Preparing exact eigenstates of the open XXZ chain on a quantum computer

Abstract

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of $L$ spins with $M$ down spins, which contains a total of $\left(\genfrac{}{}{0ex}{}{L}{M}\right)2^{M}M!$ terms, the algorithm requires $L+M^2+2M$ qubits.

18 pages, 3 figures; v2: references added and further minor improvements - to appear in J. Phys. A

References in corpus (6)

• Simulating Hamiltonian dynamics with a truncated Taylor series
• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• On Actual Preparation of Dicke State on a Quantum Computer

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• The Bethe Ansatz as a Quantum Circuit
• Deterministic Bethe state preparation
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• State preparation of AGP on a quantum computer without number projection
• Spin-s Dicke states and their preparation
• Symmetric quantum states: a review of recent progress
• Estimating Bethe roots with VQE
• All product eigenstates in Heisenberg models from a graphical construction
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• 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
• Spin-$s$ $U(1)$-eigenstate preparation
• Effective Bethe Ansatz for Spin-1 Non-integrable Models