Deterministic Bethe state preparation

TL;DR

This paper introduces a deterministic quantum circuit for preparing specific eigenstates of the $U(1)$ symmetry in quantum systems, notably including the XXZ spin chain, without ancillary qubits or QR decompositions.

Contribution

It provides a novel, explicit quantum circuit that efficiently prepares eigenstates of the XXZ model, advancing state preparation methods in quantum computing.

Findings

Circuit prepares arbitrary $U(1)$-eigenstates with exactness.

No ancillary qubits or QR decompositions needed.

Efficient implementation with specific gate counts.

Abstract

We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-1/2 XXZ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.