Logical Resource Estimation for Quantum State Preparation with Compilation

TL;DR

This paper compares rotation-based and sampling-based quantum state preparation methods, analyzing their resource costs and compilation overhead, and introduces a software tool for circuit compilation.

Contribution

It provides a practical comparison of state preparation methods considering total gate count and compilation overhead, and offers a new compilation software package.

Findings

Sampling-based methods have lower asymptotic T-count.

Sampling methods maintain overall advantage after overhead.

Numerical experiments support the resource analysis.

Abstract

Quantum state preparation is a fundamental primitive in quantum algorithms for encoding classical data into quantum amplitudes. We compare the cost of preparing general $n$-qubit states with real amplitudes using two common paradigms: rotation-based methods, based on controlled rotations, and sampling-based methods, based on a structured representation of the target state. Although these approaches are often theoretically compared using CNOT count and $T$-count, their relative performance in total gate count remains less well understood practically. We compare representative rotation-based and sampling-based methods using $T$-count and total gate count, and analyze how compilation overhead affects their relative performance. We also develop a software package for compiling state preparation circuits, designed as a practical subroutine for more general quantum computations. Numerical experiments on resource states and quantum states related to quantum chemistry, condensed matter physics, and simulation via Magnus expansion over a range of target accuracies $\epsilon$ support the analysis. Our results show that sampling-based methods achieve asymptotically lower $T$-count and retain an overall advantage after accounting for total gate count and compilation overhead.