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arXiv:2006.15093

Proposal to measure out-of-time-ordered correlations using Bell states

Bhuvanesh Sundar

Published Jun 26, 2020• 1 citation
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Abstract

We present a protocol to experimentally measure the infinite-temperature out-of-time-ordered correlation (OTOC) -- which is a probe of quantum information scrambling in a system -- for systems with a Hamiltonian which has either a chiral symmetry or a particle-hole symmetry. We show that the OTOC can be obtained by preparing two entangled systems, evolving them with the Hamiltonian, and measuring appropriate local observables. At the cost of requiring two copies of the system and putting restrictions on the Hamiltonian's symmetries, we show that our method provides some advantages over existing methods -- it can be implemented without reversing the sign of the Hamiltonian, it requires fewer measurements than schemes based on implementing the SWAP operator, and it is robust to imperfections like some earlier methods. Our ideas can be implemented in currently available quantum platforms.

DOI
10.48550/arxiv.2006.15093

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We present a protocol to experimentally measure the infinite-temperature out-of-time-ordered correlation (OTOC) -- which is a probe of quantum information scrambling in a system -- for systems with a Hamiltonian which has either a chiral symmetry or a particle-hole symmetry. We show that the OTOC can be obtained by preparing two entangled systems, evolving them with the Hamiltonian, and measuring appropriate local observables. At the cost of requiring two copies of the system and putting restrictions on the Hamiltonian's symmetries, we show that our method provides some advantages over existing methods -- it can be implemented without reversing the sign of the Hamiltonian, it requires fewer measurements than schemes based on implementing the SWAP operator, and it is robust to imperfections like some earlier methods. Our ideas can be implemented in currently available quantum platforms.
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.
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. Here we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. The protocol accounts for both pure and mixed initial states, and is applicable to systems that interact with environmental degrees of freedom. We demonstrate the application of our protocol by the characterization of scrambling in a periodically driven spin that exhibits quantum chaos.
The out-of-time-ordered correlator (OTOC) is a powerful tool for probing quantum information scrambling, a fundamental process by which local information spreads irreversibly throughout a quantum many-body system. Experimentally measuring the OTOC, however, is notoriously challenging due to the need for time-reversed evolution. Here, we present an experimental evaluation of the OTOC on a quantum computer, using three distinct protocols to address this challenge: the rewinding time method (RTM), the weak-measurement method (WMM), and the irreversibility-susceptibility method (ISM). Our experiments investigate the quantum dynamics of an XXZ spin-1/2 chain prepared in a thermal Gibbs state. As a key contribution, we provide the first experimental demonstration of the ISM, using the trapped-ion quantum computer, reimei. We also conduct a detailed comparative analysis of all three methods, revealing method-dependent behaviors in the measured OTOC. This work not only validates these protocols as practical tools for exploring quantum chaos on near-term hardware but also offers crucial insights into their respective advantages and limitations, providing a practical framework for future experimental investigations.
Out-of-time-order correlators (OTOCs) are the main tool for probing quantum chaos and scrambling, and have become crucial probes in many areas of quantum computing. However, the measurement of OTOCs is difficult to implement on analog quantum computers due to the requirement of backward time evolution. In this paper, we develop and implement a randomized measurement protocol to compute OTOCs on Aquila by QuEra Computing. Unlike traditional methods that require backward time evolution, our approach utilizes a sequence of global randomized quenches that approximates the unitary 2-design properties necessary for extracting infinite-temperature OTOCs from statistical correlations. We demonstrate the protocol's success by explicitly observing the lightcone of information propagation in 1D Rydberg chains, and compare hardware results to both state-vector simulations and matrix product state (MPS) tensor network calculations. This work establishes the first demonstration of fully analog randomized OTOC measurements in neutral-atom simulators, providing a scalable pathway to probe quantum chaos in complex many-body systems.
We provide a general protocol to measure out-of-time-order correlation functions. These correlation functions are of broad theoretical interest for diagnosing the scrambling of quantum information in interacting quantum systems and have recently received particular attention in the study of chaos and black holes within holographic duality. Measuring them requires an echo-type sequence in which the sign of a many-body Hamiltonian is reversed. We illustrate our protocol by detailing an implementation employing cold atoms and cavity quantum electrodynamics to probe spin models with nonlocal interactions. To verify the feasibility of the scheme with current technology, we analyze the effects of dissipation in a chaotic kicked-top model. Finally, we propose a number of other experimental platforms where similar out-of-time-order correlation functions can be measured.
Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new measurement method on a 4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use random Hamiltonian evolutions to generate the random operations that are required by the randomized OTOC detection protocol. Our experimental results are in good agreement with the theoretical predictions, thus confirming the feasibility of the protocols. Therefore, our work represents a step in exploring realistic quantum chaotic dynamics in complicated quantum systems.