Deterministic Bethe state preparation

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 $\left(\genfrac{}{}{0ex}{}{L}{M}\right)-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.

14 pages + supplementary material (qiskit code); v2: minor improvements; v3: improvements in the presentation and code, version accepted by Quantum

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• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• Quantum states supported by matroids
• Preparation of the single-spinon wave function on a quantum computer
• Spin-$s$ $U(1)$-eigenstate preparation
• Effective Bethe Ansatz for Spin-1 Non-integrable Models