Continuous Hamiltonian dynamics on digital quantum computers without discretization error

• URL: http://arxiv.org/abs/2308.03694v2
• Date: Fri, 17 Nov 2023 15:05:15 GMT
• Title: Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Authors: Etienne Granet and Henrik Dreyer
• Abstract summary: We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers. The algorithm achieves zero discretization error with finite depth. The gate count for simulation up to time $t$ is $O(t2mu2)$ with $mu$ the $1$-norm of the Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number of gates comes at the cost of an attenuation of the measured expectation value by a known amplitude, requiring more shots per circuit. The gate count for simulation up to time $t$ is $O(t^2\mu^2)$ with $\mu$ the $1$-norm of the Hamiltonian, without dependence on the precision desired on the result, providing a significant improvement over previous algorithms. The only dependence in the norm makes it particularly adapted to non-sparse Hamiltonians. The algorithm generalizes to time-dependent Hamiltonians, appearing for example in adiabatic state preparation. These properties make it particularly suitable for present-day relatively noisy hardware that supports only circuits with moderate depth.

Related papers

• Robust analog quantum simulators by quantum error-detecting codes [22.034646136056804]
  We provide a recipe for error-resilient Hamiltonian simulations, making use of an excited encoding subspace stabilized by solely $2$-local commuting Hamiltonians. Our method is scalable as it only requires penalty terms that scale to system size.
  arXiv  Detail & Related papers  (2024-12-10T18:58:05Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Quantum simulation of highly-oscillatory many-body Hamiltonians for near-term devices [2.487329273327606]
  We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems. We exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion. Our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian.
  arXiv  Detail & Related papers  (2023-12-13T17:29:29Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices [3.1952399274829775]
  We develop a tool called quantum eigenvalue transformation of unitary matrices with reals (QET-U) This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground state energy. We demonstrate the performance of the algorithm using IBM Qiskit for the transverse field Ising model.
  arXiv  Detail & Related papers  (2022-04-12T17:11:40Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion [6.338178373376447]
  We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. We demonstrate that the cost of the algorithm is independent of the Hamiltonian's frequencies.
  arXiv  Detail & Related papers  (2021-03-29T05:02:02Z)
• Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware [6.445605125467574]
  We develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model. We analyse the impact of these techniques under the standard error model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions.
  arXiv  Detail & Related papers  (2020-03-15T18:22:02Z)

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.