Bowtie VarQTE: A Resource-Efficient Quantum State Preparation Primitive

TL;DR

Bowtie VarQTE offers a resource-efficient method for quantum state preparation by combining classical and quantum simulations, reducing quantum resource needs while maintaining high fidelity.

Contribution

It introduces a novel framework that leverages causal light-cones and classical simulation to optimize quantum state preparation, improving stability and resource efficiency.

Findings

Achieves comparable fidelities to tensor-network methods without classical state representation.

Reduces quantum requirements in 2D systems compared to Krylov diagonalization.

Enables a hybrid simulation pipeline for imaginary and real time evolution.

Abstract

The preparation of quantum states is a fundamental requirement for many quantum algorithms. A native route to preparing physically structured states is based on short-time simulation of dynamical processes, such as real or imaginary time evolution. This work presents a resource-efficient framework for the approximation thereof with \textit{bowtie \ac{VarQTE}} which uses classical simulation where possible and quantum resources where necessary. We introduce a framework that leverages existing causal light-cones to minimize quantum resource requirements in the evaluation of gradient and quantum geometric tensor terms by utilizing classical simulation methods for causally relevant subcircuits. This in turn enables exact parameter updates according to McLachlan's variational principle and, thereby, improves numerical stability. We conduct a comparison with a state preparation method that is based on a tensor-network compiled Trotter algorithm: approximate quantum compilation (AQC). In recent work, this approach has shown impressive performance. However, its key-bottleneck is the necessity to have a classical (approximate) representation of the target state. Our numerical experiments indicate that bowtie VarQTE can achieve comparable fidelities without this requirement. We further illustrate how bowtie VarQTE can facilitate a state-preparation pipeline that combines the simulation of imaginary and real time evolution for a sample-based quantum algorithm. In fact, results on 2D systems show how bowtie VarQTE can reduce the quantum requirements compared to standard, sample-based Krylov diagonalization calculations. Our results indicate that VarQTE is a promising primitive for the preparation of physically structured quantum states that reduces requirements on quantum resources by leveraging existing structures and the associated possibility of enabling classical simulations.