### What is qudit-based quantum computing?

Quantum computers exploit the laws of nature that govern at the microscopic level of individual atoms, quantum mechanics, to perform calculations that can be vastly faster than what any classical computer could achieve. To do this, conventional quantum computers use two internal levels, denoted \(|0\rangle \) and \(|1\rangle \) and together called a quantum bit (or qubit in short), in analogy to the common classical bits. The laws of quantum mechanics allow the quantum computer to compute not only with individual bit strings (such as 0110010…), but with arbitrary superpositions (such as \( |0110010 \ldots\rangle + |1010010 \ldots\rangle + |0110111 \ldots\rangle + \ldots \)). That is, many different possibilities of the qubit register are present simultaneously in the quantum computer, enabling it to parallelize certain tasks and to use interference effects to arrive faster at a solution.

The aim of NeQST is to lift this concept to the next level. Namely, we will develop the full stack of quantum computing using not only two but \(d\) levels, \(|0\rangle, |1\rangle \ldots |d-1\rangle \): a qudit. This approach permits us to compactify quantum information. It also permits users to directly tackle problems whose natural description is in terms of \(d\)-dimensional degrees of freedom, and thus to avoid overhead that normally arises due to decomposition into qubits.

### How does a trapped-ion quantum computer work?

In a trapped-ion quantum computer, individual charged atoms (ions) are trapped using electrical fields. Using laser cooling methods, the ions are cooled to extremely low temperatures, such that they arrange themselves in a linear chain and are essentially sitting completely still. Each ion can be individually manipulated with targeted laser beams. Quantum information is then stored in the electronic state of each ion, i.e., the orbital of the electrons around the charged nucleus. The lowest energy state is usually called \(|0\rangle \), and conventional quantum computers would pick another suitable state as \(|1\rangle \) to build a qubit.

However, depending on the ion species and isotope, there are many more than just two energy states and all of them can be used to store information. Trapped-ion quantum computers have already demonstrated that \(d\)-dimensional qudits can be controlled with the same lasers and the same precision as conventional qubits. The final ingredient for a quantum computer is quantum entanglement, which trapped-ion quantum computers generate by using controlled ion motion as a quantum bus to mediate interactions between the electronic states of different ions. The big opportunity and challenge of operating quantum computers with qudits is the much richer space of possible ways to interact the information carriers and process the quantum information. Within NeQST, we aim to develop automated design solutions to allow us to get the best out of this new hardware.

### Why lattice gauge theories?

Lattice gauge theories describe fundamental theories of nature, for example how elementary particles such as electrons and positrons interact with electromagnetic fields or how quarks and gluons interact with each other. They can also emerge as exotic phases of matter in certain materials. Despite their ubiquity in fundamental science, no efficient algorithm exists to compute their dynamical behavior on classical computers. The main difficulty is an intrinsic inefficiency when mapping the quantum mechanical state of complex many-particle systems onto the bits available in classical computers. This difficulty makes lattice gauge theories an excellent use case for quantum computers: a quantum computer being itself governed by the laws of quantum mechanics can naturally represent the quantum mechanical state.

In this endeavor, qudits can give a great advantage over qubit-based platforms, since lattice gauge theories require the description of many degrees of freedom simultaneously, which can more naturally be realized if a larger number of levels is available. Finding efficient ways to compute the dynamics of lattice gauge theories may have important impact across the physical sciences, in particular in high-energy, nuclear, and condensed-matter physics, and can lead to answering fundamental and practical questions about the nature of elementary particles and states of matter.

### Why bidirectional electric vehicle charging?

For the transformation to a fully renewable energy system, many challenges in different sectors need to be overcome (heating, electricity, mobility, …). Particularly important challenges arise rom the integration of the growing number of electric vehicles (EVs), which will substantially increase the demand for electric energy, as well as the rising proportion of renewable energy. Both challenges will lead to sizable increase in the load on the electricity grid as well as larger variability in the electricity production and consumption. Optimizng the bidirectional charging (i.e, charging and discharging) of the batteries of the large number of EVs provides a great opportunity to address both challenges. Green energy, generated by photovoltaic (PV) systems during the sunny daytimes, can be stored and fed back into the grid in the evening or morning hours when demand is high. This reduces the stress on the electricity grid and fosters the transition to a grid with more locally produced and consumed energy. Additionally, owners of EV charging stations can participate in the electricity market to reduce their charging cost. However, optimizing this kind of distributed operations requires novel algorithmic and technical approaches.

Quantum computers offer a promising pathway towards solving such difficult optimization problems, as they can exploit quantum tunneling and interference effects in order to arrive quickly at a solution to the computation. In the context of bidirectional EV charging, the multiple levels of qudits have a distinctive advantage over qubits: Many of the currently used EV charging stations operate with multiple predefined discrete power levels for charging and discharging, which can be naturally and directly encoded in multi-level qudits.

### Why is it important to cerfiticate quantum devices and softwares?

A quantum computer is supposed to solve a problem that is out of reach for classical computers. However, present quantum computers are noisy and it is therefore often unclear if the obtained solutions are correct, or just good enough, because they cannot be benchmarked by any classical means. Another relevant question in this context is to understand if and which quantum phenomena play a decisive role to solve the given computation problem. All these questions are addressed by quantum certification. Within NEQST, we plan to provide recipes to certify that (i) the results provided by qudit quantum hardware are good and (ii) to obtain these results the quantum hardware actually uses phenomena that are intrinsic to qudits and beyond qubits.

### What is the role of design automation?

Recent accomplishments in the physical realization of quantum computers are leading to an increasing complexity that often is not and soon cannot be handled manually anymore. This demands dedicated and particularly automated methods that provide assistance in the design and realization of applications for quantum computers. The effort spent on design automation for classical computers was a key to enable their ubiquity we see to today. We believe it has the potential to be an enabler for quantum computing as well. While much effort is being done in academia and industry for qubit systems, much less is being done on qudits. To this end, we want to push the boundaries on simulation, compilation, and verification as the pillars of design automation and apply them to higher-dimensional qudits to fully exploit their potential.

### Project details

Acronym | NeQST |
---|---|

Grand Agreement ID | 101080086 |

Period | 1 November 2022 - 31 October 2025 |

Funded under | HORIZON.2.4 |

Overall budget | €3 207 671.25 |

EU Contributions | €3 207 671 |

Coordinated by | University of Trento (IT) |

Participants | 8 |