Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward

TL;DR

This paper introduces measurement and feedforward techniques to significantly reduce circuit depth in quantum state preparation for quantum simulation, balancing depth and width for more efficient quantum algorithms.

Contribution

It proposes new parallelization strategies using measurements and feedforward to lower circuit depth while maintaining manageable circuit width in quantum state preparation.

Findings

Unary encoding reduces depth for state preparation.

Probabilistic preparation of Bethe wave function in constant depth.

Techniques improve initial state preparation for quantum simulation.

Abstract

Reducing circuit depth and identifying an optimal trade-off between circuit depth and width is crucial for successful quantum computation. In this context, midcircuit measurement and feedforward have been shown to significantly reduce the depth of quantum circuits, particularly in implementing logical gates. By leveraging these techniques, we propose several parallelization strategies that reduce quantum circuit depth at the expense of increasing width in preparing various quantum states relevant to quantum simulation. With measurements and feedforward, we demonstrate that utilizing unary encoding as a bridge between two quantum states substantially reduces the circuit depth required for preparing quantum states, such as sparse quantum states and sums of Slater determinants within the first quantization framework, while maintaining an efficient circuit width. Additionally, we show that a Bethe wave function, characterized by its high degree of freedom in its phase, can be probabilistically prepared in a constant-depth quantum circuit using measurements and feedforward. We anticipate that our study will contribute to the reduction of circuit depth in initial state preparation, particularly for quantum simulation, which is a critical step toward achieving quantum advantage.