Conserved charges in the quantum simulation of integrable spin chains

Abstract

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. The Trotter error in integrable spin chains can be under control if the discrete time evolution preserves integrability. In this work we implement, on a real quantum computer and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of the time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

26 pages, data and codes available at https://github.com/takuoku/integrable-trotterization

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• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
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• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Generalized hydrodynamics of integrable quantum circuits
• Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Geometric representations of braid and Yang-Baxter gates
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
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• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
• Absence of local conserved charges of the Fredkin spin chain and its truncated versions