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Physical review applied 19(2), 024047 (2023). doi:10.1103/PhysRevApplied.19.024047, Published by American Physical Society, College Park, Md. [u.a.]

Frontiers in physics 10, 907160 (2022). doi:10.3389/fphy.2022.907160 special issue: "Quantum Computing and Machine Learning", Published by Frontiers Media, Lausanne

We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance., new experiments to test the conjecture about unused couplers (appendix B)

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a QUBO correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances., 6 pages, 6 figures

NIC Symposium 2022 : 29-30 September 2022 I Jülich, Germany : proceedings / John von Neumann Institute for Computing (NIC) ; M. Müller, Ch. Peter, A. Trautmann (editors) 11. NIC Symposium, Jülich, Germany, 29 Sep 2022 - 30 Sep 2022; Jülich : Forschungszentrum Jülich GmbH, Zentralbibliothek, Verlag, NIC series 51, 3-23 (2022)., Published by Forschungszentrum Jülich GmbH, Zentralbibliothek, Verlag, Jülich

We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results., This article is a book contribution. The book is freely available at http://hdl.handle.net/2128/31840

Journal of the Physical Society of Japan : JPSJ 90(1), 012001 (2021). doi:10.7566/JPSJ.90.012001, Published by The Physical Society of Japan, Tokyo

We use discrete-event simulation on a digital computer to study two different models of experimentally realizable quantum walks. The simulation models comply with Einstein locality, are as "realistic" as the one of the simple random walk in that the particles follow well-defined trajectories, are void of concepts such as particle-wave duality and wave-function collapse, and reproduce the quantum-theoretical results by means of a cause-and-effect, event-by-event process. Our simulation model for the quantum walk experiment presented in [C. Robens et al., Phys. Rev. X 5, 011003 (2015)] reproduces the result of that experiment. Therefore, the claim that the result of the experiment "rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories" needs to be revised., open source code available at https://jugit.fz-juelich.de/qip/quantum-walk

Frontiers in physics 8, 160 (2020). doi:10.3389/fphy.2020.00160, Published by Frontiers Media, Lausanne

We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern-Gerlach and the Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schr\"odinger equation., Comment: Complete rewrite, except for the technical parts. Accepted for publication in Ann. Phys

Annals of physics 396, 96-118 (2018). doi:10.1016/j.aop.2018.07.014, Published by Elsevier, Amsterdam [u.a.]

A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, and on Intel Xeon based clusters, implying that the combination of parallelization and hardware can track the exponential scaling due to the increasing number of qubits. Results of executing simple quantum circuits and Shor's factorization algorithm on quantum computers containing up to 48 qubits are presented., Comment: Substantially rewritten + new data. Published in Computer Physics Communication

Dissertation, RWTH Aachen University, 2023; Aachen : RWTH Aachen University 1 Online-Ressource : Illustrationen, Diagramme (2023). = Dissertation, RWTH Aachen University, 2023, In this thesis we study aspects of Hamiltonian models which can affect the time evolution of transmon systems. We model the time evolution of various systems as a unitary real-time process by numerically solving the time-dependent Schrödinger equation (TDSE). We denote the corresponding computer models as non-ideal gate-based quantum computer (NIGQC) models since transmons are usually used as transmon qubits in superconducting prototype gate-based quantum computers (PGQCs).We first review the ideal gate-based quantum computer (IGQC) model and provide a distinction between the IGQC, PGQCs and the NIGQC models we consider in this thesis. Then, we derive the circuit Hamiltonians which generate the dynamics of fixed-frequency and flux-tunable transmons. Furthermore, we also provide clear and concise derivations of effective Hamiltonians for both types of transmons. We use the circuit and effective Hamiltonians we derived to define two many-particle Hamiltonians, namely a circuit and an associated effective Hamiltonian. The interactions between the different subsystems are modelled as dipole-dipole interactions. Next, we develop two product-formula algorithms which solve the TDSE for the many-particle Hamiltonians we defined. Afterwards, we use these algorithms to investigate how various frequently applied approximations (assumptions) affect the time evolution of transmon systems modelled with the many-particle effective Hamiltonian when a control pulse is applied. Here we also compare the time evolutions generated by the effective and circuit Hamiltonian. We find that the approximations we investigate can substantially affect the time evolution of the probability amplitudes we model. Next, we investigate how susceptible gate-error quantifiers are to approximations which make up the NIGQC model. We find that the approximations (assumptions) we consider clearly affect gate-error quantifiers like the diamond distance and the average infidelity. Furthermore, we provide clear and concise theoretical explanations for many of the findings we present in this thesis., Published by RWTH Aachen University, Aachen

Dissertation, RWTH Aachen University, 2022; Aachen : RWTH Aachen University 1 Online-Ressource : Illustrationen, Diagramme (2022). = Dissertation, RWTH Aachen University, 2022, The primary subject of this dissertation is the analysis and improvement of variational methods that combine the use of classical and gate based quantum computers. The secondary subject is the development of matrix based error mitigation and benchmarking protocols for noisy quantum computers. Variational methods run on quantum computer emulators are used to find the ground state energies of the Heisenberg and Hubbard models and selected molecules in chemistry. An algorithm is developed and deployed to automate the creation of variational circuits. The theory and overview of variational methods and gradient based optimisation algorithms are presented. We learn that while variational methods make it possible to use current generation quantum computers, guarantees of always finding the ground state energy are elusive. We introduce noise in our emulations and adapt the optimisation algorithms to withstand it. We observe the emergence of local minima and barren plateaus which hinder variational methods from finding the ground state energies. It is discerned that clever choices of initial states and parameters are necessary ingredients for success. We develop the technique of quasi-dynamical evolution inspired by quantum annealing. It overcomes the limitations of standard variational algorithms by systematically improving the ground state energy estimate. Our tests show that the heuristic improves the energy estimate even in facile settings. We introduce seven criteria for ideal error mitigation protocols. A new protocol is developed on its basis. Our tests on IBM Q quantum computers show noticeable error mitigation. The matrix generated during the execution of the protocol helps detect and visualise errors and biases. We invent and use small depth quantum circuits for benchmarking quantum computers., Published by RWTH Aachen University, Aachen

Dissertation, RWTH Aachen University, 2020; Aachen 1 Online-Ressource (IX, 237 Seiten) : Illustrationen, Diagramme (2020). = Dissertation, RWTH Aachen University, 2020, We develop a simulator for quantum computers composed of superconducting transmon qubits. The simulation model supports an arbitrary number of transmons and resonators. Quantum gates are implemented by time-dependent pulses. Nontrivial effects such as crosstalk, leakage to non-computational states, entanglement between transmons and resonators, and control errors due to the pulses are inherently included. The time evolution of the quantum computer is obtained by solving the time-dependent Schrödinger equation. The simulation algorithm shows excellent scalability on high-performance supercomputers. We present results for the simulation of up to 16 transmons and resonators. Additionally, the model can be used to simulate environments, and we demonstrate the transition from an isolated system to an open quantum system governed by a Lindblad master equation. We also describe a procedure to extract model parameters from electromagnetic simulations or experiments. We compare simulation results to experiments on several NISQ processors of the IBM Q Experience. We find nearly perfect agreement between simulation and experiment for quantum circuits designed to probe crosstalk in transmon systems. By studying common gate metrics such as the fidelity or the diamond distance, we find that they cannot reliably predict the performance of repeated gate applications or practical quantum algorithms. As an alternative, we find that the results from two-transmon gate set tomography have an exceptional predictive power. Finally, we test a protocol from the theory of quantum error correction and fault tolerance. We find that the protocol systematically improves the performance of transmon quantum computers in the presence of characteristic control and measurement errors., Published by Aachen

Dissertation, RWTH Aachen University, 2020; Aachen 1 Online-Ressource (VIII, 163 Seiten) : Illustrationen, Diagramme (2020). = Dissertation, RWTH Aachen University, 2020, In this thesis, we study the operation of existing quantum annealers by simulating the real-time dynamics of two coupled flux qubits based on SQUIDs (superconducting quantum interference devices) during quantum annealing processes. We investigate two aspects. First, we study the influence of the higher energy levels which are neglected when deriving the qubit Hamiltonian from the superconducting circuit model including the tunable coupler. Second, we investigate the influence of an environment on the qubit system during quantum annealing. For the latter, we examine two different models for the environment, a generic spin bath and non-interacting two-level systems. For simulating the dynamics, we use the Suzuki-Trotter product-formula algorithm to solve the time-dependent Schrödinger equation numerically. We find that the higher energy levels as well as the presence of the tunable coupler have little influence on the performance of the quantum annealing process for most of the investigated problem instances, suggesting that the two-level approximation works very well. However, we find that for a particular class of instances, the results of the SQUID model and the qubit model show certain deviations. Additionally, we perform experiments on the D-Wave 2000Q quantum annealer. Our study of the two models for the environment suggests that the model of non-interacting two-level systems is better suited to describe the data obtained from the real device than the generic spin bath model., Published by Aachen

Dissertation, RWTH Aachen University, 2018; Aachen 1 Online-Ressource (viii, 135 Seiten) : Illustrationen, Diagramme (2018). = Dissertation, RWTH Aachen University, 2018, Bogoliubov quasiparticle excitations are detrimental for the operation of many superconducting devices. In superconducting qubits, quasiparticles interact with the qubit degree of freedom when tunneling through a Josephson junction, and this interaction can lead to qubit relaxation. At millikelvin temperatures, there is substantial evidence of nonequilibrium quasi- particles. While there is no agreed upon explanation for the origin of these excess quasiparticles, it is nevertheless possible to limit the quasiparticle-induced relaxation by steering quasiparticles away from qubit active elements. In this thesis, we study quasiparticle traps that are formed by a normal-metal in tunnel contact with the superconducting electrode of a qubit. We develop a model to explain how a trap can influence the dynamics of the excess quasiparticles injected in a transmontype qubit. This model makes it possible to find the time it takes to evacuate the injected quasiparticles from the transmon as a function of trap parameters. We show when the trap size is increased, the evacuation time decreases monotonically and saturates at a level that depends on the quasiparticles diffusion constant and the qubit geometry. We find the characteristic trap size needed for the evacuation time to approach the saturation value. It turns out that the bottleneck limiting the trapping rate is the slow quasiparticle energy relaxation inside the normal-metal trap, a quantity that is very hard to control. In order to optimize normal-metal quasiparticle trapping, we study the effects of trap size, number, and placement. These factors become important when the trap size increases beyond the characteristic length. We discuss for some experimentally relevant examples how to shorten the evacuation time of the excess quasiparticle density. Moreover, we show that a trap in the vicinity of a Josephson junction can significantly suppress the steady-state quasiparticle density near that junction and reduce the impact of fluctuations in the generation rate of quasiparticles. When such normal-metal elements are connected to a superconducting material, Cooper- pairs can leak into the normal-metal trap. This modifies the superconductor properties and, in turn, affects the qubit coherence. Using the Usadel formalism, we first revisit the proximity effect in uniform NS bilayers; despite the long history of this problem, we present novel findings for the density of states. We then extend our results to describe a non-uniform system in the vicinity of a trap edge. Using these results together with the previously developed model for the suppression of the quasiparticle density due to the trap, we find in a transmon qubit an optimum trap-junction distance at which the qubit relaxation rate is minimized. This optimum distance, of the order of 4 to 20 coherence lengths, originates from the competition between proximity effect and quasiparticle density suppression. We conclude that the harmful influence of the proximity effect can be avoided so long as the trap is farther away from the junction than this optimum., Published by Aachen