Efficient circuits for leaf-separable state preparation

TL;DR

This paper introduces a recursive, efficient quantum circuit algorithm for preparing leaf-separable states, significantly reducing circuit depth and gate count compared to traditional methods, enabling scalable quantum state preparation.

Contribution

The paper presents a novel recursive algorithm combining binary partition trees and gWDBs for efficient leaf-separable state preparation in quantum computing.

Findings

Achieves circuit depth of O(k log(n/k) + 2^k)

Uses O(n(k+2^k)) two-qubit gates

Provides analysis of trade-offs with and without ancilla qubits

Abstract

Efficient state preparation is a challenging and important problem in quantum computing. In this work, we present a recursive state preparation algorithm that combines logarithmic-depth Dicke state circuits with Hamming weight encoders for efficiently preparing ``leaf-separable" quantum states. The algorithm is built on binary partition trees, generalized weight distribution blocks (gWDBs), and leaf-level encoders. We evaluate the performance of the algorithm by numerically simulating it on randomly generated target states with between 4 and 15 qubits. Compared to general state preparation approaches which require $O(2^n)$ CX gates, our algorithm achieves a circuit depth of $O(k\log\frac{n}{k} + 2^k)$ and uses $O(n(k+2^k))$ two-qubit gates, where $k < n$ denotes the subtree size. We also compare implementations of the algorithm with and without the use of ancilla qubits, providing a detailed analysis of the trade-offs in circuit depth and two-qubit gate counts. These results contribute to scalable state preparation for quantum algorithms that require structured inputs such as Dicke or near-Dicke states.