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arXiv:2112.11046 · New Journal of Physics

A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator

Simone Notarnicola, Andreas Elben, Thierry Lahaye, Antoine Browaeys, Simone Montangero, Benoît Vermersch

Published Sep 25, 2023• 27 citations
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Abstract

Abstract We present a toolbox to probe quantum many-body states implemented on Rydberg-atoms quantum hardware via randomized measurements. We illustrate the efficacy of this measurement toolbox in the context of probing entanglement, via the estimation of the purity, and of verifying a ground-state preparation using measurements of the Hamiltonian variance. To achieve this goal, we develop and discuss in detail a protocol to realize independent, local unitary rotations. We benchmark the protocol by investigating the ground state of the one-dimensional Su–Schrieffer–Heeger model, recently realized on a chain of Rydberg atom, and the state resulting after a sudden quench in a staggeredXYchain. We probe the robustness of our toolbox by taking into account experimental imperfections, such as pulse fluctuations and measurement errors.

DOI
10.1088/1367-2630/acfcd3

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Abstract We present a toolbox to probe quantum many-body states implemented on Rydberg-atoms quantum hardware via randomized measurements. We illustrate the efficacy of this measurement toolbox in the context of probing entanglement, via the estimation of the purity, and of verifying a ground-state preparation using measurements of the Hamiltonian variance. To achieve this goal, we develop and discuss in detail a protocol to realize independent, local unitary rotations. We benchmark the protocol by investigating the ground state of the one-dimensional Su–Schrieffer–Heeger model, recently realized on a chain of Rydberg atom, and the state resulting after a sudden quench in a staggeredXYchain. We probe the robustness of our toolbox by taking into account experimental imperfections, such as pulse fluctuations and measurement errors.
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second R\'enyi entropy of highly mixed quantum states consisting of up to ten qubits in a trapped-ion quantum simulator [Brydges et al., Science 364, 260 (2019)]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in one experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.
A major application of analog quantum hardware is quantum simulation, where a system evolves over time according to a given Hamiltonian. One challenge when implementing the Hamiltonian on a programmable quantum simulator is the availability of distinct coupling types, many of which go beyond the conventional ZZ-couplings found in Ising Hamiltonians that are naturally implemented by various platforms. In prior work, we have developed a method based on domain wall encoding to simulate one-dimensional spin chains using only Ising Hamiltonians, which would otherwise require XX+YY-couplings as well. Here, we implement the method on a commercially accessible Rydberg atom quantum device, and simulate the time evolution of the Heisenberg XXZ model with various anisotropies. We successfully probe the XY and Ising phases of the model and reproduce the qualitative behavior of several one- and two-body observables in both phases, as well as at the critical point. Our work augments the toolbox to simulate canonical quantum many-body systems on analog quantum simulators.
The development and spread of entanglement in complex quantum systems is central to exploring many-body phenomena out of equilibrium. Measuring entanglement dynamics can shed light on information scrambling and thermalisation, namely on transitions from many-body quantum chaos to localisation in disordered, interacting systems. In quantum computing systems, entanglement entropy and other nonlinear functions of the density matrix have been recently measured, in particular by using the randomised measurement toolbox. However, it is difficult to implement the required arbitrary unitary rotations on specific subsystems without universal local control. Here we devise and demonstrate the measurement of entanglement entropy in a programmable analogue quantum simulator using a randomised measurement protocol that leverages local energy tuning together with a global field to bypass the need for local gate control. We implement this on a commercially available neutral-atom quantum simulator, QuEra's Aquila, and use it to show how programmable disorder in the local Hamiltonian parameters leads to a transition from chaotic to localised entanglement dynamics. Given current decoherence times, we clearly resolve disorder-specific, time-dependent entanglement spreading in small systems. Our work extends the utility of programmable analogue quantum simulators, and opens further opportunities for wider randomised measurement toolboxes in a range of other analogue systems.
There have been recently significant progress in quantum technologies to realize physically diverse quantum computation and simulation platforms.The aim of this thesis is to develop theoretical approaches based on measurement protocols to experimentally characterize entanglement generated in these state-of-art quantum technological platforms. In the past few years, protocols belonging to the "randomized measurements toolbox" (RM toolbox) have shown to have the ability to measure bipartite entanglement (entanglement between two parts of a quantum system). These protocols have been implemented in several experimental platforms consisting of quantum simulators and quantum computers beyond the regime of full state tomography.The aim of this manuscript is principally dedicated to the development of new approaches based on the RM toolbox to provide experimental groups with advanced tools and methods to probe new fundamental quantities of interest related to entanglement prepared in large quantum platforms.The first objective of this thesis is to provide a new protocol to optimize the existing RM protocol by reducing the statistical errors in the estimation of the quantities. This is done with two approaches: (i) via importance sampling of local random unitaries and (ii) by implementing common randomized measurements. These techniques automatically enable us to implement the RM toolbox to estimate properties associated to entanglement on larger experimental platforms. Then, a central part of this work proposes an alternate effective protocol to measure a fundamental quantity in quantum metrology known as the "quantum Fisher information" that enables us to characterize the multipartite entanglement content of the underlying quantum state. This novel protocol is based on estimating the QFI via the RM toolbox, as a converging series of lower bound polynomials of the density matrix.Additionally, the manuscript also focuses on solving a practical bottleneck of the current RM toolbox caused by the over-burdening classical cost to post-process experimental RM data to evaluate unbiased estimations of relevant quantities.This motivates the introduction of the "batch shadow formalism" that circumvents this problem and provides an efficient data treatment technique with rigorous performance guarantees to get estimates of quantities accessible from the experimental RM data. Lastly, owing to these developments of the RM toolbox, the manuscript reports estimation of some quantities that were accessed for the first time by experimental implementation of this toolbox on two different architectures of quantum platform consisting of superconducting qubits and trapped ions.
We introduce a protocol that gives access to out-of-time-ordered correlation functions in many-body quantum systems. Unlike other such protocols, our proposal, which can be applied to arbitrary initial states, neither requires ancilla degrees of freedom to the quantum system of interest, nor has the need for randomized measurements. Nontrivial experimental capabilities required to implement the protocol are single-site measurements, single-site rotations, and backwards time evolution. To exemplify the implementation of the protocol, we put forward a strategy for Hamiltonian sign inversion $H\ensuremath{\rightarrow}\ensuremath{-}H$ in arrays of Rydberg-dressed atoms. In this way, a complete and practical toolbox is obtained for the measurement of out-of-time-ordered correlations in equilibrium and nonequilibrium situations.