Research Roundup for December 2022

By Dr Chris Mansell, Senior Scientific Writer at Terra Quantum

Hardware

Title: Quantum Feature Maps for Graph Machine Learning on a Neutral Atom Quantum Processor Organizations: PASQAL; Sorbonne Université; Université Paris-Saclay; CNRS Researchers are currently unsure whether processing data on a quantum computer will be useful if those data only contain classical correlations. In this paper, a neutral atom quantum processor was used to classify data about the toxicity of different molecules. From a structural perspective, a molecule consists of atoms that are chemically bonded together, which means that nodes in a mathematical graph can represent the atoms and the graph’s edges can represent the bonds. Data in this form was encoded into arrays of up to 32 atomic qubits. Both classical and quantum feature maps were used to analyse the data. The experiment provided evidence that the latter approach can capture aspects of the data the former approach would miss. Link: https://arxiv.org/abs/2211.16337

Title: Constrained quantum optimization for extractive summarization on a trapped-ion quantum computer Organizations: JPMorgan Chase; NIST; University of Maryland Many industries have to optimise an important metric while taking practical constraints into account. Extractive optimisation - where sentences are chosen from a long document in order to summarise it - can be framed as a constrained optimisation problem that is NP-hard to exactly solve. In this paper, three algorithms were given this task: the Quantum Approximate Optimization Algorithm, the Layer Variational Quantum Eigensolver algorithm and the XY-Quantum Alternating Operator Ansatz (XY-QAOA). These algorithms were not only implemented on Quantinuum’s 20-qubit ion trap quantum computer but also noiselessly simulated and noisily emulated. No error mitigation was deployed in the ion trap despite the circuits having a depth of over 100 two-qubit gates. Even so, the results of the XY-QAOA algorithm were significantly better than chance. Link: https://www.nature.com/articles/s41598-022-20853-w

Title: High-fidelity qutrit entangling gates for superconducting circuits Organizations: University of California, Berkeley; Lawrence Berkeley National Laboratory; Keysight Technologies Canada A qutrit is a three-level quantum system that has several advantages over qubits in quantum information processing. There are, however, concerns over whether the benefits are outweighed by additional experimental complications. In this new research, a high-fidelity two-qutrit logic gate is performed between two superconducting transmons. Microwaves were employed to generate differential AC Stark shifts, which enabled the gate to be both simple and flexible. The gate was thoroughly benchmarked and its expressibility and the resulting entanglement were both studied. The next step might be to involve more than two transmons in the experiment. Link: https://www.nature.com/articles/s41467-022-34851-z

Title: Benchmarking simulated and physical quantum processing units using quantum and hybrid algorithms Organizations: Terra Quantum; QMware As quantum hardware improves, it becomes easier to design and test new and exciting quantum algorithms that then, in a positive feedback loop, increase the incentives to develop better quantum processing units (QPUs). High-performance classical computing systems that noiselessly simulate physical QPUs can also facilitate investigations of cutting-edge quantum circuits. In this study, a representative sample of publicly accessible services were compared with one another in terms of runtime, accuracy and price. These metrics scaled with the number of qubits in different ways for the tested physical and simulated platforms, making the report interesting reading for the quantum computing community. Link: https://arxiv.org/abs/2211.15631

Title: Quick Quantum Steering: Overcoming Loss and Noise with Qudits Organizations: Heriot-Watt University; University of Geneva Long-distance quantum communication protocols are technologically demanding because photons are lost, interactions with the environment introduce noise and measuring devices have inefficiencies. High-dimensional entanglement can help some of these obstacles be overcome. However, earlier work with entangled qudits has required complex measurement set-ups and long measurement times. In this research, 53-dimensional optical qudits with excellent loss tolerance and noise robustness properties were measured at the end of a quantum steering protocol in a considerably simpler and faster way than ever before. This demonstration is another step towards the goal of practical, robust and secure quantum networks. Link: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041023

Title: Engineering Symmetry-Selective Couplings of a Superconducting Artificial Molecule to Microwave Waveguides Organization: Chalmers University of Technology Waveguides are structures, like optical fibers, that enable waves to travel in one direction without spreading out. The study of quantum electrodynamics within waveguides has applications in various quantum technologies. In this paper, superconducting transmon qubits are coupled with microwave waveguides in a novel way. The coupling depends on the permutation symmetry of the quantum state. For example, a bright state (that radiates rapidly) and a dark state (that does so slowly) have opposite permutation symmetry but they can be coupled together such that a coherent population transfer is efficiently performed via a Raman process. The scheme could work for other physical systems with near-field coupling. Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.123604

Title: Dual-rail encoding with superconducting cavities Organization: Yale University Designing quantum hardware that efficiently implements quantum error correction is an active area of research. The authors of this preprint introduced the idea of using the intrinsic noise bias of coupled superconducting microwave cavities in combination with a dual-rail single-photon encoding. Experimentally creating such a qubit with current technology would lead to error rates significantly below the relevant threshold. Furthermore, these rates will rapidly decrease when, with continued research, the coherence time of the underlying components improves. Link: https://arxiv.org/abs/2212.12077

Software

Title: Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections Organization: PsiQuantum Surface code schemes for implementing fault-tolerant quantum computation have a cost that scales with both the number of qubits and the number of non-Clifford gates. In this preprint, a new approach is shown to have a cost that only depends on the number of logical operations. For a factoring algorithm with thousands of logical qubits, the ensuing improvements in the runtime would be at least an order of magnitude. Each logical qubit needs to be connected to logarithmically many other logical qubits, which is a challenge for some physical systems but could be realised in an implementation where photonic qubits are sent through optical fibers. Link: https://arxiv.org/abs/2211.15465

Title: Training Variational Quantum Circuits with CoVaR: Covariance Root Finding with Classical Shadows Organization: University of Oxford Variational quantum algorithms (VQAs) typically aim to minimise a single target function, such as a classical energy landscape, by sampling from it with a quantum processor. In this paper, the goal of the algorithm is to find an eigenstate but instead of optimising over a single property of the state, many properties are measured. Doing this efficiently - by using the classical shadows technique and offloading work to a classical computer - allows up to ten million covariances to be simultaneously estimated. When the values of these covariances approach zero, it indicates that the eigenstate has been found. The algorithm appears to be robust to the issues that VQAs usually encounter (including local traps, noise and barren plateaus) and it converges many orders of magnitude faster. Future work might address one of its current limitations, which is its vulnerability to random parameter initialisation. Link: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041022

Title: A super-polynomial quantum advantage for combinatorial optimization problems Organizations: Technische Universität Berlin; Freie Universität Berlin; Fraunhofer Heinrich Hertz Institute; Fraunhofer SIT Numerous practical problems, such as scheduling, routing or job allocation, are in the form of a combinatorial optimisation problem and efficiently approximating the optimal solutions is important for many industries. In this preprint, the researchers approach NP-hard instances of such problems using tools from cryptography, specifically from Shor’s algorithm. They showed that a fault tolerant quantum computer can approximate the solutions super-polynomially more efficiently than a classical computer. Helpfully, they also connect their findings to the variational quantum algorithms that are widely studied in this context. Link: https://arxiv.org/abs/2212.08678

Title: Tight Bounds on the Convergence of Noisy Random Circuits to the Uniform Distribution Organizations: NIST; University of Maryland; Caltech; University of Chicago There are two obstacles in the NISQ era of quantum computing: noise and system size. In this paper, the output distributions of differently sized circuits are studied as they experience local Pauli noise and converge to the uniform distribution. The circuits consist of Haar-random two-qubit gates, which the authors discovered can be theoretically mapped to a model in statistical mechanics. The findings have implications for proof techniques in complexity theory, benchmarking studies, near-term algorithms and entanglement phase transitions. Link: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.040329

Title: Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra Organizations: Massachusetts Institute of Technology; Turing Inc. Kernel matrices have entries that are found by evaluating a smooth function known as the kernel function. They are generally full-rank, dense and find applications in mathematical physics, engineering and machine learning. Classically, there are hierarchical methods for performing matrix multiplications on kernel matrices that are significantly faster than generic methods. In this paper, a quantum algorithm is presented for factoring kernel matrices into hierarchical matrices that are efficiently block-encoded inside a unitary operator, which can be repeatedly queried. The runtime is exponentially faster than quantum algorithms for dense matrices. This work therefore expands the scope of quantum algorithms to include matrices that are neither low-rank nor sparse. Future investigations may consider whether these ideas are applicable to variational quantum algorithms or a quantum version of neural networks. Link: https://quantum-journal.org/papers/q-2022-12-13-876/

Title: Algorithmic Shadow Spectroscopy Organizations: University of Oxford; Quantum Motion Quantum simulation has many potential applications in chemistry, many-body physics and material science. Existing quantum simulation algorithms have short circuit depths but either require ancillary qubits or an overwhelming number of measurement repeats. In this work, the researchers present an algorithm that circumvents these issues and can be seen as a generalisation of spectroscopy. By following the time-evolution of the observables of a quantum system using classical shadow techniques, it allows the energy differences between the eigenstates of the system’s Hamiltonian to be determined with Heisenberg-limited precision. The researchers perform numerical simulations of their algorithm and envision how it could be used most profitably as we move from one era of quantum hardware development to the next. They find that the algorithm is robust to noise and requires as few as just ten measurement repetitions per time step. Link: https://arxiv.org/abs/2212.11036

Title: Tensor Network Assisted Variational Quantum Algorithm Organizations: Peking University; The University of Western Australia; Freie Universität Berlin Tensor networks are ways of representing structured tensors as combinations of smaller tensors. They are helpful for studying quantum many-body physics. Classical computers and quantum computers have different strengths and weaknesses when it comes to manipulating these mathematical objects. The former can algorithmically handle tensor networks that have restricted expressivity. In theory, the latter could reach higher levels of expressivity but in practice, decoherence prevents this. In this paper, the authors study the benefits of using quantum and classical computers together. The tensors that are encoded in quantum circuits are contracted with measurements while the tensors on the classical computer are simply calculated. By numerically simulating their entire approach for systems like Ising models and time crystals, they find that it greatly enhances the expressivity of shallow quantum circuits. Link: https://arxiv.org/abs/2212.10421

December 28, 2022