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 | Stanford University, Max Planck Institute for the Physics of Complex Systems |
| Citations | 92 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Quantum Programming a Discrete Time Crystal
Section titled âTechnical Documentation & Analysis: Quantum Programming a Discrete Time CrystalâExecutive Summary
Section titled âExecutive SummaryâThis documentation analyzes the feasibility and requirements for realizing a genuine Many-Body Localized Discrete Time Crystal (MBL DTC) phase, focusing on the capabilities of Next Generation (NextGen) quantum simulators, specifically Googleâs Sycamore processor.
- Core Achievement: The research validates a Floquet DTC circuit design suitable for implementation on the Sycamore superconducting platform, confirming the realization of a robust, non-equilibrium many-body phase of matter.
- MBL Stabilization: The study confirms that MBL stabilization requires short-range, dominantly Ising interactions with Ising-even disorder, a key engineering challenge that Sycamoreâs circuit structure naturally addresses.
- Coherence & Noise Robustness: Numerical simulations, incorporating conservative depolarizing noise estimates ($p \approx 10^{-2}$), predict the DTC signal is observable for up to $n^* = 303$ Floquet cycles, demonstrating high robustness.
- Detection Requirements: Unambiguous detection of the asymptotic DTC phase necessitates extensive capabilities: truly many-body systems (> 50 qubits), long coherence times, widely tunable initial states, and crucial site-resolved measurements.
- Solid-State Platform Limitations: The paper highlights that âFirst Generationâ solid-state platforms, such as Nitrogen Vacancy (NV) centers in 3D diamond, failed to stabilize MBL DTC due to long-range dipolar interactions and insufficient site-resolved readout, emphasizing the need for advanced material engineering.
- 6CCVD Value Proposition: 6CCVD specializes in high-purity Single Crystal Diamond (SCD) and custom metalization, providing the foundational materials necessary to overcome the limitations of FirstGen NV platforms and enable future, scalable solid-state quantum simulators.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points are extracted from the analysis of the DTC simulation requirements and the performance metrics of the Sycamore processor.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Target System Size (Sycamore) | ~50 | Qubits | Required for âtruly many-bodyâ description |
| FirstGen System Size (NV/NMR) | > 106 | Constituents | Operating in the thermodynamic regime |
| Predicted DTC Signal Lifetime ($n^*$) | 303 | Floquet Cycles | Sycamore, based on $p = 10^{-2}$ and $N_s = 10^6$ samples |
| Conservative Pauli Error Rate ($p$) | 10-2 | Dimensionless | Depolarizing noise model for two-qubit gates |
| Single-Qubit Error Rate ($p_1$) | 10-3 | Dimensionless | Current Sycamore technology estimate |
| Two-Qubit Error Rate ($p_2$) | 10-2 | Dimensionless | Current Sycamore technology estimate |
| Measurement Error Rate ($p_m$) | 2.5 | % | Sycamore readout fidelity |
| Disorder Values ($M$) | 8 | Discrete Values | Used for Ising-even disorder stabilization |
| Average Controlled-Phase Angle ($\bar{\phi}$) | $\pi$ | Radians | Corresponds to Ising coupling $J = \pi/4$ |
| Disorder Strength ($W$) | $\pi/2$ | Radians | Used to ensure $\phi$ angles are far from 0 |
Key Methodologies
Section titled âKey MethodologiesâThe realization of the Floquet DTC on the Sycamore processor relies on precise quantum circuit implementation and specific disorder engineering parameters to ensure MBL stabilization.
- System Geometry: The simulation is confined to a 1D path (a âsnakeâ) on the 2D Sycamore chip to align with theoretical requirements for MBL stability in 1D systems.
- Floquet Unitary Decomposition: The canonical DTC Hamiltonian evolution is approximated by a Trotterized quantum circuit sequence, $U_F$, consisting of alternating layers of two-qubit gates and single-qubit X rotations.
- Gate Implementation: The circuit utilizes Sycamoreâs native high-fidelity gates, including single-qubit $R_X$ rotations and modified two-qubit gates ($\tilde{G}_{i,j}$) derived from the fermionic simulation gate ($fSim$).
- Disorder Protocol: Ising-even disorder is introduced by randomly sampling the controlled-phase angles ($\phi_{i,j}$) of the two-qubit gates from a discrete set of $M=8$ values, centered around $\bar{\phi} = \pi$.
- MBL Stabilization: The disorder is applied to the Ising couplings ($J_{i,j} Z_i Z_j$) rather than the Ising-odd longitudinal fields ($h_i Z_i$), as the latter are shown to be âechoed outâ over two cycles, failing to stabilize the MBL DTC phase.
- Phase Diagnostics: The MBL DTC phase is identified using three key diagnostics:
- Level Repulsion: Measured via the level-spacing ratio ($r$), which approaches the Poisson value ($r \approx 0.39$) in the MBL phase.
- Real-Time Oscillations: Persistent period-doubled oscillations in the temporal autocorrelator $C(n) \propto (-1)^n$.
- Spatiotemporal Order: Detection of long-range spatial correlations using the Edwards-Anderson spin glass order parameter ($X^{SG}$).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâAs an expert material scientist and technical sales engineer, 6CCVD recognizes that while this research focuses on superconducting qubits, the fundamental challenges identified regarding MBL stabilization and coherence time in solid-state systems (specifically NV centers in diamond) are directly addressable by our advanced MPCVD diamond products.
The paper notes that FirstGen NV center experiments failed to realize asymptotic MBL DTC due to long-range interactions and insufficient site-resolved measurement capabilities. 6CCVD provides the engineered diamond substrates necessary for NextGen solid-state quantum simulators to overcome these limitations.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate or extend this research onto a robust solid-state platform (e.g., improved NV center arrays or other defect-based quantum systems), the following 6CCVD materials are required:
- Optical Grade Single Crystal Diamond (SCD): Essential for maximizing the $T_2$ coherence time of NV centers. Our ultra-high purity SCD wafers feature nitrogen concentrations significantly below 1 part per billion (ppb), minimizing decoherence caused by paramagnetic impurities, thereby extending the observable DTC signal lifetime far beyond the 100 cycles achieved in FirstGen experiments.
- Boron-Doped Diamond (BDD) Films: Highly conductive BDD layers can be integrated as transparent electrodes for localized electric field control or high-speed readout, enabling the site-resolved measurements ($<Z_i Z_j>$) critical for distinguishing genuine MBL DTC from prethermal variants.
Customization Potential
Section titled âCustomization Potentialâ6CCVDâs in-house capabilities directly support the complex engineering requirements of quantum simulation hardware:
| Research Requirement | 6CCVD Custom Capability | Technical Advantage |
|---|---|---|
| Large-Scale Arrays (Many-Body) | Custom Dimensions: Plates/wafers up to 125mm (PCD) and large SCD wafers. | Supports scaling up solid-state simulators to the required > 50 qubit regime without compromising material quality. |
| Integrated Quantum Circuits | Custom Metalization: Internal capability for depositing Au, Pt, Pd, Ti, W, and Cu films. | Allows for the integration of high-fidelity control lines and readout circuitry directly onto the diamond surface for precise qubit manipulation. |
| Interaction Engineering | Precision Polishing: SCD surfaces polished to Ra &lt; 1nm. | Enables fabrication of high-quality micro-structures (e.g., photonic crystal cavities or waveguides) necessary to control and shorten the range of dipolar interactions, a critical step for MBL stabilization. |
| Novel Device Geometries | Custom Substrates and Thicknesses: SCD (0.1”m - 500”m) and Substrates (up to 10mm). | Provides flexibility for engineers designing novel 3D architectures or thin-film devices required for advanced Floquet protocols. |
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team offers specialized consultation to assist researchers in selecting and optimizing diamond materials for complex quantum projects. We provide expertise in material selection, defect engineering, and surface preparation to ensure optimal performance for Discrete Time Crystal (DTC) and Many-Body Localization (MBL) simulation projects.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
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