Inverse iteration quantum eigensolvers assisted with a continuous variable

• URL: http://arxiv.org/abs/2010.03236v2
• Date: Tue, 8 Mar 2022 02:50:43 GMT
• Title: Inverse iteration quantum eigensolvers assisted with a continuous variable
• Authors: Min-Quan He, Dan-Bo Zhang, and Z. D. Wang
• Abstract summary: We propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum-classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.

Related papers

• Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
  This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum. We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
  arXiv  Detail & Related papers  (2024-10-28T08:43:40Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Spin coupling is all you need: Encoding strong electron correlation on quantum computers [0.0]
  We show that quantum computers can efficiently simulate strongly correlated molecular systems by directly encoding the dominant entanglement structure in the form of spin-coupled initial states. Our work paves the way towards scalable quantum simulation of electronic structure for classically challenging systems.
  arXiv  Detail & Related papers  (2024-04-29T17:14:21Z)
• 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)
• Higher-order quantum transformations of Hamiltonian dynamics [0.8192907805418581]
  We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. By way of example, we demonstrate the simulation of negative time-reversal, and perform a Hamiltonian learning task.
  arXiv  Detail & Related papers  (2023-03-17T06:01:59Z)
• Simulating Markovian open quantum systems using higher-order series expansion [1.713291434132985]
  We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. Our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding.
  arXiv  Detail & Related papers  (2022-12-05T06:02:50Z)
• Quantum Heaviside Eigen Solver [1.027974860479791]
  We propose a quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the general Hamiltonian for quantum computers. The present algorithm is a universal quantum eigen solver for Hamiltonian in quantum many-body systems and quantum chemistry.
  arXiv  Detail & Related papers  (2021-11-16T08:26:47Z)
• 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)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)

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.