Contextual Subspace Variational Quantum Eigensolver
- URL: http://arxiv.org/abs/2011.10027v2
- Date: Wed, 12 May 2021 14:06:17 GMT
- Title: Contextual Subspace Variational Quantum Eigensolver
- Authors: William M. Kirby, Andrew Tranter, and Peter J. Love
- Abstract summary: We describe a hybrid quantum-classical algorithm for approximating the ground state energy of a Hamiltonian.
The number of qubits required to reach chemical accuracy can be reduced by more than a factor of two.
This indicates that CS-VQE is a promising approach for eigenvalue computations on noisy intermediate-scale quantum devices.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We describe the contextual subspace variational quantum eigensolver (CS-VQE),
a hybrid quantum-classical algorithm for approximating the ground state energy
of a Hamiltonian. The approximation to the ground state energy is obtained as
the sum of two contributions. The first contribution comes from a noncontextual
approximation to the Hamiltonian, and is computed classically. The second
contribution is obtained by using the variational quantum eigensolver (VQE)
technique to compute a contextual correction on a quantum processor. In general
the VQE computation of the contextual correction uses fewer qubits and
measurements than the VQE computation of the original problem. Varying the
number of qubits used for the contextual correction adjusts the quality of the
approximation. We simulate CS-VQE on tapered Hamiltonians for small molecules,
and find that the number of qubits required to reach chemical accuracy can be
reduced by more than a factor of two. The number of terms required to compute
the contextual correction can be reduced by more than a factor of ten, without
the use of other measurement reduction schemes. This indicates that CS-VQE is a
promising approach for eigenvalue computations on noisy intermediate-scale
quantum devices.
Related papers
- Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States [37.69303106863453]
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage.
We use a specific class of VQA named variational quantum eigensolvers (VQEs) to benchmark them at entanglement witnessing and entangled ground state detection.
Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
arXiv Detail & Related papers (2024-07-05T12:06:40Z) - Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers.
Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
arXiv Detail & Related papers (2024-06-17T14:10:10Z) - Truncation technique for variational quantum eigensolver for Molecular
Hamiltonians [0.0]
variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for noisy quantum devices.
We propose a physically intuitive truncation technique that starts the optimization procedure with a truncated Hamiltonian.
This strategy allows us to reduce the required number of evaluations for the expectation value of Hamiltonian on a quantum computer.
arXiv Detail & Related papers (2024-02-02T18:45:12Z) - Solving the Lipkin model using quantum computers with two qubits only
with a hybrid quantum-classical technique based on the Generator Coordinate
Method [0.0]
We discuss the possibility of using the generator coordinate method (GCM) using hybrid quantum-classical algorithms with reduced quantum resources.
We show that, ultimately, only two qubits is enough to solve the problem regardless of the particle number.
As an alternative to this technique, we also explored how the quantum state deflation method can be adapted to the GCM problem.
arXiv Detail & Related papers (2023-12-07T21:18:27Z) - Variational quantum eigensolver for closed-shell molecules with
non-bosonic corrections [6.3235499003745455]
We introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic terms.
We find our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.
arXiv Detail & Related papers (2023-10-11T16:47:45Z) - On the feasibility of performing quantum chemistry calculations on quantum computers [0.0]
We propose two criteria for evaluating two leading quantum approaches for finding the ground state of molecules.
The first criterion applies to the variational quantum eigensolver (VQE) algorithm.
The second criterion applies to the quantum phase estimation (QPE) algorithm.
arXiv Detail & Related papers (2023-06-05T06:41:22Z) - Error Mitigation-Aided Optimization of Parameterized Quantum Circuits:
Convergence Analysis [42.275148861039895]
Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy processors.
gate noise due to imperfections and decoherence affects the gradient estimates by introducing a bias.
Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits.
QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently small.
arXiv Detail & Related papers (2022-09-23T10:48:04Z) - Unitary Partitioning and the Contextual Subspace Variational Quantum
Eigensolver [0.0]
The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground state energy of a given qubit Hamiltonian.
We show that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices.
arXiv Detail & Related papers (2022-07-07T17:28:36Z) - Quantum algorithms for grid-based variational time evolution [36.136619420474766]
We propose a variational quantum algorithm for performing quantum dynamics in first quantization.
Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
arXiv Detail & Related papers (2022-03-04T19:00:45Z) - Numerical Simulations of Noisy Quantum Circuits for Computational
Chemistry [51.827942608832025]
Near-term quantum computers can calculate the ground-state properties of small molecules.
We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
arXiv Detail & Related papers (2021-12-31T16:33:10Z) - Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves.
We find both methods provide good estimates of the energy and ground state.
gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
arXiv Detail & Related papers (2020-11-02T19:52:04Z)
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.