Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains

Abstract

Information scrambling, which is the spread of local information through a system's many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle-hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.

19 pages, 7 figures + References + Appendix; Added Figures 7, A2, D1-D4

References in corpus (17)

• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Entanglement hamiltonians in two-dimensional conformal field theory
• Quantum Computing with NMR
• Measurement of many-body chaos using a quantum clock
• Jarzynski-like equality for the out-of-time-ordered correlator
• Probing quantum information propagation with out-of-time-ordered correlators
• How to Build the Thermofield Double State
• Minimal Model for Fast Scrambling
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Quantum Variational Learning of the Entanglement Hamiltonian
• Interferometric Approach to Probing Fast Scrambling
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Detecting scrambling via statistical correlations between randomized measurements on an NMR quantum simulator
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Verifying quantum information scrambling dynamics in a fully controllable superconducting quantum simulator
• Proposal to measure out-of-time-ordered correlations using Bell states

Cited by in corpus (11)

• Quasiprobabilities in quantum thermodynamics and many-body systems
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Volume-entangled exact scar states in the PXP and related models in any dimension
• Information scrambling -- a quantum thermodynamic perspective
• Information propagation in one-dimensional XY-$\Gamma$ chains
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Quantifying operator spreading and chaos in Krylov subspaces with quantum state reconstruction
• Robust Estimation of Nonlinear Properties of Quantum Processes
• Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos