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Kuantum bilgisayarlarda gerçekleştirilen ayrık zaman kristallerinin gürültü direnci

Aytemiz, Muhammet Enes Kubilay

Published Aug 27, 2025• 0 citations
OpenAlex

Abstract

Discrete Time Crystals (DTCs) are a non-equilibrium phase of matter that breaks the time-translation symmetry. This manifests as robust oscillations observed in driven Hamiltonians. Realizing DTCs on current Noisy Intermediate-Scale Quantum (NISQ) computers can be challenging due to the environmental noise, decoherence of qubits and computational errors. This thesis investigates the resilience and robustness of DTC and examines recent developments, and possible improvements of DTC stabilization using current quantum processors. Generally, an externally driven many-body system is expected to heat up to an infinite temperature state. This process, which is called thermalization, prevents the time-crystalline order. The two primary mechanisms that protect time-crystalline order are many-body localization (MBL) which has a strong disorder that prevents the thermalization, and Floquet prethermalization where its high frequency driving prevents the thermalization. These two processes allow us to realize and investigate the time crystals before a quantum system thermalizes.

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Discrete Time Crystals (DTCs) are a non-equilibrium phase of matter that breaks the time-translation symmetry. This manifests as robust oscillations observed in driven Hamiltonians. Realizing DTCs on current Noisy Intermediate-Scale Quantum (NISQ) computers can be challenging due to the environmental noise, decoherence of qubits and computational errors. This thesis investigates the resilience and robustness of DTC and examines recent developments, and possible improvements of DTC stabilization using current quantum processors. Generally, an externally driven many-body system is expected to heat up to an infinite temperature state. This process, which is called thermalization, prevents the time-crystalline order. The two primary mechanisms that protect time-crystalline order are many-body localization (MBL) which has a strong disorder that prevents the thermalization, and Floquet prethermalization where its high frequency driving prevents the thermalization. These two processes allow us to realize and investigate the time crystals before a quantum system thermalizes.
The simulation of non-equilibrium quantum many-body systems on noisy intermediate-scale quantum (NISQ) processors represents a central challenge and opportunity in modern condensed matter physics. Periodically driven (Floquet) systems can host exotic phases of matter with no equilibrium counterpart, most notably discrete time crystals (DTCs) characterized by spontaneous breaking of discrete time-translation symmetry and robust subharmonic responses. However, the realization of DTCs faces fundamental obstacles: driven many-body systems generically absorb energy and thermalize to an infinite-temperature state, destroying time-crystalline order. Two primary mechanisms have been identified to stabilize DTCs—many-body localization (MBL) through strong disorder, and Floquet prethermalization wherein high-frequency driving suppresses heating over exponentially long timescales. This work investigates the digital quantum simulation of prethermal DTCs on current superconducting quantum processors, with a focus on understanding and mitigating the impact of hardware noise. Recent experiments on 133-qubit heavy-hexagonal devices have demonstrated the realization of clean two-dimensional DTCs and incommensurately modulated DTCs (IM-DTCs) using kicked Ising models, observing period-doubling oscillations persisting for up to 100 Floquet cycles . Crucially, these simulations reveal that quantum noise, often perceived as detrimental, can in certain regimes stabilize novel prethermal DTC phases—a phenomenon identified as noise-induced DTCs supported by symmetry charge pumping or random gate fluctuations . The heavy-hexagonal lattice geometry, compared to square lattices, exhibits significantly slower quantum scrambling, thereby extending the prethermal plateau and enhancing DTC stability. We address two key challenges limiting the scalability of DTC simulations: limited qubit connectivity and environmental noise. By leveraging the universality of native gate sets, we demonstrate how to implement effective couplings among physically disconnected qubits at the cost of increased circuit depth, enabling the study of interaction-range effects on DTC stabilization—a phenomenon previously unobserved experimentally . Furthermore, we benchmark the performance of error mitigation protocols based on depolarising noise models, achieving excellent agreement between error-mitigated hardware data and tensor-network simulations in regimes where classical computations remain tractable . Our results highlight the complementary roles of quantum hardware and classical simulation: quantum processors provide access to regimes where entanglement growth outpaces tensor-network methods, while careful validation against classical benchmarks ensures the reliability of quantum outcomes. This study establishes a concrete pathway for using NISQ devices as experimental platforms for synthesizing and probing novel non-equilibrium quantum phases, advancing both our fundamental understanding of Floquet many-body dynamics and the practical capabilities of quantum simulation. The identification of noise as an active ingredient in phase stabilization suggests new directions for quantum engineering of spatiotemporal orders on near-term hardware.
We report on the first experimental observation of a non-equilibrium phase of matter, the discrete time crystal (DTC). A DTC breaks time-translational symmetry and displays spatio-temporal quantum order in all of its eigenstates, a feature dubbed “eigenstate order”. We implement Floquet dynamics on a 1D chain of 20 superconducting qubits [2]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing the non-equilibrium phase [3]. We carefully validate the phase structure of the DTC by probing the average response of all eigenstates belonging to the Floquet unitary. Using a suitable choice of order parameter, we further identify the location of the MBL-ergodicity crossover via experimentally observed finite-size effects. These results open a direct path to studying quantum phase transitions and critical phenomena on NISQ quantum processors.
The study of topologically ordered states has given rise to a growing interest in symmetry-protected states in quantum matter. Recently, this theory has been extended to quantum many-body systems, which demonstrate ordered states at low temperatures. An example of this is the discrete time crystal (DTC), which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected from disorder to a certain extent. In general, DTCs can be classified into two phases: the stable many-body localization (MBL) state and the disordered thermal state. This work demonstrates the by generalizing DTCs to two dimensions, where there was an decrease in the thermal noise and an increase in the operating range of the MBL range in the presence of disorder.
Given recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices, we explore their implications for quantum many-body physics in a practical sense: we ask which physical phenomena in the realm of quantum statistical mechanics can these devices realize better than any other experimental platform. As a target, we identify discrete time crystals (DTCs), novel out-of-equilibrium phases of matter that break time translation symmetry, and are realized in the intrinsically nonequilibrium setting of periodically driven quantum systems stabilized by disorder and many-body localization. While precursors of time-crystals have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers - each of these lacks one or more of the necessary ingredients for realizing a true incarnation of this phase, and detecting the long-range spatiotemporal order that is its defining feature. We show that a new generation of quantum simulators, such as Google's Sycamore processor, can be programmed to realize the DTC phase and to experimentally verify its dynamical properties using a wide range of observables and initial states. We also discuss the effects of environmental decoherence, and show that already with existing technology one could observe the persistence of DTC spatiotemporal order over hundreds periods, with parametric improvements to come as the technology advances in the future.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
Discrete-Time Crystals (DTC) are a non-equilibrium phase of matter characterized by the breaking of time-translation symmetry in periodically driven quantum systems. In this work, we present a detailed thermodynamic analysis of a DTC in a one-dimensional spin-1/2 chain coupled to a thermal bath. We derive a master equation from the microscopic model, and we explore key thermodynamic quantities, such as work, heat, and entropy production. Our results reveal that the DTC signature inevitably decays in the presence of environmental noise, but we show that a periodic measurement scheme can mitigate the effects of decoherence, stabilizing the subharmonic oscillations of the DTC for extended periods. These findings provide insights into the robustness of time-crystalline phases and potential strategies for protecting them in experimental settings.