Many-Body Physics in the NISQ Era - Quantum Programming a Discrete Time Crystal
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-09-20 |
| Journal | PRX Quantum |
| Authors | Matteo Ippoliti, Kostyantyn Kechedzhi, Roderich Moessner, S. L. Sondhi, Vedika Khemani |
| Institutions | Max Planck Institute for the Physics of Complex Systems, Princeton University |
| Citations | 92 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis analysis outlines a theoretical proposal for realizing a Many-Body Localized (MBL) Discrete Time Crystal (DTC) using Googleâs Sycamore Noisy Intermediate-Scale Quantum (NISQ) processor.
- Core Value Proposition: The DTC represents a new paradigm of out-of-equilibrium quantum statistical mechanics, exhibiting spontaneous breaking of discrete time translation symmetry. Its realization serves as a critical, physics-forward application for current NISQ devices.
- Platform Suitability: The Sycamore architecture, based on programmable quantum circuits and nearest-neighbor interactions, is naturally suited to implement the required periodically driven (Floquet) Kicked Ising model.
- MBL Stabilization: The DTC phase requires MBL stabilization against heating, which is achieved by deliberately engineering strong, Ising-even disorder into the two-qubit controlled-phase gates (a feature easily implemented on Sycamore).
- Detection Capabilities: Sycamoreâs extensive capabilities for preparing varied initial states and performing site-resolved measurements are essential for unambiguously detecting the defining spatiotemporal order and distinguishing the asymptotic MBL DTC from transient prethermal variants.
- Robustness to Noise: Numerical simulations incorporating conservative depolarizing noise estimates (Pauli error rate p â 10-2) predict that the DTC signal remains observable for hundreds of Floquet cycles (periods).
- Scalability: Crucially, the signal lifetime is limited by external decoherence, not internal thermalization, and is predicted to be independent of system size (L), allowing for future scaling without a corresponding loss of experimental time.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Simulated System Size (L) | 8 to 22 | Qubits | Used for numerical phase diagram mapping and dynamics. |
| Target NISQ Size | 50 to 200 | Qubits | Required for a âtruly many-bodyâ system demonstration. |
| Two-Qubit Pauli Error Rate (p) | 10-2 (1%) | Dimensionless | Conservative estimate for depolarizing noise (p2). |
| Single-Qubit Pauli Error Rate (p1) | 10-3 (0.1%) | Dimensionless | Estimated single-qubit depolarizing noise (p1 = p/10). |
| Observable Lifetime (n*) | ~303 | Floquet Cycles | Predicted maximum observable time based on p=10-2 and Ns=106 samples. |
| Pulse Imperfection (Îľ) | Ď/40 | Radians | Corresponds to the center of the MBL DTC phase (g = 39Ď/80). |
| Average Controlled-Phase Angle (Ď) | Ď | Radians | Sets the average Ising coupling J = Ď/4. |
| Disorder Strength (W) | Ď/2 | Radians | Strength of discrete disorder in controlled-phase angles. |
| Number of Disorder Values (M) | 8 | Dimensionless | Discrete set size used for generating disorder realizations. |
| Gate Calibration Error (Îθ) | Ď/50 (3.6°) | Radians | Standard deviation for residual Z rotations (h angles). |
Key Methodologies
Section titled âKey Methodologiesâ- Platform and Geometry Selection: The experiment is proposed for Googleâs Sycamore processor, utilizing a one-dimensional path (âsnakeâ) of nearest-neighbor couplers mapped onto the 2D chip to ensure the MBL phase is firmly established on theoretical grounds.
- Floquet Unitary Implementation: The time evolution operator (UF) is implemented as a Trotterized quantum circuit, consisting of alternating layers of two-qubit Ising gates and single-qubit X rotations (Rx).
- Gate Construction: The two-qubit Ising interaction (e-iJ ZiZj) is realized using a modified Sycamore G gate, which is based on the native fermionic simulation (fSim) gate.
- Disorder Engineering: MBL stabilization is achieved by introducing Ising-even disorder: the controlled-phase angles (Ďij) are drawn randomly from a discrete set of M=8 values, while small residual single-qubit Z rotations (h angles) are included as random variables (Îh = Ď/50) to break integrability.
- Initial State Preparation: The protocol requires the ability to prepare a wide variety of computational basis states (product states in the Z basis) to test the robustness of the DTC signal, a capability inherent to programmable simulators.
- Detection Protocol: Spatiotemporal order is confirmed by measuring site-resolved temporal autocorrelators (Cii(n)) and spatial correlation functions (e.g., Edwards-Anderson order parameter XSG) across many disorder realizations and initial states.
- Noise Analysis: The effects of experimental imperfections (decoherence, control errors) are modeled using one- and two-qubit depolarizing error channels and simulated via quantum trajectories to determine the signalâs observable lifetime.
Commercial Applications
Section titled âCommercial ApplicationsâThe successful realization and characterization of the MBL DTC on a NISQ device provides foundational insights and protocols relevant to several high-impact areas:
- Quantum Computing Benchmarking: DTCs offer a complex, non-trivial, and classically hard-to-simulate target for benchmarking the performance, coherence, and scalability of next-generation quantum processors (e.g., Sycamore and trapped ion systems).
- Non-Equilibrium Quantum Simulation: Establishes a robust methodology for simulating exotic out-of-equilibrium phases of matter (Floquet phases, MBL phases) that are inaccessible to classical computation, accelerating discovery in quantum statistical mechanics.
- Error Mitigation and Fault Tolerance: The study of how MBL dynamics localize the effects of noise provides crucial data for developing error mitigation strategies in structured quantum circuits, particularly showing that signal decay time is independent of system size (L).
- Quantum Algorithm Validation: Provides a testbed for validating the performance of core quantum algorithms, such as Trotterization, under realistic hardware constraints (noise, finite coherence time, and engineered disorder).
- Fundamental Physics Research: Enables experimental finite-size scaling studies of the MBL-to-thermal phase transition, addressing open theoretical questions regarding the nature of quantum chaos and localization boundaries.
View Original Abstract
Recent progress in the realm of noisy, intermediate scale quantum (NISQ)\ndevices represents an exciting opportunity for many-body physics, by\nintroducing new laboratory platforms with unprecedented control and measurement\ncapabilities. We explore the implications of NISQ platforms for many-body\nphysics in a practical sense: we ask which {\it physical phenomena}, in the\ndomain of quantum statistical mechanics, they may realize more readily than\ntraditional experimental platforms. As a particularly well-suited target, we\nidentify discrete time crystals (DTCs), novel non-equilibrium states of matter\nthat break time translation symmetry. These can only be realized in the\nintrinsically out-of-equilibrium setting of periodically driven quantum systems\nstabilized by disorder induced many-body localization. While precursors of the\nDTC have been observed across a variety of experimental platforms - ranging\nfrom trapped ions to nitrogen vacancy centers to NMR crystals - none have\n\emph{all} the necessary ingredients for realizing a fully-fledged incarnation\nof this phase, and for detecting its signature long-range \emph{spatiotemporal\norder}. We show that a new generation of quantum simulators can be programmed\nto realize the DTC phase and to experimentally detect its dynamical properties,\na task requiring extensive capabilities for programmability, initialization and\nread-out. Specifically, the architecture of Googleâs Sycamore processor is a\nremarkably close match for the task at hand. We also discuss the effects of\nenvironmental decoherence, and how they can be distinguished from `internalâ\ndecoherence coming from closed-system thermalization dynamics. Already with\nexisting technology and noise levels, we find that DTC spatiotemporal order\nwould be observable over hundreds of periods, with parametric improvements to\ncome as the hardware advances.\n