arXiv subjects

Kristel Michielsen

Publications and source records attributed to Kristel Michielsen.

At least 73 records · Page 4Linked to original sources

arXiv2022

On the hardness of quadratic unconstrained binary optimization problems

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.

quant-ph↗

arXiv2022

Assessment of the variational quantum eigensolver: application to the Heisenberg model

We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer simulator, we observe that a low-depth-circuit ansatz advantageously exploits the efficiently preparable Néel initial state, avoids potential barren plateaus, and works for both one- and two-dimensional lattices. The analysis reflects the decisive ingredients required for a simulation by comparing different ansätze, initial parameters, and gradient-based versus gradient-free optimizers. Extrapolation to the thermodynamic limit accurately yields the analytical value for the ground state energy, given by the Bethe ansatz. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.

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

Quantum annealing for hard 2-SAT problems : Distribution and scaling of minimum energy gap and success probability

In recent years, quantum annealing has gained the status of being a promising candidate for solving various optimization problems. Using a set of hard 2-satisfiabilty (2-SAT) problems, consisting of upto 18-variables problems, we analyze the scaling complexity of the quantum annealing algorithm and study the distributions of the minimum energy gap and the success probability. We extend the analysis of the standard quantum annealing Hamiltonian by introducing an additional term, the trigger Hamiltonian, which can be of two types : ferromagnetic and antiferromagnetic. We use these trigger Hamiltonians to study their influence on the success probability for solving the selected 2-SAT problems. We found that although the scaling of the run-time is exponential for the standard and modified quantum annealing Hamiltonians, the scaling constant in case of adding the trigger Hamiltonians can be significantly smaller. Furthermore, certain choices for the trigger Hamiltonian and annealing times can result in a better scaling than that for simulated annealing. Lastly, we also use the quantum annealers of D-Wave Systems Inc. to study their performance in solving the 2-SAT problems and compare it with the simulation results.

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.

quant-ph↗

arXiv2021

Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems

We study the performance of quantum annealing for two sets of problems, namely, 2-satisfiability (2-SAT) problems represented by Ising-type Hamiltonians, and nonstoquastic problems which are obtained by adding extra couplings to the 2-SAT problem Hamiltonians. In addition, we add to the transverse Ising-type Hamiltonian used for quantum annealing a third term, the trigger Hamiltonian with ferromagnetic or antiferromagnetic couplings, which vanishes at the beginning and end of the annealing process. We also analyze some problem instances using the energy spectrum, average energy or overlap of the state during the evolution with the instantaneous low lying eigenstates of the Hamiltonian, and identify some non-adiabatic mechanisms which can enhance the performance of quantum annealing.

quant-ph↗

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

Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices

We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices. Focusing on dynamics at formally infinite temperature, we particularly consider the autocorrelation functions of local densities, where the time evolution is governed either by the linear Schrödinger equation in the quantum case, or the nonlinear Hamiltonian equations of motion in the case of classical mechanics. While, in full generality, a quantitative agreement between quantum and classical dynamics can therefore not be expected, our large-scale numerical results for spin-$1/2$ systems with up to $N = 36$ lattice sites in fact defy this expectation. Specifically, we observe a remarkably good agreement for all geometries, which is best for the nonintegrable quantum models in quasi-one or two dimensions, but still satisfactory in the case of integrable chains, at least if transport properties are not dominated by the extensive number of conservation laws. Our findings indicate that classical or semi-classical simulations provide a meaningful strategy to analyze the dynamics of quantum many-body models, even in cases where the spin quantum number $S = 1/2$ is small and far away from the classical limit $S \to \infty$.

cond-mat.stat-mech↗

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

General error mitigation for quantum circuits

A general method to mitigate the effect of errors in quantum circuits is outlined. The method is developed in sight of characteristics that an ideal method should possess and to ameliorate an existing method which only mitigates state preparation and measurement errors. The method is tested on different IBM Q quantum devices, using randomly generated circuits with up to four qubits. A large majority of results show significant error mitigation.

quant-ph↗

arXiv2020

Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers

Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating photon number $\bar{n}$ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing $\bar{n}$ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of $\bar{n}$, up to $\bar{n}\approx200$. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing $\bar{n}$. Even without the use of a parametric amplifier, at $\bar{n}=74$, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.

quant-ph↗

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.

quant-ph↗

arXiv2020

Exponential damping induced by random and realistic perturbations

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-$1/2$ ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.

cond-mat.stat-mech↗

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.

quant-ph↗

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.

quant-ph↗