arXiv subjects

Dennis Willsch

Publications and source records attributed to Dennis Willsch.

35 records · Page 2Linked to original sources

arXiv2022

Hybrid Quantum Classical Simulations

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.

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arXiv2022

Numerical analysis of effective models for flux-tunable transmon systems

Simulations and analytical calculations that aim to describe flux-tunable transmons are usually based on effective models of the corresponding lumped-element model. However, when a control pulse is applied, in most cases it is not known how much the predictions made with the effective models deviate from the predictions made with the original lumped-element model. In this work we compare the numerical solutions of the time-dependent Schrödinger equation for both the effective and the lumped-element models, for microwave and unimodal control pulses (external fluxes). These control pulses are used to model single-qubit (X) and two-qubit gate (Iswap and Cz) transitions. First, we derive a non-adiabatic effective Hamiltonian for a single flux-tunable transmon and compare the pulse response of this model to the one of the corresponding circuit Hamiltonian. Here we find that both models predict similar outcomes for similar control pulses. Then, we study how different approximations affect single-qubit (X) and two-qubit gate (Iswap and Cz) transitions in two different two-qubit systems. For this purpose we consider three different systems in total: a single flux-tunable transmon and two two-qubit systems. In summary, we find that a series of commonly applied approximations (individually and/or in combination) can change the response of a system substantially, when a control pulse is applied.

quant-ph↗

arXiv2022

GPU-accelerated simulations of quantum annealing and the quantum approximate optimization algorithm

We study large-scale applications using a GPU-accelerated version of the massively parallel Jülich universal quantum computer simulator (JUQCS--G). First, we benchmark JUWELS Booster, a GPU cluster with 3744 NVIDIA A100 Tensor Core GPUs. Then, we use JUQCS--G to study the relation between quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). We find that a very coarsely discretized version of QA, termed approximate quantum annealing (AQA), performs surprisingly well in comparison to the QAOA. It can either be used to initialize the QAOA, or to avoid the costly optimization procedure altogether. Furthermore, we study the scaling of the success probability when using AQA for problems with 30 to 40 qubits. We find that the case with the largest discretization error scales most favorably, surpassing the best result obtained from the QAOA.

quant-ph↗

arXiv2022

Benchmarking Advantage and D-Wave 2000Q quantum annealers with exact cover problems

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.

quant-ph↗

arXiv2022

Lecture Notes: Programming Quantum Computers

Quantum computing is a new emerging computer technology. Current quantum computing devices are at a development stage where they are gradually becoming suitable for small real-world applications. This lecture is devoted to the practical aspects of programming such quantum computing devices. The first part of these lecture notes focuses on programming gate-based quantum computers, and the second part shows how to program quantum annealers.

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arXiv2021

Garden optimization problems for benchmarking quantum annealers

We benchmark the 5000+ qubit system Advantage coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the Advantage system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system DW2000Q sometimes produce more favourable results if they can solve the problems.

quant-ph↗

arXiv2021

Support vector machines on the D-Wave quantum annealer

Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We introduce a method to train SVMs on a D-Wave 2000Q quantum annealer and study its performance in comparison to SVMs trained on conventional computers. The method is applied to both synthetic data and real data obtained from biology experiments. We find that the quantum annealer produces an ensemble of different solutions that often generalizes better to unseen data than the single global minimum of an SVM trained on a conventional computer, especially in cases where only limited training data is available. For cases with more training data than currently fits on the quantum annealer, we show that a combination of classifiers for subsets of the data almost always produces stronger joint classifiers than the conventional SVM for the same parameters.

cs.LG↗

arXiv2020

Random State Technology

We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations of physically relevant properties such as the density of states of large single particle systems, the specific heat, current-current correlations, density-density correlations, and electron spin resonance spectra of many-body systems. We explore a new field of applications of the random state technology by showing that it can be used to analyze numerical simulations and experiments that aim to realize quantum supremacy on a noisy intermediate-scale quantum processor. Additionally, we show that concepts of the random state technology prove useful in quantum information theory.

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arXiv2020

Supercomputer simulations of transmon quantum computers

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.

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arXiv2020

Benchmarking the Quantum Approximate Optimization Algorithm

The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation ratio. The set of problem instances studied consists of weighted MaxCut problems and 2-satisfiability problems. The Ising model representations of the latter possess unique ground states and highly-degenerate first excited states. The quantum approximate optimization algorithm is executed on quantum computer simulators and on the IBM Q Experience. Additionally, data obtained from the D-Wave 2000Q quantum annealer is used for comparison, and it is found that the D-Wave machine outperforms the quantum approximate optimization algorithm executed on a simulator. The overall performance of the quantum approximate optimization algorithm is found to strongly depend on the problem instance.

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arXiv2020

Discrete-event simulation of an extended Einstein-Podolsky-Rosen-Bohm experiment

We use discrete-event simulation to construct a subquantum model that can reproduce the quantum-theoretical prediction for the statistics of data produced by the Einstein-Podolsky-Rosen-Bohm experiment and an extension thereof. This model satisfies Einstein's criterion of locality and generates data in an event-by-event and cause-and-effect manner. We show that quantum theory can describe the statistics of the simulation data for a certain range of model parameters only.

quant-ph↗

arXiv2020

Discrete-event simulation of quantum walks

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.

quant-ph↗

arXiv2020

Real-time simulation of flux qubits used for quantum annealing

The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schrödinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as non-interacting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.

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arXiv2019

Benchmarking Supercomputers with the Jülich Universal Quantum Computer Simulator

We use a massively parallel simulator of a universal quantum computer to benchmark some of the most powerful supercomputers in the world. We find nearly ideal scaling behavior on the Sunway TaihuLight, the K computer, the IBM BlueGene/Q JUQUEEN, and the Intel Xeon based clusters JURECA and JUWELS. On the Sunway TaihuLight and the K computer, universal quantum computers with up to 48 qubits can be simulated by means of an adaptive two-byte encoding to reduce the memory requirements by a factor of eight. Additionally, we discuss an alternative approach to alleviate the memory bottleneck by decomposing entangling gates such that low-depth circuits with a much larger number of qubits can be simulated.

quant-ph↗

arXiv2019

Separation of conditions as a prerequisite for quantum theory

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/Schrödinger equation.

quant-ph↗

arXiv2018

Massively parallel quantum computer simulator, eleven years later

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.

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arXiv2017

Benchmarking gate-based quantum computers

With the advent of public access to small gate-based quantum processors, it becomes necessary to develop a benchmarking methodology such that independent researchers can validate the operation of these processors. We explore the usefulness of a number of simple quantum circuits as benchmarks for gate-based quantum computing devices and show that circuits performing identity operations are very simple, scalable and sensitive to gate errors and are therefore very well suited for this task. We illustrate the procedure by presenting benchmark results for the IBM Quantum Experience, a cloud-based platform for gate-based quantum computing.

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