Quantum Krylov subspace algorithms for ground and excited state energy
estimation
- URL: http://arxiv.org/abs/2109.06868v3
- Date: Thu, 14 Oct 2021 14:15:38 GMT
- Title: Quantum Krylov subspace algorithms for ground and excited state energy
estimation
- Authors: Cristian L. Cortes and Stephen K. Gray
- Abstract summary: Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm.
We show that a wide class of Hamiltonians relevant to condensed matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test.
We develop a unified theory of quantum Krylov subspace algorithms and present three new quantum-classical algorithms for the ground and excited-state energy estimation problems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost
alternative to the conventional quantum phase estimation algorithm for
estimating the ground and excited-state energies of a quantum many-body system.
While QKSD algorithms typically rely on using the Hadamard test for estimating
Krylov subspace matrix elements of the form, $\langle
\phi_i|e^{-i\hat{H}\tau}|\phi_j \rangle$, the associated quantum circuits
require an ancilla qubit with controlled multi-qubit gates that can be quite
costly for near-term quantum hardware. In this work, we show that a wide class
of Hamiltonians relevant to condensed matter physics and quantum chemistry
contain symmetries that can be exploited to avoid the use of the Hadamard test.
We propose a multi-fidelity estimation protocol that can be used to compute
such quantities showing that our approach, when combined with efficient
single-fidelity estimation protocols, provides a substantial reduction in
circuit depth. In addition, we develop a unified theory of quantum Krylov
subspace algorithms and present three new quantum-classical algorithms for the
ground and excited-state energy estimation problems, where each new algorithm
provides various advantages and disadvantages in terms of total number of calls
to the quantum computer, gate depth, classical complexity, and stability of the
generalized eigenvalue problem within the Krylov subspace.
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