Bethe states on a quantum computer: success probability and correlation functions

Abstract

A probabilistic algorithm for preparing Bethe eigenstates of the spin-1/2 Heisenberg spin chain on a quantum computer has recently been found. We derive an exact formula for the success probability of this algorithm in terms of the Gaudin determinant, and we study its large-length limit. We demonstrate the feasibility of computing antiferromagnetic ground-state spin-spin correlation functions for short chains. However, the success probability decreases exponentially with the chain length, which precludes the computation of these correlation functions for chains of moderate length. Some conjectures for estimates of the Gaudin determinant are noted in an appendix.

arXiv comment15 pages; v2: result for XXZ added; v3: references added, to appear in J. Phys. A

References in corpus (16)

• Quantum Amplitude Amplification and Estimation
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Simulating Physical Phenomena by Quantum Networks
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Solving strongly correlated electron models on a quantum computer
• Computation of dynamical correlation functions of Heisenberg chains in a field
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain
• Correlation functions of integrable models: a description of the ABACUS algorithm
• Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain
• Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
• First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators
• Preparing exact eigenstates of the open XXZ chain on a quantum computer

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• Spin-s Dicke states and their preparation
• Symmetric quantum states: a review of recent progress
• Estimating Bethe roots with VQE
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• Effective Bethe Ansatz for Spin-1 Non-integrable Models
• Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
• Spin-$s$ $U(1)$-eigenstate preparation