The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data.
The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data.
The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data. Published by the American Physical Society 2024
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.
Floquet many-body phases such as discrete time crystals (DTCs) are typically fragile to imperfections, and stabilizing them on noisy quantum hardware remains a central challenge in nonequilibrium quantum physics. Here, we use IBM Eagle and Heron superconducting processors to implement Floquet dynamics of a kicked Ising model on two-dimensional Kagome lattices, engineered via ancilla-assisted embeddings into the heavy-hex connectivity of the devices. By combining error-mitigated measurements on quantum hardware with matrix-product-state simulations incorporating an ancilla-noise model constructed from experimental device data, we observe long-lived subharmonic magnetization oscillations that are stabilized -- rather than destroyed -- by structured quantum noise. Across different two-dimensional lattice geometries, increasing cases beyond Kagome lattices, and with or without boundary symmetry-charge pumping, ancilla errors effectively act as spatiotemporal disorder that induces stochastic sign flips of the Ising couplings, providing a unified mechanism for robust period-doubling responses. When symmetry-charge pumping is present, intrinsic boundary-localized π modes cooperate with this disorder to yield a boundary-assisted DTC characterized by suppressed scrambling and sharply localized dynamics. In contrast, in implementations without pumping, the noiseless dynamics rapidly thermalize and exhibit no subharmonic order, whereas the same noise process alone generates a DTC-like long-lived subharmonic response over experimentally accessible time windows. These results identify engineered ancilla noise as a practical control knob for inducing, stabilizing, and geometrically tailoring nonequilibrium dynamical order on scalable superconducting quantum processors.
Periodically driven interacting quantum many-body systems can exhibit long-lived prethermal dynamics, where local observables retain coherent structure even as entanglement and operator complexity grow. Accessing this regime at the system sizes and times needed to determine physical properties of the prethermal state remains a central challenge: state-of-the-art classical methods become unreliable, while noise in quantum hardware degrades observable expectation values. Here we overcome these limitations for a Floquet Ising magnet realized on a heavy-hex lattice. Using the advanced error mitigation software QESEM on an IBM Heron r3 superconducting quantum processor, we measure magnetization dynamics with percent-level precision and resolve long-lived subharmonic prethermal oscillations in systems of up to 74 qubits. These experiments reach regimes for which leading tensor-network simulations fail to converge, while sparse Pauli-path simulations remain strongly truncation dependent despite extensive computations on advanced GPUs and the Fugaku supercomputer. Leveraging this quantum-accessible regime, we extend finite-size scaling to larger systems and find an unexpectedly slow decrease of the oscillation amplitude with system size, providing strong evidence that this oscillatory response persists in the thermodynamic limit of heavy-hex ladders. A hierarchy of mitigation and validation tests, including unbiased error mitigation, agreement between independent mitigation estimators, noise-model validation on the superconducting hardware, and cross-platform corroboration at selected Floquet cycles on Quantinuum System Model H2 and Quantinuum Helios trapped-ion hardware, supports the reliability of these findings. Our work establishes error-mitigated quantum processors as quantitative scientific instruments for discovering new physics in non-equilibrium quantum matter.
Quantum processors based on superconducting circuitry have reached the scale of hundreds of qubits and demonstrated computational capabilities that challenge state-of-the-art classical methods for carefully designed problems. Despite these advances, fundamental questions persist over how to best improve and scale the computational power of this emerging technology. Most transmon-based quantum processors encode information in two-level systems, or qubits, leaving the rich multilevel structure of the transmon largely unexploited. In this thesis, we demonstrate how the capabilities of these devices can be meaningfully extended by harnessing this intrinsic multilevel structure to encode qudits — d-level quantum systems that access a larger and more connected Hilbert space than their qubit counterparts. We begin by demonstrating universal single-qudit operation before turning to microwave-activated entanglement to realize scalable two-qudit gates. We present a high-fidelity, fully entangling two-qutrit CZ gate based on a novel tunable cross-Kerr mechanism. We further explore two-qudit gates that selectively entangle subspaces of the full Hilbert space via two-photon multipartite Raman transitions, employing these operations to generate large entangled states across a transmon array. To address the noisy nature of near-term qudit computation, we introduce and characterize error suppression techniques for qudit circuits, including dynamical decoupling and quantum error mitigation. We then synthesize these directions by exploring simulations of quantum systems that have innate multilevel interactions and are therefore well tailored to qudit operation. First we investigate digital quantum simulations of collective neutrino oscillations and the spin-1 truncated Abelian Higgs model, finding error mitigation methods critical for improving circuit performance. Finally, out of equilibrium --- or Floquet --- spin-1 systems are realized using an array of 15 superconducting qutrits to probe a novel Z3 discrete time crystalline (DTC) phase of matter with intrinsically chiral interactions. This DTC result demonstrates that native qudit hardware provides powerful access to non-equilibrium phases rooted in higher discrete symmetries, opening a route to a broader landscape of dynamical orders beyond the Z2 Ising paradigm.
We simulate the dynamics of a spin-1/2 chain with nearest neighbor Ising interactions, quenched disorder and periodic driving over 57 qubits on a current quantum computer. A transition between time crystalline behaviour and non-symmetry breaking dynamics is observed via critical fluctuations in the sub-harmonic frequency response of the system. We probe shorter time scales by implementing the Floquet unitary directly, as well as longer time scales by making use of an equivalent Hamiltonian description. In order to extract the signal from the noisy data produced by current quantum computer devices, we develop a strategy for error mitigation and show that the results are robust under variations of the parameters introduced in this scheme. Our findings are in agreement with previous numerical simulations but add larger system size data points to the phase diagram.