arXiv subjects

Jasper Verbree

Publications and source records attributed to Jasper Verbree.

6 recordsLinked to original sources

arXiv2026

Evaluating Quantum Wire Cutting for QAOA: Performance Benchmarks in Ideal and Noisy Environments

Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these techniques called quantum circuit cutting. With circuit cutting, a quantum circuit is decomposed into smaller sub-circuits, each of which can be run on smaller quantum hardware. We compare the performance of quantum circuit cutting with different cutting strategies, and then apply circuit cutting to a QAOA algorithm. Using simulations, we first show that Randomized Clifford measurements outperform both Pauli and random unitary measurements. Second, we show that circuit cutting has trouble providing correct answers in noisy settings, especially as the number of circuits increases.

quant-ph↗

arXiv2025

Probability distribution reconstruction using circuit cutting applied to a variational classifier

Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New techniques can aid in using smaller quantum computers to run larger quantum algorithms. One of these techniques is circuit cutting. With this method, a circuit is broken into multiple pieces, each of which is run on quantum hardware independently and then recombined to obtain the overall answer. These circuit cutting techniques require additional circuit evaluations, which can form a bottleneck for algorithms requiring many interactions. This work explores the potential of circuit cutting techniques precisely in this regime of many interactions. We consider two different models, a standard method based on expectation values, and a novel method based on probability distribution reconstruction. Next, we compare two different training methods we call train-then-cut and cut-then-train and show that in practice, cut-then-train still produces good results. This observation brings closer the practical applicability of circuit cutting techniques, as a train-then-cut strategy is often infeasible. We conclude by implementing a cut and uncut circuit and find that circuit cutting helps achieve higher fidelity results.

quant-ph↗

arXiv2023

Wardrop equilibrium and Braess's paradox for varying demand

This work explores the relationship between the set of Wardrop equilibria~(WE) of a routing game, the total demand of that game, and the occurrence of Braess's paradox~(BP). The BP formalizes the counter-intuitive fact that for some networks, removing a path from the network decreases congestion at WE. For a single origin-destination routing games with affine cost functions, the first part of this work provides tools for analyzing the evolution of the WE as the demand varies. It characterizes the piece-wise affine nature of this dependence by showing that the set of directions in which the WE can vary in each piece is the solution of a variational inequality problem. In the process we establish various properties of changes in the set of used and minimal-cost paths as demand varies. As a consequence of these characterizations, we derive a procedure to obtain the WE for all demands above a certain threshold. The second part of the paper deals with detecting the presence of BP in a network. We supply a number of sufficient conditions that reveal the presence of BP and that are computationally tractable. We also discuss a different perspective on BP, where we establish that a path causing BP at a particular demand must be strictly beneficial to the network at a lower demand. Several examples throughout this work illustrate and elaborate our findings.

cs.GT↗

arXiv2022

Stochastic approximation approaches for CVaR-based variational inequalities

This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR at each iteration. The first algorithm constrains the iterates to the feasible set using projection. To overcome the computational burden of projections, the second one handles inequality and equality constraints defining the feasible set differently. Particularly, projection onto to the affine subspace defined by the equality constraints is achieved by matrix multiplication and inequalities are handled by using penalty functions. Finally, the third algorithm discards projections altogether by introducing multiplier updates. We establish asymptotic convergence of all our schemes to any arbitrary neighborhood of the solution of the VI. A simulation example concerning a network routing game illustrates our theoretical findings.

math.OC↗

arXiv2021

Inferring the prior in routing games using public signalling

This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling scheme and participants form a posterior belief about the state of the network based on prior beliefs and the received signal. They subsequently select routes minimizing their individual expected travel time under their posterior beliefs, giving rise to a Wardrop equilibrium. We investigate how the TIS can infer the prior beliefs held by the participants by designing suitable signalling schemes, and observing the equilibrium flows under different signals. We show that under mild conditions a signalling scheme that allows for exact inference of the prior exists. We then provide an iterative algorithm that finds such a scheme in a finite number of steps. We show that schemes designed by our algorithm are robust, in the sense that they can still identify the prior after a small enough perturbation. We also investigate the case where the population is divided among multiple priors, and give conditions under which the fraction associated to each prior can be identified. Several examples illustrate our results.

math.OC↗

arXiv2020

Stochastic approximation of CVaR-based variational inequalities

In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to solve these VIs. We investigate convergence of these algorithms under various assumptions on the monotonicity of the VI and accuracy of the CVaR estimate. Our first algorithm is shown to converge to the exact solution of the VI when the estimation error of the CVaR becomes progressively smaller along any execution of the algorithm. When the estimation error is nonvanishing, we provide two algorithms that provably converge to a neighborhood of the solution of the VI. For these schemes, under strong monotonicity, we provide an explicit relationship between sample size, estimation error, and the size of the neighborhood to which convergence is achieved. A simulation example illustrates our theoretical findings.

math.OC↗