A Quantum Approach for Stochastic Constrained Binary Optimization

• URL: http://arxiv.org/abs/2301.01443v1
• Date: Wed, 4 Jan 2023 04:24:26 GMT
• Title: A Quantum Approach for Stochastic Constrained Binary Optimization
• Authors: Sarthak Gupta and Vassilis Kekatos
• Abstract summary: Quantum-based algorithms have been shown to generate high-quality solutions to hard problems. This work puts forth quantum vectors to cope with binary quadratically constrained programs. The method builds upon dual decomposition and entails solving a sequence of judiciously modified standard VQE tasks.
• Score: 2.6803492658436032
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) have been shown numerically to generate high-quality solutions to hard combinatorial problems, yet incorporating constraints to such problems has been elusive. To this end, this work puts forth a quantum heuristic to cope with stochastic binary quadratically constrained quadratic programs (QCQP). Identifying the strength of quantum circuits to efficiently generate samples from probability distributions that are otherwise hard to sample from, the variational quantum circuit is trained to generate binary-valued vectors to approximately solve the aforesaid stochastic program. The method builds upon dual decomposition and entails solving a sequence of judiciously modified standard VQE tasks. Tests on several synthetic problem instances using a quantum simulator corroborate the near-optimality and feasibility of the method, and its potential to generate feasible solutions for the deterministic QCQP too.

Related papers

• Subgradient Method using Quantum Annealing for Inequality-Constrained Binary Optimization Problems [0.4915744683251151]
  We show that inequality constraints can be relaxed into a similar objective function through statistical mechanics. We evaluate the performance of this method in a typical inequality-constrained optimization problem, the quadratic knapsack problem.
  arXiv  Detail & Related papers  (2024-11-11T11:59:50Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• 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)
• Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems [6.407238428292173]
  We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained optimization problems (COPs) pVSQA combines the variational methods and the post-processing technique. We implement pVSQA on a quantum annealer and a gate-type quantum device.
  arXiv  Detail & Related papers  (2023-09-15T03:09:16Z)
• 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)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• 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)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• VQE Method: A Short Survey and Recent Developments [5.9640499950316945]
  The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been successfully applied to solve the electronic Schr"odinger equation for a variety of small molecules. Modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze.
  arXiv  Detail & Related papers  (2021-03-15T16:25:36Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)
• Quantum Approximate Optimization for Hard Problems in Linear Algebra [0.0]
  We explore using QAOA for Binary Linear Least Squares (BLLS) as a building block of several other hard problems in linear algebra. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. Our numerics show that Simulated Annealing can outperform QAOA for BLLS at a QAOA depth of $pleq3$ for the probability of sampling the ground state.
  arXiv  Detail & Related papers  (2020-06-27T20:13:24Z)

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.