Optimizing sparse quantum state preparation with measurement and feedforward

TL;DR

This paper introduces two new algorithms for sparse quantum state preparation that significantly reduce circuit depth by utilizing measurement and feedforward techniques, improving efficiency over previous methods.

Contribution

The paper presents two depth-optimized SQSP algorithms that leverage measurement and feedforward, reducing circuit depth with limited ancilla qubits compared to prior work.

Findings

One algorithm achieves $O(n ext{log}d)$ depth.

Another reduces depth to $O(n)$ using measurement and feedforward.

Both algorithms have size $O(dn)$ and use $O(d)$ ancilla qubits.

Abstract

Quantum state preparation (QSP) is a key component in many quantum algorithms. In particular, the problem of sparse QSP (SQSP) $\unicode{x2013}$ the task of preparing the states with only a small number of non-zero amplitudes $\unicode{x2013}$ has garnered significant attention in recent years. In this work, we focus on reducing the circuit depth of SQSP with limited number of ancilla qubits. We present two SQSP algorithms: one with depth $O(n\log d)$, and another that reduces depth to $O(n)$. The latter leverages mid-circuit measurement and feedforward, where intermediate measurement outcomes are used to control subsequent quantum operations. Both constructions have size $O(dn)$ and use $O(d)$ ancilla qubits. Compared to the state-of-the-art SQSP algorithm in arXiv:2108.06150, which allows an arbitrary number of ancilla qubits $m>0$, both of our algorithms achieve lower circuit depth when $m=d$.