Noisy Bayesian optimization for variational quantum eigensolvers
- URL: http://arxiv.org/abs/2112.00426v1
- Date: Wed, 1 Dec 2021 11:28:55 GMT
- Title: Noisy Bayesian optimization for variational quantum eigensolvers
- Authors: Giovanni Iannelli and Karl Jansen
- Abstract summary: The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian.
This work proposes an implementation of GPR and BO specifically tailored to perform VQE on quantum computers already available today.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The variational quantum eigensolver (VQE) is a hybrid quantum-classical
algorithm used to find the ground state of a Hamiltonian using variational
methods. In the context of this Lattice symposium, the procedure can be used to
study lattice gauge theories (LGTs) in the Hamiltonian formulation. Bayesian
optimization (BO) based on Gaussian process regression (GPR) is a powerful
algorithm for finding the global minimum of a cost function, e.g. the energy,
with a very low number of iterations using data affected by statistical noise.
This work proposes an implementation of GPR and BO specifically tailored to
perform VQE on quantum computers already available today.
Related papers
- Matrix product state ansatz for the variational quantum solution of the
Heisenberg model on Kagome geometries [0.0]
We develop a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm.
We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems.
arXiv Detail & Related papers (2024-01-04T16:53:47Z) - Optimization strategies in WAHTOR algorithm for quantum computing
empirical ansatz: a comparative study [0.0]
This work introduces a non-adiabatic version of the WAHTOR algorithm and compares its efficiency with three implementations.
Calculating first and second-order derivatives of the Hamiltonian at fixed VQE parameters does not introduce a prototypical QPU overload.
We find out that in the case of Hubbard model systems the trust region non-adiabatic optimization is more efficient.
arXiv Detail & Related papers (2023-06-19T15:07:55Z) - Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity.
We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
arXiv Detail & Related papers (2022-03-01T19:47:16Z) - Quantum algorithm for stochastic optimal stopping problems with
applications in finance [60.54699116238087]
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in optimal stopping theory.
We propose a quantum LSM based on quantum access to a process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo.
arXiv Detail & Related papers (2021-11-30T12:21:41Z) - Variational Adiabatic Gauge Transformation on real quantum hardware for
effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
We introduce the Variational Adiabatic Gauge Transformation (VAGT)
VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit.
The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
arXiv Detail & Related papers (2021-11-16T20:50:08Z) - Using gradient-based algorithms to determine ground state energies on a
quantum computer [0.0]
Variational algorithms are promising candidates to be implemented on near-term quantum computers.
We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and noise of the quantum computer.
arXiv Detail & Related papers (2021-09-17T09:12:43Z) - 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) - Quantum Approximate Optimization Algorithm Based Maximum Likelihood
Detection [80.28858481461418]
Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
arXiv Detail & Related papers (2021-07-11T10:56:24Z) - An optimal quantum sampling regression algorithm for variational
eigensolving in the low qubit number regime [0.0]
We introduce Quantum Sampling Regression (QSR), an alternative hybrid quantum-classical algorithm.
We analyze some of its use cases based on time complexity in the low qubit number regime.
We demonstrate the efficacy of our algorithm for a benchmark problem.
arXiv Detail & Related papers (2020-12-04T00:01:15Z) - Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices.
We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT)
Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
arXiv Detail & Related papers (2020-10-01T18:14:11Z) - The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy
profiles of parameterized Hamiltonians for quantum simulation [0.0]
We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian.
We test this algorithm with a XXZ spin chain, an electronic H$_4$ Hamiltonian and a single-transmon quantum simulation.
arXiv Detail & Related papers (2020-09-28T18:00:15Z)
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.