Quantum Algorithm for Spectral Measurement with Lower Gate Count

TL;DR

This paper introduces two novel quantum techniques that significantly reduce gate counts for spectral measurements, improving ground state preparation efficiency in quantum simulations by avoiding certain approximations and optimizing single-qubit rotation usage.

Contribution

The paper presents a new unitary operator for energy measurement and a lattice-specific method to minimize costly single-qubit rotations, advancing quantum spectral measurement methods.

Findings

Exact implementation of a unitary operator avoids Taylor/Trotter errors.

Reduction in generic single-qubit rotations scales with Hamiltonian parameters.

Method improves efficiency for lattice model simulations.

Abstract

We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.