Logical qubit implementation for quantum annealing: augmented Lagrangian approach

• URL: http://arxiv.org/abs/2301.12393v1
• Date: Sun, 29 Jan 2023 08:45:36 GMT
• Title: Logical qubit implementation for quantum annealing: augmented Lagrangian approach
• Authors: Hristo N. Djidjev
• Abstract summary: Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits. We propose an optimization-based approach for producing suitable logical qubits representations that results in smaller chain weights.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between the chain qubits, are applied so that the physical qubits in a chain favor taking the same value in low energy samples. Assigning a good chain-strength value is crucial for the ability of quantum annealing to solve hard problems, but there are no general methods for computing such a value and, even if an optimal value is found, it may still not be suitable by being too large for accurate annealing results. In this paper, we propose an optimization-based approach for producing suitable logical qubits representations that results in smaller chain weights and show that the resulting optimization problem can be successfully solved using the augmented Lagrangian method. Experiments on the D-Wave Advantage system and the maximum clique problem on random graphs show that our approach outperforms both the default D-Wave method for chain-strength assignment as well as the quadratic penalty method.

Related papers

• Qubit-efficient quantum combinatorial optimization solver [0.0]
  We develop a qubit-efficient algorithm that overcomes the limitation by mapping a candidate bit solution to an entangled wave function of fewer qubits. This approach could benefit near-term intermediate-scale and future fault-tolerant small-scale quantum devices.
  arXiv  Detail & Related papers  (2024-07-22T11:02:13Z)
• An Analysis of Quantum Annealing Algorithms for Solving the Maximum Clique Problem [49.1574468325115]
  We analyse the ability of quantum D-Wave annealers to find the maximum clique on a graph, expressed as a QUBO problem. We propose a decomposition algorithm for the complementary maximum independent set problem, and a graph generation algorithm to control the number of nodes, the number of cliques, the density, the connectivity indices and the ratio of the solution size to the number of other nodes.
  arXiv  Detail & Related papers  (2024-06-11T04:40:05Z)
• Quantum Annealers Chain Strengths: A Simple Heuristic to Set Them All [0.0]
  Solving problems that do not directly map the chip topology remains challenging for quantum computers. The creation of logical qubits as sets of interconnected physical qubits overcomes limitations imposed by the sparsity of the chip. We show that densely connected logical qubits require a lower chain strength to maintain the ferromagnetic coupling.
  arXiv  Detail & Related papers  (2024-04-08T12:24:03Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Quantum-inspired optimization for wavelength assignment [51.55491037321065]
  We propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications.
  arXiv  Detail & Related papers  (2022-11-01T07:52:47Z)
• Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement [0.0]
  Reinforcement is one of the strategies that can be used to circumvent the exponentially small energy gaps of the system. In this study, we take a local entropy in the configuration space for the reinforcement and apply the algorithm to a number of easy and hard optimization problems.
  arXiv  Detail & Related papers  (2022-02-22T14:16:27Z)
• Efficiently Solve the Max-cut Problem via a Quantum Qubit Rotation Algorithm [7.581898299650999]
  We introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA) The approximate solution of the max-cut problem can be obtained with probability close to 1. We compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.
  arXiv  Detail & Related papers  (2021-10-15T11:19:48Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• SiMaN: Sign-to-Magnitude Network Binarization [165.5630656849309]
  We show that our weight binarization provides an analytical solution by encoding high-magnitude weights into +1s, and 0s otherwise. We prove that the learned weights of binarized networks roughly follow a Laplacian distribution that does not allow entropy. Our method, dubbed sign-to- neural network binarization (SiMaN), is evaluated on CIFAR-10 and ImageNet.
  arXiv  Detail & Related papers  (2021-02-16T07:03:51Z)
• Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics [77.34726150561087]
  We propose direct optimal control as a robust and flexible alternative to indirect control theory. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential.
  arXiv  Detail & Related papers  (2020-10-08T07:59:29Z)
• Advanced unembedding techniques for quantum annealers [0.0]
  We present tailored unembedding techniques for four important NP-hard problems. Our techniques are simple and yet make use of structural properties of the problem being solved.
  arXiv  Detail & Related papers  (2020-09-10T17:49:43Z)

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.