing the hypervolume indicator in a quantum-classical hybrid fashion. We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives. We investigate the influence of the classical optimizer and the circuit depth, and compare them to results from classical optimization algorithms. We find that the algorithm is robust to shot noise and produces good results with as few as 128 measurement shots in each iteration. These promising results open the possibility to run the algorithm on near-term quantum hardware.

Publications: Unveiling Eigenstate Thermalization for Non-Hermitian systems

Thu, 08 May 2025 00:00:00 +0000

Authors: Sudipto Singha Roy, Soumik Bandyopadhyay, Ricardo Costa de Almeida, and Philipp Hauke

Journal reference: Phys. Rev. Lett. 134, 180405 — Published May 08, 2025

Preprint: arXiv:2309.00049 [quant-ph]

The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce a framework that extends the ETH to non-Hermitian systems, within which expectation values of local operators reproduce statistical and scaling predictions known from Hermitian ETH. We illustrate the validity of the framework on non-Hermitian random-matrix and Sachdev-Ye-Kitaev models. Further, we show numerically how the static ETH predictions become imprinted onto the dynamics of local observables. Finally, we present a prescription for observing both ETH-obeying and ETH-violating regimes in an optical-lattice experiment that implements a disordered interacting Hatano-Nelson model. Our results generalize the celebrated ETH to the non-Hermitian setting, and they show how it affects the system dynamics, and how the salient signatures can be observed in present-day cold-atom experiments.

Publications: Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions

Fri, 02 May 2025 00:00:00 +0000

Authors: Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, and Aditi Sen De

Journal reference: Phys. Rev. A 111, 052402 — Published May 02, 2025

Preprint: arXiv:2407.21668 [quant-ph]

Preprint: Zenodo data repository

We examine the impact of long-range Dzyaloshinskii-Moriya (DM) interaction in the extended \(XY\) model on the phase diagram as well as the static and dynamical properties of quantum and classical correlation functions. It is known that in the nearest-neighbor \(XY\) model with DM interaction, the transition from the gapless chiral phase to a gapped one occurs when the strengths of the DM interaction and anisotropy coincide. We exhibit that the critical line gets modified with the range of interactions which decay according to power law. Specifically, instead of being gapless in the presence of a strong DM interaction, a gapped region emerges which grows with the increase of the moderate fall-off rate (quasi-long-range regime) in the presence of a transverse magnetic field. The gapless chiral phase can also be separated from a gapped one by the decay patterns of quantum mutual information and classical correlation with distant sites of the ground state which are independent of the fall-off rate in the gapless zone. We observe that the corresponding critical lines that depend on the fall-off rate can also be determined from the effective central charge involved in the scaling of entanglement entropy. We illustrate that in a nonequilibrium setting, the relaxation dynamics of classical correlation, the decay rate of total correlation, and the growth rate of entanglement entropy can be employed to uncover whether the evolving Hamiltonian and the Hamiltonian corresponding to the initial state are gapped or gapless.

Publications: Quantum-enhanced sensing with variable-range interactions

Wed, 30 Apr 2025 00:00:00 +0000

Authors: Monika Mothsara, Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, and Aditi Sen De

Journal reference: Phys. Rev. A 111, 042628 — Published April 30, 2025

Preprint: arXiv:2307.06901 [quant-ph]

Preprint: Zenodo data repository

The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a variable-range many-body quantum spin chain with a moderate transverse magnetic field. We report the threefold benefits of employing a long-range system as a quantum sensor. First, sensors with quasi-long-range interactions can always beat the SQL for all values of the coordination number, while a sensor with long-range interactions does not have this ubiquitous quantum advantage. Second, a long-range Hamiltonian outperforms a nearest-neighbor (NN) Hamiltonian in terms of both estimating precision and system-size scaling. Finally, we observe that the system with long-range interactions can go below the SQL in the presence of a high temperature of the initial state, while sensors having NN interactions cannot. Furthermore, a sensor based on the long-range Ising Hamiltonian proves to be robust against impurities in the magnetic field and when the time-inhomogeneous dephasing noise acts during interaction of the probe with the system.

Publications: A Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack

Fri, 25 Apr 2025 00:00:00 +0000

Authors: Andoni Agirre, Evert van Nieuwenburg, and Matteo M Wauters

Journal reference: New J. Phys. 27 043014 — Published April 25, 2025

Preprint: arXiv:2408.12648 [quant-ph]

Preprint: Zenodo data repository

The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQAs) are a promising family of hybrid quantum–classical methods tailored to cope with the limited capability of near-term quantum hardware. However, their effectiveness is hampered by the complexity of the classical parameter optimization which is prone to getting stuck either in local minima or in flat regions of the cost-function landscape. The clever design of efficient optimization methods is therefore of fundamental importance for fully leveraging the potential of VQAs. In this work, we approach parameter optimization as a sequential decision-making problem and tackle it with an adaptation of Monte Carlo Tree Search, a powerful artificial intelligence technique designed for efficiently exploring complex decision graphs. We show that leveraging regular parameter patterns deeply affects the decision-tree structure and allows for a flexible and noise-resilient optimization strategy suitable for near-term quantum devices. Our results shed further light on the interplay between artificial intelligence and quantum information and provide a valuable addition to the toolkit of variational quantum circuits.

Publications: Temporal Bell inequalities in non-relativistic many-body physics

Thu, 17 Apr 2025 00:00:00 +0000

Authors: A. Tononi and M. Lewenstein

Journal reference: Quantum Sci. Technol. 10 03LT01 — Published April 17, 2025

Preprint: arXiv:2409.17290 [quant-ph]

Analyzing the spreading of information in many-body systems is crucial to understanding their quantum dynamics. At the most fundamental level, this task is accomplished by Bell inequalities, whose violation by quantum mechanics implies that information cannot always be stored locally. While Bell-like inequalities, such as the one of Clauser and Horne, envisage a situation in which two parties perform measurements on systems at different positions, one could formulate temporal inequalities, in which the two parties measure at different times. However, for causally-connected measurement events, these extensions are compatible with a local description, so that no intrinsically-quantum information spreading is involved in such temporal correlations. Here we show that a temporal Clauser–Horne inequality for two spins is violated for a nonzero time interval between the measurements if the two measured parties are connected by a spin chain. Since the chain constitutes the sole medium for the spreading of quantum information, it prevents the immediate vanishing of Bell correlations after the first measurement and it induces violation revivals. The dynamics we analyze shows that, as expected in a non-relativistic setup, the spreading of information is fundamentally limited by the Lieb–Robinson bound. New insights on many-body quantum dynamics could emerge through future applications of our temporal Bell inequality to more general systems.

Publications: Qudit-native measurement protocol for dynamical correlations using Hadamard tests

Thu, 03 Apr 2025 00:00:00 +0000

Authors: Pavel P. Popov, Kevin T. Geier, Valentin Kasper, Maciej Lewenstein, and Philipp Hauke

Journal reference: Phys. Rev. A 111, 042604 — Published April 03, 2025

Preprint: arXiv:2407.03421 [quant-ph]

Dynamical correlations reveal important out-of-equilibrium properties of the underlying quantum many-body system, yet they are notoriously difficult to measure in experiments. While measurement protocols for dynamical correlations based on Hadamard tests for qubit quantum devices exist, they do not straightforwardly extend to qudits. Here, we propose a modified protocol to overcome this limitation by decomposing qudit observables into unitary operations that can be implemented and probed in a quantum circuit. We benchmark our algorithm numerically at the example of quench dynamics in a spin-1 \(XXZ\) chain with finite shot noise and demonstrate advantages in terms of the signal-to-noise ratio over established protocols based on linear response. Our scheme can readily be implemented on various platforms and offers a wide range of applications like variational quantum optimization and probing thermalization in many-body systems.

Publications: Quantum Algorithms in Practice: Application to Ground-State Energy Estimation

Tue, 01 Apr 2025 00:00:00 +0000

Authors: Oriel Kiss, Utkarsh Azad, Borja Requena, Alessandro Roggero, David Wakeham, and uan Miguel Arrazol

Journal reference: Quantum 9, 1682 — Published April 01, 2025

We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure of a Hamiltonian and the identification of its discontinuities. Scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states. To address these challenges, we propose a signal processing approach to find these estimates automatically, in the regime where the quality of the initial state is unknown. Rather than aiming for exact ground-state energy, we advocate for improving classical estimates by targeting the low-energy support of the initial state. Additionally, we provide quantitative resource estimates, demonstrating a constant factor improvement in the number of samples required to detect a specified change in CDF. Our numerical experiments, conducted on a 26-qubit fully connected Heisenberg model, leverage a truncated density-matrix renormalization group (DMRG) initial state with a low bond dimension. The results show that the predictions from the quantum algorithm align closely with the DMRG-converged energies at larger bond dimensions while requiring several orders of magnitude fewer samples than theoretical estimates suggest. These findings underscore that CDF-based quantum algorithms are a practical and resource-efficient alternative to quantum phase estimation, particularly in resource-constrained scenarios.

Publications: Symmetry-protection Zeno phase transition in monitored lattice gauge theories

Fri, 28 Mar 2025 00:00:00 +0000

Authors: Matteo M. Wauters, Edoardo Ballini, Alberto Biella, and Philipp Hauke

Journal reference: Phys. Rev. B 111, 094315 — Published March 28, 2025

Preprint: arXiv:2405.18504 [quant-ph, hep-lat]

Preprint: Zenodo data repository

Quantum measurements profoundly influence system dynamics. They lead to complex nonequilibrium phenomena like the quantum Zeno effect, and they can be used for mitigating errors in quantum simulations. Such an ability is particularly valuable for lattice gauge theories (LGTs), which require the challenging preservation of an extensive number of local conservation laws. While it is known that tailored quantum measurements can soften violations of gauge symmetry, the nature of this protection, and in particular the possibility of a threshold behavior, is still unexplored. Here, we demonstrate the existence of a sharp transition, triggered by the measurement rate, between a protected gauge-theory regime resistant to simulation errors and an irregular regime. Our results are based on the paradigmatic example of a 1+1d \(Z2\) LGT. We study in detail the protection through projective measurements of ancillary qubits coupled to the local symmetry generators, and compare this approach with analog (weak) measurement protocols. We show that, while the resulting ensemble averages in the continuous-time limit share the same Liouvillian dynamics, different physical implementations of the stochastic gauge protection protocol yield trajectory unravelings with vastly different statistics. Additionally, we design an on-chip feedback mechanism that corrects bit-flip errors and significantly enhances the discrete-time scheme. Our results shed light on the dissipative criticality of strongly-interacting, highly-constrained quantum systems, and they offer valuable insights into error mitigation and correction of gauge-theory quantum simulations.

Publications: Simulating two-dimensional lattice gauge theories on a qudit quantum computer

Tue, 25 Mar 2025 00:00:00 +0000

Authors: Michael Meth, Jinglei Zhang, Jan F. Haase, Claire Edmunds, and Lukas Postler et al.

Journal reference: Nat. Phys. 21, 570–576 — Published March 25, 2025

Preprint: arXiv:2310.12110 [quant-ph]

Preprint: Zenodo data repository

Particle physics describes the interplay of matter and forces through gauge theories. Yet, the intrinsic quantum nature of gauge theories makes important problems notoriously difficult for classical computational techniques. Quantum computers offer a promising way to overcome these roadblocks. We demonstrate two essential requirements on this path: first, we perform a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. Second, we show how to refine the gauge-field discretization beyond its minimal representation, using a trapped-ion qudit quantum processor, where quantum information is encoded in several states per ion. Such qudits are ideally suited for describing gauge fields, which are naturally high dimensional, leading to reduced register size and circuit complexity. We prepare the ground state of the model using a variational quantum eigensolver and observe the effect of dynamical matter on quantized magnetic fields. By controlling the qudit dimension, we also show how to seamlessly observe the effect of different gauge-field truncations. Finally, we experimentally study the dynamics of pair creation and magnetic energy. Our results open the door for hardware-efficient quantum simulations of gauge theories with qudits in near-term quantum devices.

Publications: Genuine multipartite entanglement in quantum optimization

Thu, 20 Feb 2025 00:00:00 +0000

Authors: Gopal Chandra Santra, Sudipto Singha Roy, Daniel J. Egger, and Philipp Hauke

Journal reference: Phys. Rev. A 111, 022434 — Published February 20, 2025

Preprint: arXiv:2411.08119 [quant-ph]

Preprint: Zenodo data repository

The ability to generate bipartite entanglement in quantum computing technologies is widely regarded as pivotal. However, the role of genuinely multipartite entanglement is much less understood than bipartite entanglement, particularly in the context of solving complicated optimization problems using quantum devices. It is thus crucial from both the algorithmic and hardware standpoints to understand whether multipartite entanglement contributes to achieving a good solution. Here we tackle this challenge by analyzing genuine multipartite entanglement—quantified by the generalized geometric measure—generated in Trotterized quantum annealing and the quantum approximate optimization algorithm. Using numerical benchmarks, we analyze its occurrence in the annealing schedule in detail. We observe a multipartite-entanglement barrier, and we explore how it correlates to the algorithm's success. We also prove how multipartite entanglement provides an upper bound to the overlap of the instantaneous state with an exact solution. Vice versa, the overlaps to the initial and final product states, which can be easily measured experimentally, offer upper bounds for the multipartite entanglement during the entire schedule. Our results help to shed light on how complex quantum correlations come to bear as a resource in quantum optimization.

Publications: Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model

Wed, 22 Jan 2025 00:00:00 +0000

Authors: Kacper Cybiński, Marcin Płodzień, Michał Tomza, Maciej Lewenstein, Alexandre Dauphin, and Anna Dawid

Journal reference: Mach. Learn.: Sci. Technol. 6 015014 — Published January 22, 2025

Machine learning (ML) is a promising tool for the detection of phases of matter. However, ML models are also known for their black-box construction, which hinders understanding of what they learn from the data and makes their application to novel data risky. Moreover, the central challenge of ML is to ensure its good generalization abilities, i.e. good performance on data outside the training set. Here, we show how the informed use of an interpretability method called class activation mapping, and the analysis of the latent representation of the data with the principal component analysis can increase trust in predictions of a neural network (NN) trained to classify quantum phases. In particular, we show that we can ensure better out-of-distribution (OOD) generalization in the complex classification problem by choosing such an NN that, in the simplified version of the problem, learns a known characteristic of the phase. We also discuss the characteristics of the data representation learned by a network that are predictors of its good OOD generalization. We show this on an example of the topological Su–Schrieffer–Heeger model with and without disorder, which turned out to be surprisingly challenging for NNs trained in a supervised way. This work is an example of how the systematic use of interpretability methods can improve the performance of NNs in scientific problems.

Publications: Cold-atom quantum simulators of gauge theories

Wed, 15 Jan 2025 00:00:00 +0000

Authors: Jad C. Halimeh, Monika Aidelsburger, Fabian Grusdt, Philipp Hauke, and Bing Yang

Journal reference: Nat. Phys. 21, 25–36 — Published January 15, 2025

Gauge theories constitute the basis of the Standard Model and provide useful descriptions of various phenomena in condensed matter. Realizing gauge theories on tunable tabletop quantum devices such as cold-atom quantum simulators offers the possibility to study their dynamics from first principles and to probe effects that are out of reach of dedicated particle colliders, such as deviations from gauge invariance. These quantum simulators can potentially provide insights into high-energy and nuclear physics questions, while also serving as a versatile tool for the exploration of topological phases and ergodicity-breaking mechanisms relevant to low-energy many-body physics. Recent years have seen substantial progress in the implementation of (1 + 1)D Abelian gauge theories using ultracold atoms. In this Review, we chronicle these advances, highlighting key developments in stabilizing gauge invariance and scaling up from basic building blocks to large-scale realizations where gauge-theory phenomena can be probed. We offer an outlook on future directions and the requirements for advancing this technology to the next level.

Publications: Engineering a Josephson junction chain for the simulation of the quantum clock model

Wed, 15 Jan 2025 00:00:00 +0000

Authors: Matteo M. Wauters, Lorenzo Maffi, and Michele Burrello

Journal reference: Phys. Rev. B 111, 045418 — Published January 15, 2025

Preprint: arXiv:2408.14549 [cond-mat.mes-hall]

Preprint: Zenodo data repository

The continuous improvement of fabrication techniques and high-quality semiconductor-superconductor interfaces allows for an unprecedented tunability of Josephson junction arrays (JJA), making them a promising candidate for analog quantum simulations of many-body phenomena. While most experimental proposals so far focused on quantum simulations of ensembles of two-level systems, the possibility of tuning the current-phase relation beyond the sinusoidal regime paves the way for studying statistical physics models with larger local Hilbert spaces. Here, we investigate a particular JJA architecture that can be mapped into a ℤ3 clock model. Through matrix-product-states simulations and bosonization analysis, we show that few experimentally accessible control parameters allow for the exploration of the rich phase diagrams of the associated low-energy field theories. Our results expand the horizon for analog quantum simulations with JJAs towards models that can not be efficiently captured with qubit architectures.

Publications: Confinement in a \(Z2\) lattice gauge theory on a quantum computer

Mon, 13 Jan 2025 00:00:00 +0000

Authors: Julius Mildenberger, Wojciech Mruczkiewicz, Jad C. Halimeh, Zhang Jiang, and Philipp Hauke

Journal reference: Nat. Phys. 21, 312–317 — Published January 13, 2025

Gauge theories describe the fundamental forces in the standard model of particle physics and play an important role in condensed-matter physics. The constituents of gauge theories, for example, charged matter and electric gauge field, are governed by local gauge constraints, which lead to key phenomena such as the confinement of particles that are not fully understood. In this context, quantum simulators may address questions that are challenging for classical methods. Although engineering gauge constraints is highly demanding, recent advances in quantum computing are beginning to enable digital quantum simulations of gauge theories. Here we simulate confinement dynamics in a \(Z2\) lattice gauge theory on a superconducting quantum processor. Tuning a term that couples only to the electric field produces confinement of charges, a manifestation of the tight bond that the gauge constraint generates between both. Moreover, we show how a modification of the gauge constraint from \(Z2\) towards U(1) symmetry freezes the system dynamics. Our work illustrates the restriction that the underlying gauge constraint imposes on the dynamics of a lattice gauge theory, showcases how gauge constraints can be modified and protected, and promotes the study of other models governed by multibody interactions.

Publications: Inherent quantum resources in the stationary spin chains

Thu, 09 Jan 2025 00:00:00 +0000

Authors: Marcin Płodzień, Jan Chwedeńczuk, and Maciej Lewenstein

Journal reference: Phys. Rev. A 111, 012417 — Published January 09, 2025

Preprint: arXiv:2405.16974 [quant-ph]

The standard way to generate many-body quantum correlations is via a dynamical protocol: an initial product state is transformed by interactions that generate nonclassical correlations at later times. Here, we show that many-body Bell correlations are inherently present in the eigenstates of a variety of spin-1/2 chains. In particular, we show that the eigenstates and thermal states of the collective Lipkin-Meshkov-Glick model possess many-body Bell correlations. We demonstrate that the Bell correlations present in the eigenstates of the Lipkin-Meshkov-Glick model can take on quantized values that change discontinuously with variations in the total magnetization. Finally, we show that these many-body Bell correlations persist even in the presence of both diagonal and off-diagonal disorder.

Publications: Observation of microscopic confinement dynamics by a tunable topological θ-angle

Fri, 20 Dec 2024 00:00:00 +0000

Authors: Wei-Yong Zhang, Ying Liu, and Yanting Cheng et al.

Journal reference: Nat. Phys. 21, 155–160 — Published December 20, 2024

The topological θ-angle is central to several gauge theories in condensed-matter and high-energy physics. For example, it is responsible for the strong CP problem in quantum chromodynamics and can emerge in effective theories of electrodynamics in topological insulators. Although analogue quantum simulators potentially offer a venue for realizing and controlling the θ-angle, doing so has hitherto remained an outstanding challenge. Here, we describe the experimental realization of a tunable topological θ-angle in a Bose–Hubbard gauge-theory quantum simulator, which was implemented through a tilted superlattice potential that induces an effective background electric field. We demonstrate the emerging physics through the direct observation of the confinement–deconfinement transition of (1 + 1)-dimensional quantum electrodynamics. Using an atomic-precision quantum gas microscope, we distinguish between the confined and deconfined phases by monitoring the real-time evolution of particle–antiparticle pairs. Our work provides a step forward in the realization of topological terms on modern quantum simulators.

Publications: Observing dynamical localization on a trapped-ion qudit quantum processor

Tue, 17 Dec 2024 00:00:00 +0000

Authors: Gonzalo Camacho, Claire L. Edmunds, Michael Meth, Martin Ringbauer, and Benedikt Fauseweh

Journal reference: arXiv:2412.13141 [quant-ph] — Published December 17, 2024

The advancements of quantum processors offer a promising new window to study exotic states of matter. One striking example is the possibility of non-ergodic behaviour in systems with a large number of local degrees of freedom. Here we use a trapped-ion qudit quantum processor to study a disorder-free \(S=1\) Floquet model, which becomes prethermal by dynamic localization due to local spin interactions. We theoretically describe and experimentally observe an emergent \(3T\) subharmonic response, demonstrating the ability to witness non-ergodic dynamics beyond qubit systems. Our numerical simulations reveal the role played by multipartite entanglement through the Quantum Fisher Information, showing how this quantity successfully reflects the transition between ergodic and localized regimes in a non-equilibrium context. These results pave the way for the study of ergodicity-breaking mechanisms in higher-dimensional quantum systems.

Publications: Qudit-inspired optimization for graph coloring

Mon, 02 Dec 2024 00:00:00 +0000

Authors: David Jansen, Timothy Heightman, Luke Mortimer, Ignacio Perito, and Antonio Acín

Journal reference: Phys. Rev. Applied 22, 064002 — Published December 02, 2024

Preprint: arXiv:2406.00792 [quant-ph]

We introduce a quantum-inspired algorithm for graph coloring problems (GCPs) that utilizes qudits in a product state, with each qudit representing a node in the graph and parameterized by 𝑑-dimensional spherical coordinates. WWe introduce a quantum-inspired algorithm for graph coloring problems (GCPs) that utilizes qudits in a product state, with each qudit representing a node in the graph and parameterized by 𝑑-dimensional spherical coordinates. We propose and benchmark two optimization strategies: qudit gradient descent, initiating qudits in random states and employing gradient descent to minimize a cost function; and qudit local quantum annealing, which adapts the local quantum annealing method to optimize an adiabatic transition from a tractable initial function to a problem-specific cost function. Our approaches are benchmarked against established solutions for standard GCPs, showing that our methods not only rival but frequently surpass the performance of recent state-of-the-art algorithms in terms of solution quality and computational efficiency. The adaptability of our algorithm and its high-quality solutions, achieved with minimal computational resources, point to an advancement in the field of quantum-inspired optimization, with potential applications extending to a broad spectrum of optimization problems.e propose and benchmark two optimization strategies: qudit gradient descent, initiating qudits in random states and employing gradient descent to minimize a cost function; and qudit local quantum annealing, which adapts the local quantum annealing method to optimize an adiabatic transition from a tractable initial function to a problem-specific cost function. Our approaches are benchmarked against established solutions for standard GCPs, showing that our methods not only rival but frequently surpass the performance of recent state-of-the-art algorithms in terms of solution quality and computational efficiency. The adaptability of our algorithm and its high-quality solutions, achieved with minimal computational resources, point to an advancement in the field of quantum-inspired optimization, with potential applications extending to a broad spectrum of optimization problems.

Publications: Variational quantum simulation using non-Gaussian continuous-variable systems

Tue, 26 Nov 2024 00:00:00 +0000

Authors: Paolo Stornati, Antonio Acin, Ulysse Chabaud, Alexandre Dauphin, Valentina Parigi, and Federico Centrone

Journal reference: Phys. Rev. Research 6, 043212 — Published November 26, 2024

Preprint: arXiv:2310.15919 [quant-ph]

Preprint: Github

This work introduces an approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians associated with infinite-dimensional systems, such as those arising in quantum field theory. We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space, opening the possibility to investigate the scenarios where one of the two formalisms performs better. We apply it to the study of static properties of the Bose-Hubbard model and demonstrate its effectiveness and practicality, highlighting the potential of continuous-variable quantum simulations in addressing complex problems in quantum physics.

Publications: Protein Design by Integrating Machine Learning and Quantum-Encoded Optimization

Fri, 15 Nov 2024 00:00:00 +0000

Authors: Veronica Panizza, Philipp Hauke, Cristian Micheletti, and Pietro Faccioli

Journal reference: PRX Life 2, 043012 — Published November 15, 2024

Preprint: arXiv:2407.07177 [quant-ph]

The protein design problem involves finding polypeptide sequences folding into a given three-dimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces. Structure searches can now be bypassed thanks to recent machine-learning breakthroughs, which have enabled accurate and rapid structure predictions. Similarly, sequence searches might be entirely transformed by the advent of quantum annealing machines and by the required new encodings of the search problem, which could be performative even on classical machines. In this work, we introduce a general protein design scheme where algorithmic and technological advancements in machine learning and quantum-inspired algorithms can be integrated, and an optimal physics-based scoring function is iteratively learned. In this first proof-of-concept application, we apply the iterative method to a lattice protein model amenable to exhaustive benchmarks, finding that it can rapidly learn a physics-based scoring function and achieve promising design performances. Strikingly, our quantum-inspired reformulation outperforms conventional sequence optimization even when adopted on classical machines. The scheme is general and can be extended, e.g., to encompass off-lattice models, and it can integrate progress on various computational platforms, thus representing a new paradigm approach for protein design.

Publications: Challenges and opportunities in quantum optimization

Mon, 28 Oct 2024 00:00:00 +0000

Authors: Amira Abbas, Andris Ambainis, and Brandon Augustino et al.

Journal reference: Nat Rev Phys 6, 718–735 — Published October 28, 2024

Preprint: arXiv:2312.02279 [quant-ph]

Quantum computers have demonstrable ability to solve problems at a scale beyond brute-force classical simulation. Interest in quantum algorithms has developed in many areas, particularly in relation to mathematical optimization — a broad field with links to computer science and physics. In this Review, we aim to give an overview of quantum optimization. Provably exact, provably approximate and heuristic settings are first explained using computational complexity theory, and we highlight where quantum advantage is possible in each context. Then, we outline the core building blocks for quantum optimization algorithms, define prominent problem classes and identify key open questions that should be addressed to advance the field. We underscore the importance of benchmarking by proposing clear metrics alongside suitable optimization problems, for appropriate comparisons with classical optimization techniques, and discuss next steps to accelerate progress towards quantum advantage in optimization.

Publications: Digital Quantum Simulation of a (1+1)D SU(2) Lattice Gauge Theory with Ion Qudits

Mon, 21 Oct 2024 00:00:00 +0000

Authors: Giuseppe Calajó, Giuseppe Magnifico, Claire Edmunds, Martin Ringbauer, Simone Montangero, and Pietro Silvi

Journal reference: PRX Quantum 5, 040309 — Published October 21, 2024

Preprint: arXiv:2402.07987 [quant-ph]

Preprint: Zenodo data repository

We present a quantum simulation strategy for a (1+1)-dimensional SU(2) non-Abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion-qudit quantum processor, as recently experimentally realized [Nat. Phys. 18, 1053 (2022)]. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss’s law. We discuss the experimental feasibility of generalized Mølmer-Sørensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically relevant properties specific to non-Abelian field theories, such as baryon excitations.

Publications: MQT Qudits: A Software Framework for Mixed-Dimensional Quantum Computing

Thu, 03 Oct 2024 00:00:00 +0000

Authors: Kevin Mato, Martin Ringbauer, Lukas Burgholzer, and Robert Wille

Journal reference: arXiv:2410.02854 [quant-ph] — Published October 03, 2024

Preprint: Github

Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on multi-level, qudit, systems offers a range of advantages, including expanded gate sets, higher information density, and improved computational efficiency, which might play a key role in overcoming not only the limitations of classical machines but also of current qubit-based quantum devices. However, working with qudits faces challenges not only in experimental control but particularly in algorithm development and quantum software. In this work, we introduce MQT Qudits, an open-source tool, which, as part of the Munich Quantum Toolkit (MQT), is built to assist in designing and implementing applications for mixed-dimensional qudit devices. We specify a standardized language for mixed-dimension systems and discuss circuit specification, compilation to hardware gate sets, efficient circuit simulation, and open challenges.

Publications: Enhancing quantum state tomography via resource-efficient attention-based neural networks

Wed, 04 Sep 2024 00:00:00 +0000

Authors: Adriano Macarone Palmieri, Guillem Müller-Rigat, Anubhav Kumar Srivastava, Maciej Lewenstein, Grzegorz Rajchel-Mieldzioc, and Marcin Płodzien

Journal reference: Phys. Rev. Research 6, 033248 — Published September 04, 2024

Preprint: arXiv:2309.10616 [quant-ph]

In this paper, we propose a method for denoising experimental density matrices that combines standard quantum state tomography with an attention-based neural network architecture. The algorithm learns the noise from the data itself, without a priori knowledge of its sources. Firstly, we show how the proposed protocol can improve the averaged fidelity of reconstruction over linear inversion and maximum likelihood estimation in the finite-statistics regime, reducing at least by an order of magnitude the amount of necessary training data. Next, we demonstrate its use for out-of-distribution data in realistic scenarios. In particular, we consider squeezed states of few spins in the presence of depolarizing noise and measurement/calibration errors and certify its metrologically useful entanglement content. The protocol introduced here targets experiments involving few degrees of freedom and afflicted by a significant amount of unspecified noise. These include NISQ devices and platforms such as trapped ions or photonic qudits.

Publications: Learning symmetry-protected topological order from trapped-ion experiments

Fri, 09 Aug 2024 00:00:00 +0000

Authors: Nicolas Sadoune, Ivan Pogorelov, Claire L. Edmunds, Giuliano Giudici, Giacomo Giudice, Christian D. Marciniak, Martin Ringbauer, Thomas Monz, and Lode Pollet

Journal reference: arXiv:2408.05017 [quant-ph] — Published August 09, 2024

Classical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. Our results demonstrate that the TK-SVM method successfully distinguishes the two phases across all noisy experimental datasets, highlighting its robustness and effectiveness in quantum data interpretation.

Publications: Quantum computing for high-energy physics: State of the art and challenges

Mon, 05 Aug 2024 00:00:00 +0000

Authors: Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W Bauer, Kerstin Borras, Stefano Carrazza, and Arianna Crippa et al.

Journal reference: PRX Quantum 5, 037001 — Published August 05, 2024

Preprint: arXiv:2307.03236 [quant-ph]

Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage—namely, a significant (in some cases exponential) speedup of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small-scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models that are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this Roadmap paper, led by CERN, DESY, and IBM, we provide the status of high-energy physics quantum computations and give examples of theoretical and experimental target benchmark applications, which can be addressed in the near future. Having in mind hardware with about 100 qubits capable of executing several thousand two-qubit gates, where possible, we also provide resource estimates for the examples given using error-mitigated quantum computing. The ultimate declared goal of this task force is therefore to trigger further research in the high-energy physics community to develop interesting use cases for demonstrations on near-term quantum computers.

Publications: Certifying Ground-State Properties of Many-Body System

Thu, 11 Jul 2024 00:00:00 +0000

Authors: Jie Wang, Jacopo Surace, Irénée Frérot, Benoît Legat, Marc-Olivier Renou, Victor Magron, and Antonio Acín

Journal reference: Phys. Rev. X 14, 031006 — Published July 11, 2024

Preprint: arXiv:2310.05844v5 [quant-ph]

Preprint: Github

A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalization quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: Energy is minimized over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all that variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin-1/2 Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way.

Publications: Connecting the Hamiltonian structure to the QAOA performance and energy landscape

Fri, 05 Jul 2024 00:00:00 +0000

Authors: Daniel Müssig, Markus Wappler, Steve Lenk, and Jörg Lässig

Journal reference: INFORMATIK 2024 — Published July 05, 2024

Preprint: arXiv:2407.04435 [quant-ph]

Quantum computing holds promise for outperforming classical computing in specialized applications such as optimization. With current Noisy Intermediate Scale Quantum (NISQ) devices, only variational quantum algorithms like the Quantum Alternating Operator Ansatz (QAOA) can be practically run. QAOA is effective for solving Quadratic Unconstrained Binary Optimization (QUBO) problems by approximating Quantum Annealing via Trotterization. Successful implementation on NISQ devices requires shallow circuits, influenced by the number of variables and the sparsity of the augmented interaction matrix. This paper investigates the necessary sparsity levels for augmented interaction matrices to ensure solvability with QAOA. By analyzing the Max-Cut problem with varying sparsity, we provide insights into how the Hamiltonian density affects the QAOA performance. Our findings highlight that, while denser matrices complicate the energy landscape, the performance of QAOA remains largely unaffected by sparsity variations. This study emphasizes the algorithm’s robustness and potential for optimization tasks on near-term quantum devices, suggesting avenues for future research in enhancing QAOA for practical applications.