Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians

TL;DR

This paper introduces a variational classical optimization method to construct efficient PREPARE circuits for quantum phase estimation in quantum chemistry, reducing T-gate counts without using ancillary qubits, suitable for early fault-tolerant quantum computers.

Contribution

It presents a novel classical variational approach to generate PREPARE circuits that are resource-efficient and do not require ancillary qubits, improving quantum phase estimation implementations.

Findings

Achieves a constant-factor reduction in T-gate count compared to previous methods.

Demonstrates effectiveness on various molecular Hamiltonians.

Suitable for early-stage fault-tolerant quantum computing with limited qubits.

Abstract

We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The $\texttt{PREPARE}$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a crucial role in the state-of-the-art efficient implementations of quantum phase estimation. We employ the automatic quantum circuit encoding algorithm [Shirakawa $\textit{et al.}$, arXiv:2112.14524] to construct $\texttt{PREPARE}$ circuits, which requires classical simulations of quantum circuits of $O(\log N)$ qubits with $N$ being the number of qubits of the Hamiltonian. The generated $\texttt{PREPARE}$ circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of $T$-gates of the obtained $\texttt{PREPARE}$ circuits for quantum chemistry Hamiltonians of various molecules, which shows a constant-factor reduction compared to previous approaches that do not use ancillary qubits. Since the number of available logical qubits and $T$ gates will be limited at the early stage of the fault-tolerant quantum computing, the proposed method is particularly of use for performing the quantum phase estimation with such limited capability.