Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors

A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the - ideally short - fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.Comment: 5+1 pages, 2 figures, 3 table

Problem-size-independent angles for a Grover-driven quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work, we consider a context in which one knows a probability density function describing how the objective function of a combinatorial optimization problem is distributed. We show that, if one knows this distribution, then the expected value of strings, sampled by measuring a Grover-driven, QAOA-prepared state, can be calculated independently of the size of the problem in question. By optimizing this quantity, optimal circuit parameters for average-case problems can be obtained on a classical computer. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem

Non-stoquastic interactions of superconducting circuits in the low frequency regime

Non-stoquastic interactions are hard to realize in experimental setups using superconducting qubits. On the other hand they are important or even necessary for the construction of adiabatic quantum computers wich show a real quantum speedup. In ArXiv:1903.06139, Ozfidan et al. show that they can realize non-stoquastic qubit-qubit interactions in a superconducting circuit architecture. The non-stoquastic nature only appears when the system is restricted to the low energy qubit subspace, since the full circuit Hamiltonian itself is stoquastic. Here we study the origin of these non-stoquastic interactions arising when projecting stoquastic Hamiltonians to the low energy spectrum. For this we use different theoretical tools, e.g. renormalization group techniques.*This work was funded by IARPA in connection with the quantum enhanced optimization (QEO) program

A real-time path integral representation of driven quantum algorithms

Both adiabatic quantum computing / quantum annealing and the quantum approximate optimization algorithm combine a problem Hamiltonian with a non-commuting driver Hamiltonian in order to efficiently explore the complete state space of an optimization problem. We develop a representation of such algorithms as a real-time path integral that directly and rigorously implements the otherwise colloquial idea that quantum algorithms follow all possible computations at the same time. We apply path integral techniques such as eikonals and semiclassics in order to provide a way to better understanding under which conditions we can expect these algorithms to reliably converge.*Funded in parts by IARPA under the QEO progra

Automatic Calibration and Characterization of Quantum Devices-Experimental Results on NISQ QPUs and Quantum Memory devices

The practical application of optimal control techniques, especially in superconducting settings, requires extensive calibration to reach high fidelities. By controlling both experiment and a high performance numerical simulation, the C3 procedure provides a framework to systematically design and apply even intricate open loop optimal control pulses.We demonstrate the characterization and tune-up of a quantum computing device with a few qubit, as well as a quantum memory device composed of a transmon with a 3D microwave cavity. The memory experiment presents different challenges, as the control protocol involves high-power sideband transitions, leading to system dynamics that are incompatible with simple models for qubit-cavity interactions.In both cases, we numerically simulate the measurement of gate sequences and, by comparing the results to experimental data, improve the model of the experiment, including both simple parameters such as qubit frequencies, as well as non-trivial aspects such as line responses and bandwidth limitations of the electronic equipment that distort and imposes constraints on control signals.*Project OpenSuperQ (820363) of the EU Flagship Quantum Technologies.IARPA through the LogiQ grant No. W911NF-16-1-011

On the interplay between optomechanics and the dynamical Casimir effect

In a cavity system with a mobile wall, the radiation pressure, stemming from the confined light, causes the motion ofthe mobile wall. On the other hand, when the frequency of the motion of a cavity wall is in resonance with the frequency of one of thecavity modes, photons can arise within the cavity: this phenomenon is called dynamical Casimir effect. In this work, we present analternative protocol to introduce both the optomechanical coupling and the photon-pair creation term starting by a static scenario

QAOA.jl: Toolkit for the Quantum and Mean-Field Approximate Optimization Algorithms

Quantum algorithms are an area of intensive research thanks to their potential for speedingup certain specific tasks exponentially. However, for the time being, high error rates on theexisting hardware realizations preclude the application of many algorithms that are basedon the assumption of fault-tolerant quantum computation. On such noisy intermediate-scale quantum (NISQ) devices (Preskill, 2018), the exploration of the potential of heuristicquantum algorithms has attracted much interest. A leading candidate for solving combinatorialoptimization problems is the so-called Quantum Approximate Optimization Algorithm (QAOA)(Farhi et al., 2014).QAOA.jl is a Julia package (Bezanson et al., 2017) that implements the mean-field Ap-proximate Optimization Algorithm (mean-field AOA) (Misra-Spieldenner et al., 2023) - aquantum-inspired classical algorithm derived from the QAOA via the mean-field approximation.This novel algorithm is useful in assisting the search for quantum advantage by providing atool to discriminate (combinatorial) optimization problems that can be solved classically fromthose that cannot. Note that QAOA.jl has already been used during the research leading toMisra-Spieldenner et al. (2023).Additionally, QAOA.jl also implements the QAOA efficiently to support the extensive classicalsimulations typically required in research on the topic. The corresponding parameterizedcircuits are based on Yao.jl (Luo et al., 2020, 2023) and Zygote.jl (Innes et al., 2019, 2023),making it both fast and automatically differentiable, thus enabling gradient-based optimization.A number of common optimization problems such as MaxCut, the minimum vertex-coverproblem, the Sherrington-Kirkpatrick model, and the partition problem are pre-implemented tofacilitate scientific benchmarking