Successive randomized compression: A randomized algorithm for the compressed MPO-MPS product

• URL: http://arxiv.org/abs/2504.06475v1
• Date: Tue, 08 Apr 2025 22:33:49 GMT
• Title: Successive randomized compression: A randomized algorithm for the compressed MPO-MPS product
• Authors: Chris Camaño, Ethan N. Epperly, Joel A. Tropp,
• Abstract summary: This paper introduces a new single-pass, randomized algorithm, called successive randomized compression (SRC)<n>The performance of the new algorithm is evaluated on synthetic problems and unitary time evolution problems for quantum spin systems.
• Score: 0.6554326244334868
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor networks like matrix product states (MPSs) and matrix product operators (MPOs) are powerful tools for representing exponentially large states and operators, with applications in quantum many-body physics, machine learning, numerical analysis, and other areas. In these applications, computing a compressed representation of the MPO--MPS product is a fundamental computational primitive. For this operation, this paper introduces a new single-pass, randomized algorithm, called successive randomized compression (SRC), that improves on existing approaches in speed or in accuracy. The performance of the new algorithm is evaluated on synthetic problems and unitary time evolution problems for quantum spin systems.

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.<n>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)
• Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
  This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
  arXiv  Detail & Related papers  (2024-07-04T21:11:05Z)
• Compact quantum algorithms for time-dependent differential equations [0.0]
  We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems.<n>We generate hybrid quantum-classical algorithms that efficiently perform matrix-vector multiplication and matrix inversion operations.
  arXiv  Detail & Related papers  (2024-05-16T02:14:58Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• 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)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Polynomial unconstrained binary optimisation inspired by optical simulation [52.11703556419582]
  We propose an algorithm inspired by optical coherent Ising machines to solve the problem of unconstrained binary optimization. We benchmark the proposed algorithm against existing PUBO algorithms, and observe its superior performance. The application of our algorithm to protein folding and quantum chemistry problems sheds light on the shortcomings of approxing the electronic structure problem by a PUBO problem.
  arXiv  Detail & Related papers  (2021-06-24T16:39:31Z)
• Randomizing multi-product formulas for Hamiltonian simulation [2.2049183478692584]
  We introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas on the other. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth.
  arXiv  Detail & Related papers  (2021-01-19T19:00:23Z)
• Efficient 2D Tensor Network Simulation of Quantum Systems [6.074275058563179]
  2D tensor networks such as Projected Entangled States (PEPS) are well-suited for key classes of physical systems and quantum circuits. We propose new algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and scalableization of a subnetwork.
  arXiv  Detail & Related papers  (2020-06-26T22:36:56Z)

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.