Speedup of high-order unconstrained binary optimization using quantum Z2 lattice gauge theory

• URL: http://arxiv.org/abs/2406.05958v1
• Date: Mon, 10 Jun 2024 01:37:18 GMT
• Title: Speedup of high-order unconstrained binary optimization using quantum Z2 lattice gauge theory
• Authors: Bi-Ying Wang, Xiaopeng Cui, Qingguo Zeng, Yemin Zhan, Yu Shi, Man-Hong Yung,
• Abstract summary: We implement a quantum adiabatic algorithm and achieve algorithmic speedup by introducing gauge symmetry into the algorithm. Gauge symmetry enforces the state to be in the instantaneous ground state, further speeding up the computation.
• Score: 2.2131426229426405
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: How to quickly solve the problem of high-order unconstrained binary optimization (HUBO) has attracted much attention, because of its importance and wide-range applications. Here we implement HUBO using a quantum adiabatic algorithm and achieve algorithmic speedup by introducing gauge symmetry into the algorithm. Gauge symmetry enforces the state to be in the instantaneous ground state, further speeding up the computation. Specifically we map the HUBO problem to quantum Z2 lattice gauge theory defined on the dual graph. The gauge operators are found by using the closed-loop-search algorithm, and subsequently the speedup scheme with gauge symmetry for HUBO problem is developed. As an example demonstrated in the classical computers, we present the mathematical formulation of our speedup scheme and propose the so-called gauged local annealing (gLQA) , which is the local quantum annealing (LQA) protected by the gauge symmetry. We then use gLQA to calculate the ground state energy of the Z2 gauge theory. gLQA reduces the computational time by one order of magnitude from that of LQA.

Related papers

• Fast Expectation Value Calculation Speedup of Quantum Approximate Optimization Algorithm: HoLCUs QAOA [55.2480439325792]
  We present a new method for calculating expectation values of operators that can be expressed as a linear combination of unitary (LCU) operators. This method is general for any quantum algorithm and is of particular interest in the acceleration of variational quantum algorithms.
  arXiv  Detail & Related papers  (2025-03-03T17:15:23Z)
• Solving quadratic binary optimization problems using quantum SDP methods: Non-asymptotic running time analysis [1.9081120388919084]
  Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods. We present an analysis of the non-asymptotic resource requirements of a quantum SDP solver.
  arXiv  Detail & Related papers  (2025-02-21T12:54:05Z)
• Optimization by Decoded Quantum Interferometry [43.55132675053983]
  We introduce a quantum algorithm for reducing classical optimization problems to classical decoding problems. We show that DQI achieves a better approximation ratio than any quantum-time classical algorithm known to us.
  arXiv  Detail & Related papers  (2024-08-15T17:47:42Z)
• Digitized Counterdiabatic Quantum Algorithms for Logistics Scheduling [33.04597339860113]
  We study a job shop scheduling problem for an automatized robot and a travelling salesperson problem. In DCQO, we find the solution of an optimization problem via an adiabatic quantum dynamics. We experimentally implement our algorithms on superconducting and trapped-ion quantum processors.
  arXiv  Detail & Related papers  (2024-05-24T16:53:30Z)
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer [27.84599956781646]
  We study the operation of a quantum-classical time-series algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies.
  arXiv  Detail & Related papers  (2023-09-19T11:59:36Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• A quantum advantage over classical for local max cut [48.02822142773719]
  Quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. Results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical.
  arXiv  Detail & Related papers  (2023-04-17T16:42:05Z)
• Solving the semidefinite relaxation of QUBOs in matrix multiplication time, and faster with a quantum computer [0.20999222360659603]
  We show that some quantum SDO solvers provide speedups in the low-precision regime. We exploit this fact to exponentially improve the dependence of their algorithm on precision. A quantum implementation of our algorithm exhibits a worst case running time of $mathcalO left(ns + n1.5 cdot textpolylog left(n, | C |_F, frac1epsilon right)$.
  arXiv  Detail & Related papers  (2023-01-10T23:12:05Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Efficient quantum implementation of 2+1 U(1) lattice gauge theories with Gauss law constraints [1.5675763601034223]
  We show how to break the exponential scaling of a naive implementation of a U(1) gauge theory in two spatial dimensions. We study the errors from finite Suzuki-Trotter time-step, circuit approximation, and quantum noise in a calculation of an explicit observable using IBMQ superconducting qubit hardware.
  arXiv  Detail & Related papers  (2022-11-18T20:14:15Z)
• On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks [31.228956832890393]
  We show that classical algorithms can't efficiently hit one well knowing the other well but Q can when given proper initial states the well. We construct a specific double-well landscape, where classical algorithms cannot efficiently hit one well knowing the other well but Q can when given proper initial states the well.
  arXiv  Detail & Related papers  (2022-09-29T01:39:20Z)
• Approximate encoding of quantum states using shallow circuits [0.0]
  A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.
  arXiv  Detail & Related papers  (2022-06-30T18:00:04Z)
• Quantum Speedup for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection [2.5272389610447856]
  We propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization problem. The proposed algorithm is capable of reducing the query complexity in the classical domain and providing a quadratic speedup in the quantum domain.
  arXiv  Detail & Related papers  (2022-05-31T00:14:49Z)
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays [39.76254807200083]
  We experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We find the problem hardness is controlled by the solution degeneracy and number of local minima. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions.
  arXiv  Detail & Related papers  (2022-02-18T19:00:01Z)
• Deterministic and Entanglement-Efficient Preparation of Amplitude-Encoded Quantum Registers [0.533024001730262]
  A classical vector $mathbfb$ is encoded in the amplitudes of a quantum state. An arbitrary state of $Q$ qubits generally requires approximately $2Q$ entangling gates. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the quantum resources required for state preparation.
  arXiv  Detail & Related papers  (2021-10-26T07:37:54Z)
• Quantum Optimization Heuristics with an Application to Knapsack Problems [5.866941279460248]
  This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions.
  arXiv  Detail & Related papers  (2021-08-19T17:22:44Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• 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)
• Quantum Approximate Optimization Algorithm with Adaptive Bias Fields [4.03537866744963]
  The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one step to improve the operators at later steps.
  arXiv  Detail & Related papers  (2021-05-25T13:51:09Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization [0.14755786263360526]
  We explore which quantum algorithms for optimization might be most practical to try out on a small fault-tolerant quantum computer. Our results discourage the notion that any quantum optimization realizing only a quadratic speedup will achieve an advantage over classical algorithms.
  arXiv  Detail & Related papers  (2020-07-14T22:54:04Z)

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.