NeQST — Publications

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.

Publications: Deconfined quantum critical points in fermionic systems with spin-charge separation

Thu, 04 Jul 2024 00:00:00 +0000

Authors: Niccolò Baldelli, Arianna Montorsi, Sergi Julià-Farré, Maciej Lewenstein, Matteo Rizzi, and Luca Barbiero

Journal reference: arXiv:2407.04073 [cond-mat.str-el] — Published July 04, 2024

Deconfined quantum critical points are intriguing transition points not predicted by the Landau-Ginzburg-Wilson symmetry-breaking paradigm which are usually identified by the appearance of a continuous phase transition between locally ordered phases. Here, we reveal the presence of deconfined quantum critical points with unexplored properties. Contrary to previously known examples, we show that the phenomenon of spin-charge separation peculiar to interacting low dimensional fermions can allow for the appearance of partially gapped deconfined quantum critical points. We first infer this point by performing a field theory analysis of generic one-dimensional fermionic systems in the low energy limit. Subsequently, we derive a microscopic model where phase transitions between different locally ordered phases can take place. Here, by performing a numerical analysis we explicitly derive, among others, the gaps, local order parameters and correlation functions behavior, supporting the presence of partially gapped deconfined quantum critical points. Our results thus provide new interesting insights on the widely investigated topic of quantum phase transitions.

Publications: Mixed-Dimensional Qudit State Preparation Using Edge-Weighted Decision Diagrams

Tue, 25 Jun 2024 00:00:00 +0000

Authors: Kevin Mato, Stefan Hillmich, and Robert Wille

Journal reference: 61st ACM/IEEE Design Automation Conference (DAC ‘24) — Published June 25, 2024

Preprint: arXiv:2308.12332 [quant-ph]

Preprint: Github

Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the underlying physics of most (if not all) of the technological platforms supports more than two levels, commonly referred to as qudits. Performing computations with qudits increases the overall complexity while, at the same time, reducing the number of operations and providing a lower error rate. Furthermore, qudits with different number of levels can be mixed in one system to ease the experimental control and keep representations as compact as possible. Exploiting these capabilities requires dedicated software support to tackle the increased complexity in an automated and efficient fashion. In this paper, we present a qudit simulator that handles mixed-dimensional systems based on Decision Diagrams (DDs). More precisely, we discuss the type of decision diagram introduced as underlying data structure as well as the resulting implementation. Experimental evaluations demonstrate that the proposed solution is capable of efficiently simulating mixed-dimensional quantum circuits, with specific use cases including more than 100 qudits in one circuit.

Publications: Synthetic dimensions for topological and quantum phases

Sat, 04 May 2024 00:00:00 +0000

Authors: Javier Argüello-Luengo, Utso Bhattacharya, Alessio Celi, Ravindra W. Chhajlany, Tobias Grass, Marcin Płodzień, Debraj Rakshit, Tymoteusz Salamon, Paolo Stornati, Leticia Tarruell, and Maciej Lewenstein

Journal reference: Commun Phys 7, 143 — Published May 04, 2024

Preprint: arXiv:2310.19549 [quant-ph]

The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Poznan (UAM), Kraków (UJ), and Allahabad (HRI). We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more.

Publications: A Framework for the Design and Realization of Alternative Superconducting Quantum Architectures

Fri, 03 May 2024 00:00:00 +0000

Authors: Jagatheesan Kunasaikaran, Kevin Mato, and Robert Wille

Journal reference: IEEE International Symposium on Multiple-Valued Logic 2024 — Published May 03, 2024

Preprint: arXiv:2305.07052 [quant-ph]

Preprint: Github

Superconducting quantum hardware architectures have been designed by considering the physical constraints of the underlying physics. These general-purpose architectures leave room for customization and optimization that can be exploited with alternative architectures specific to the quantum applications that will be executed on the quantum hardware. However, the corresponding design steps are hardly integrated yet and still rely heavily on manual labor. In this work, we provide a software framework that aims at providing a foundation to address this drawback. To this end, we first review the design of superconducting quantum hardware architectures and, afterwards, propose a cohesive framework encapsulating the design flow of an application-specific quantum hardware architecture. The resulting framework integrates high-level architecture generation optimized for a quantum application, the physical layout of the architecture, as well as optimization of the layout in a methodical manner.

Publications: Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions

Mon, 15 Apr 2024 00:00:00 +0000

Authors: Marcin Płodzień, Tomasz Wasak, Emilia Witkowska, Maciej Lewenstein, and Jan Chwedeńczuk

Journal reference: Phys. Rev. Research 6, 023050 — Published April 15, 2024

Preprint: arXiv:2306.06173 [quant-ph]

Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin-1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms.

Publications: Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion

Thu, 14 Mar 2024 00:00:00 +0000

Authors: Javier Argüello-Luengo, Manfred J. Mark, Francesca Ferlaino, Maciej Lewenstein, Luca Barbiero, and Sergi Julià-Farré

Journal reference: Quantum 8, 1285 — Published March 14, 2024

Preprint: arXiv:2308.13375 [cond-mat.quant-gas]

Thouless pumping represents a powerful concept to probe quantized topological invariants in quantum systems. We explore this mechanism in a generalized Rice-Mele Fermi-Hubbard model characterized by the presence of competing onsite and intersite interactions. Contrary to recent experimental and theoretical results, showing a breakdown of quantized pumping induced by the onsite repulsion, we prove that sufficiently large intersite interactions allow for an interaction-induced recovery of Thouless pumps. Our analysis further reveals that the occurrence of stable topological transport at large interactions is connected to the presence of a spontaneous bond-order-wave in the ground-state phase diagram of the model. Finally, we discuss a concrete experimental setup based on ultracold magnetic atoms in an optical lattice to realize the newly introduced Thouless pump. Our results provide a new mechanism to stabilize Thouless pumps in interacting quantum systems.

Publications: Almost device-independent certification of GME states with minimal measurements

Wed, 28 Feb 2024 00:00:00 +0000

Authors: Shubhayan Sarkar, Alexandre C. Orthey Jr., Gautam Sharma, and Remigiusz Augusiak

Journal reference: arXiv:2402.18522 [quant-ph] — Published February 28, 2024

Device-independent certification of quantum states allows the characterization of quantum states present inside a device by making minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. In this work, we consider the multipartite quantum steering scenario with an arbitrary number of parties but only one of which is trusted in the sense that the measurements performed by the trusted party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states, one, graph states of arbitrary local dimension, two, Schmidt states of arbitrary local dimension, and, three, -qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states.

Publications: Quantum computation of thermal averages for a non-Abelian 𝐷4 lattice gauge theory via quantum Metropolis sampling

Thu, 15 Feb 2024 00:00:00 +0000

Authors: Edoardo Ballini, Giuseppe Clemente, Massimo D’Elia, Lorenzo Maio, and Kevin Zambello

Journal reference: Phys. Rev. D 109, 034510 — Published February 15, 2024

Preprint: arXiv:2309.07090 [quant-ph]

Preprint: Zenodo data repository

In this paper, we show the application of the quantum Metropolis sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group \(𝐷4\) in \((2+1)-\)dimensions, discussing in general how some components of hybrid quantum-classical algorithms should be adapted in the case of gauge theories. In particular, we discuss the construction of random unitary operators which preserve gauge invariance and act transitively on the physical Hilbert space, constituting an ergodic set of quantum Metropolis moves between gauge invariant eigenspaces, and introduce a protocol for gauge invariant measurements. Furthermore, we show how a finite resolution in the energy measurements distorts the energy and plaquette distribution measured via QMS, and propose a heuristic model that takes into account part of the deviations between numerical results and exact analytical results, whose discrepancy tends to vanish by increasing the number of qubits used for the energy measurements.

Publications: Squeezing and quantum approximate optimization

Mon, 08 Jan 2024 00:00:00 +0000

Authors: Gopal Chandra Santra, Fred Jendrzejewski, Philipp Hauke, and Daniel J. Egger

Journal reference: Phys. Rev. A, 012413 — Published January 08, 2024

Preprint: arXiv:2205.10383 [quant-ph]

Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations therein remain unclear. Here, we shed light on this open issue by establishing a tight connection to the seemingly unrelated field of quantum metrology: Metrological applications employ quantum states of spin ensembles with a reduced variance to achieve an increased sensitivity, and we cast the generation of such squeezed states in the form of finding optimal solutions to a combinatorial MaxCut problem with an increased precision. By solving this optimization problem with a quantum approximate optimization algorithm (QAOA), we show numerically as well as on an IBM Quantum chip how highly squeezed states are generated in a systematic procedure that can be adapted to a wide variety of quantum machines. Moreover, squeezing tailored for the QAOA of the MaxCut permits us to propose a figure of merit for future hardware benchmarks. Exploiting the connection, we show how the performance can be improved by warm-starting the optimization algorithm with the squeezed state.

Publications: Spectral properties of the critical (1+1)-dimensional Abelian-Higgs model

Tue, 02 Jan 2024 00:00:00 +0000

Authors: Titas Chanda, Marcello Dalmonte, Maciej Lewenstein, Jakub Zakrzewski, and Luca Tagliacozzo

Journal reference: Phys. Rev. B 109, 045103 — Published January 02, 2024

Preprint: arXiv:2304.01030 [hep-th]

The presence of gauge symmetry in 1+1 dimensions is known to be redundant, since it does not imply the existence of dynamical gauge bosons. As a consequence, in the continuum, the Abelian-Higgs model (i.e., the theory of bosonic matter interacting with photons) just possesses a single phase, as the higher-dimensional Higgs and Coulomb phases are connected via nonperturbative effects. However, recent research published in Phys. Rev. Lett. 128, 090601 (2022) has revealed an unexpected phase transition when the system is discretized on the lattice. This transition is described by a conformal field theory with a central charge of 𝑐=3/2. In this paper, we aim to characterize the two components of this 𝑐=3/2 theory—namely the free Majorana fermionic and bosonic parts—through equilibrium and out-of-equilibrium spectral analyses.

Publications: Sublattice scars and beyond in two-dimensional U(1) quantum link lattice gauge theories

Sun, 12 Nov 2023 00:00:00 +0000

Authors: Indrajit Sau, Paolo Stornati, Debasish Banerjee, and Arnab Sen

Journal reference: Phys. Rev. D 109, 034519 — Published February 27, 2024

Preprint: arXiv:2311.06773 [hep-lat]

In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is H=Okin+λOpot, where λ is a real-valued coupling, and Okin (Opot) are summed local diagonal (off-diagonal) operators in the electric flux basis acting on the elementary plaquette □. The spectrum of the model in its spin-12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩, which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin. We demonstrate a ``triangle relation'' connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=0 eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of Okin become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another U(1) quantum link model with a staggered short-ranged diagonal term.

Publications: Eigenstate thermalization and its breakdown in quantum spin chains with inhomogeneous interactions

Mon, 30 Oct 2023 00:00:00 +0000

Authors: Ding-Zu Wang, Hao Zhu, Jian Cui, Javier Argüello-Luengo, Maciej Lewenstein, Guo-Feng Zhang, Piotr Sierant, and and Shi-Ju Ran

Journal reference: Phys. Rev. B 109, 045139 — Published January 22, 2024

Preprint: arXiv:2310.19333 quant-ph

The eigenstate thermalization hypothesis (ETH) is a successful theory that establishes the criteria for ergodicity and thermalization in isolated quantum many-body systems. In this work, we investigate the thermalization properties of a spin-1/2 XXZ chain with linearly inhomogeneous interactions. We demonstrate that introduction of the inhomogeneous interactions leads to an onset of quantum chaos and thermalization, which, however, becomes inhibited for sufficiently strong inhomogeneity. To exhibit ETH, and to display its breakdown upon varying the strength of interactions, we probe statistics of energy levels and properties of matrix elements of local observables in eigenstates of the inhomogeneous XXZ spin chain. Moreover, we investigate the dynamics of the entanglement entropy and the survival probability which further evidence the thermalization and its breakdown in the considered model. We outline a way to experimentally realize the XXZ chain with linearly inhomogeneous interactions in systems of ultracold atoms. Our results highlight a mechanism of emergence of ETH due to insertion of inhomogeneities in an otherwise integrable system and illustrate the arrest of quantum dynamics in the presence of strong interactions.

Publications: Variational quantum simulation of U(1) lattice gauge theories with qudit systems

Thu, 27 Jul 2023 00:00:00 +0000

Authors: Pavel P. Popov, Michael Meth, Maciej Lewenstein, Philipp Hauke, Martin Ringbauer, Erez Zohar, and Valentin Kasper

Journal reference: Phys. Rev. Research 6, 013202 — Published February 26, 2024

Preprint: arXiv:2307.15173 [quant-ph]

Preprint: Zenodo data repository

Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map D-dimensional U(1) Abelian lattice gauge theories onto qudit systems with local interactions for arbitrary D. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in [Nat. Phys. 18, 1053-1057 (2022)]. We describe how to implement the variational imaginary-time evolution protocol for ground state preparation as well as the variational real-time evolution protocol to simulate non-equilibrium physics on universal qudit quantum computers, supplemented with numerical simulations. Our proposal can serve as a way of simulating lattice gauge theories, particularly in higher spatial dimensions, with minimal resources, regarding both system sizes and gate count.

Publications: Topological stripe state in an extended Fermi-Hubbard model

Mon, 09 Jan 2023 00:00:00 +0000

Authors: Sergi Julià-Farré, Lorenzo Cardarelli, Maciej Lewenstein, Markus Müller, and Alexandre Dauphin

Journal reference: Phys. Rev. B 109, 075109 — Published February 06, 2024

Preprint: arXiv:2301.03312 [cond-mat.quant-gas]

Interaction-induced topological systems have attracted a growing interest for their exotic properties going beyond the single-particle picture of topological insulators. In particular, the interplay between strong correlations and finite doping can give rise to nonhomogeneous solutions that break the translational symmetry. In this work, we report the appearance of a topological stripe state in an interaction-induced Chern insulator around half-filling. In contrast to similar stripe phases in nontopological systems, here we observe the appearance of chiral edge states on top of the domain wall. Furthermore, we characterize their topological nature by analyzing the quantized transferred charge of the domains in a pumping scheme. Finally, we focus on aspects relevant to observing such phases in state-of-the-art quantum simulators of ultracold atoms in optical lattices. In particular, we propose an adiabatic state preparation protocol and a detection scheme of the topology of the system in real space.