Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing

• URL: http://arxiv.org/abs/2103.09090v1
• Date: Tue, 16 Mar 2021 14:13:29 GMT
• Title: Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing
• Authors: Ji\v{r}\'i Lebl, Asif Shakeel
• Abstract summary: Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set. We frame these problems as quantum Ising models, for which variational quantum algorithms (VQA) are particularly useful.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of balancing covariates in randomized trials have efficient randomized algorithms based on the Gram-Schmidt walk (GSW). We frame these problems as quantum Ising models, for which variational quantum algorithms (VQA) are particularly useful. Simulating an example of covariate-balancing on an IBM quantum simulator, we find that the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) yield results comparable to the GSW algorithm.

Related papers

• Performance Benchmarking of Quantum Algorithms for Hard Combinatorial Optimization Problems: A Comparative Study of non-FTQC Approaches [0.0]
  This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems. Our benchmark includes noisy intermediate-scale quantum (NISQ) algorithms, such as the variational quantum eigensolver. Our findings reveal that no single non-FTQC algorithm performs optimally across all problem types, underscoring the need for tailored algorithmic strategies.
  arXiv  Detail & Related papers  (2024-10-30T08:41:29Z)
• Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice [0.0]
  Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address optimization (CO) problems. We numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark.
  arXiv  Detail & Related papers  (2024-08-06T09:57:34Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Trainable Variational Quantum-Multiblock ADMM Algorithm for Generation Scheduling [0.0]
  This paper proposes a two-loop quantum solution algorithm for generation scheduling by quantum computing, machine learning, and distributed optimization. The aim is to facilitate noisy employing near-term quantum machines with a limited number of qubits to solve practical power system problems.
  arXiv  Detail & Related papers  (2023-03-28T21:31:39Z)
• Error Analysis of the Variational Quantum Eigensolver Algorithm [0.18188255328029254]
  We study variational quantum eigensolver (VQE) and its individual quantum subroutines. We show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call.
  arXiv  Detail & Related papers  (2023-01-18T02:02:30Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Quantum algorithm for stochastic optimal stopping problems with applications in finance [60.54699116238087]
  The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in optimal stopping theory. We propose a quantum LSM based on quantum access to a process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo.
  arXiv  Detail & Related papers  (2021-11-30T12:21:41Z)
• The Impact of Logical Errors on Quantum Algorithms [0.899910652271871]
  We evaluate six canonical quantum algorithms' intrinsic resilience to logical qubit and gate errors. The resilience of the studied quantum algorithms decreases as the number of qubits and the depth of the algorithms' circuits increase for both Pauli and Z-rotation errors.
  arXiv  Detail & Related papers  (2021-11-05T21:35:03Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.