Quantum many-body scars are an intriguing dynamical regime in which quantum systems exhibit coherent dynamics and long-range correlations when prepared in certain initial states. We use this combination of coherence and many-body correlations to benchmark the performance of present-day quantum computing devices by using them to simulate the dynamics of an antiferromagnetic initial state in mixed-field Ising chains of up to 19 sites. In addition to calculating the dynamics of local observables, we also calculate the Loschmidt echo and a nontrivial unequal-time connected correlation function that witnesses long-range many-body correlations in the scarred dynamics. We find coherent dynamics to persist over up to 40 Trotter steps even in the presence of various sources of error. To obtain these results, we leverage a variety of error-mitigation techniques including noise tailoring, zero-noise extrapolation, dynamical decoupling, and physically motivated postselection of measurement results. Crucially, we also find that using pulse-level control to implement the Ising interaction yields a substantial improvement over the standard controlled-not-based compilation of this interaction. Our results demonstrate the power of error-mitigation techniques and pulse-level control to probe many-body coherence and correlation effects on present-day quantum hardware.
Quantum many-body scars are an intriguing dynamical regime in which quantum systems exhibit coherent dynamics and long-range correlations when prepared in certain initial states. We use this combination of coherence and many-body correlations to benchmark the performance of present-day quantum computing devices by using them to simulate the dynamics of an antiferromagnetic initial state in mixed-field Ising chains of up to 19 sites. In addition to calculating the dynamics of local observables, we also calculate the Loschmidt echo and a nontrivial unequal-time connected correlation function that witnesses long-range many-body correlations in the scarred dynamics. We find coherent dynamics to persist over up to 40 Trotter steps even in the presence of various sources of error. To obtain these results, we leverage a variety of error-mitigation techniques including noise tailoring, zero-noise extrapolation, dynamical decoupling, and physically motivated postselection of measurement results. Crucially, we also find that using pulse-level control to implement the Ising interaction yields a substantial improvement over the standard controlled-not-based compilation of this interaction. Our results demonstrate the power of error-mitigation techniques and pulse-level control to probe many-body coherence and correlation effects on present-day quantum hardware.
Quantum computing gives direct access to the study of the real-time dynamics of quantum many-body systems. In principle, it is possible to directly calculate non-equal-time correlation functions, from which one can detect interesting phenomena, such as the presence of quantum scars or dynamical quantum phase transitions. In practice, these calculations are strongly affected by noise, due to the complexity of the required quantum circuits. As a testbed for the evaluation of the real-time evolution of observables and correlations, the dynamics of the Zn Schwinger model in a one-dimensional lattice is considered. To control the computational cost, we adopt a quantum-classical strategy that reduces the dimensionality of the system by restricting the dynamics to the Dirac vacuum sector and optimizes the embedding into a qubit model by minimizing the number of three-qubit gates. The time evolution of particle-density operators in a non-equilibrium quench protocol is both simulated in a bare noisy condition and implemented on a physical IBM quantum device. In either case, the convergence towards a maximally mixed state is targeted by means of different error mitigation techniques. The evaluation of the particle-density correlation shows a well-performing post-processing error mitigation for properly chosen coupling regimes.
Long-range interactions are the source of many equilibrium and out-of-equilibrium quantum many-body phenomena. Analog simulators based on ionic, atomic, superconducting, and molecular systems provide a natural platform to obtain these interactions using vibration- and photon-mediated processes. Recent experimental advances, such as their integration in multi-mode cavities and waveguides, or the use of Raman-assisted transitions, enable dynamical control over both the strength and the spatial range of these interactions, thereby rendering them programmable. Here, we develop a hybrid classical-quantum toolbox that exploits this tunability to enhance many-body state preparation in analog simulators beyond fixed-connectivity architectures. Our approach is based on classical pre-compilation in homogeneous small systems, whose optimized parameters are extrapolated iteratively to larger system sizes, and then refined on the quantum hardware using noise-aware hybrid re-optimization and error-mitigation techniques. We benchmark this strategy across several fermionic, spin-1/2, and spin-1 models, demonstrating orders-of-magnitude improvements in fidelity and energy estimation for system sizes ranging from 100 to 1000 particles. Finally, we show that the combination of such high-fidelity programmable state preparation techniques with tunable-range out-of-equilibrium dynamics enables controlled studies of many-body thermalization in regimes accessible to current experimental platforms. Our results establish programmable long-range interactions as a powerful resource for next-generation analog quantum simulators.
We investigate how to simulate a quantum many body system using near term device known as noisy intermediate scale quantum (NISQ) hardware. We explore the two different types of hardware, analog and digital device, and discuss their potential for quantum many body simulation. For instance, one of the applications is to use the analog device to simulate the slow dynamics under a strong staggered field. However, noise is a major challenge for quantum hardware. Hence, we discuss the quantum error mitigation methods which are suitable for NISQ hardware. We apply the most commonly-used quantum error mitigation techniques to our many body simulation. We simulate quantum body scar dynamics using zero noise extrapolation techniques, Pauli twirling, and dynamical decoupling. We also calculate the corresponding correlation function using direct measurement without resorting to ancilla qubits. Furthermore, we use the same error mitigation techniques to explore dynamics of energy correlators. As additional error mitigation technique, we divide the noisy correlation results by their sum, which is ideally constant due to energy conservation. By doing so, we significantly improve our result. Finally, we consider another NISQ friendly quantum algorithm for imaginary time evolution. With enough samples from minimally entangled typical thermal state algorithms, we can obtain the thermal expectation value of observable and explore their thermodynamics. In chapter 2, we provide the background knowledge for the following 4 chapters. We introduce the rydberg atom system as the analog system and their special parameter regime for interesting physics. Moreover, we introduce the digital quantum hardware and trotterization that enable one to simulate many body dynamics on the quantum hardware. We also introduce the quantum error mitigation techniques to reduce the the impact of noise from the results. Finally, we introduce the variation quantum dynamics method for the dynamics simulation. In chapter 3, we explore the Rydberg blockade regime with a strong staggered field. With the strong staggered field, any computational basis states are thermalized. Here, we investigate the slow dynamics using a Schrieffer-Wolff (SW) transformation, which is similar to perturbation theory in calculating the different-order effective Hamiltonian in terms of energy scale. As numerical result shown, the naive Schrieffer-Wolff transformation is not enough to explain the some dynamics' relaxation time. Hence, here, we also consider another conservative quantity to perform the SW transformation. The corresponding analytical result agrees with the numerical result. In chapter 4, we simulate quantum many body scarred dynamics in IBM quantum superconducting hardware. We also use custom pulse gates, quantum error mitigation techniques, and quantum error suppression methods to help us handle the noise. The error mitigated result outperforms the raw result. With the all techniques, we also explore non-trivial correlation function which also manifest the long lived oscillation in the rydberg blockade regime. In chapter 5, we use the same quantum error mitigation techniques, which we used in ch. 5, to study the energy transport properties of the mixed Ising model at infinite temperature. Here, instead of using some random state to evaluate the necessary two point energy density correlations, we use Y basis product state sampling to evaluate them. Surprisingly, few samples are enough to estimate the correlation. In addition to the quantum error mitigation techniques, we also use the fact that sum of all correlation functions is constant to renormalize the noisy results. With this trick, we are able to extract an effective dynamical exponent, which enables us to classify the transport properties. In chapter 6, we combine a variational quantum algorithm and the minimally entangled typical thermal states approach to investigate the thermodynamics of 1+1-dimensional Z2 lattice gauge theory. In particular, with a confining field, the 1+1-dimensional Z2 lattice gauge theory cannot be solved exactly. We estimate the corresponding thermal particle number density and energy density to distinguish the confined and deconfined regime. Chapter 7 provides a short review of the main results described in the thesis and a discussion of future research directions that they motivate. We mainly give insight into the recent experimental breakthrough in quantum error correction. We also clarify that quantum error mitigation methods do not become totally useless when a fault-tolerant quantum computer is realized. Finally, we also comment on variational quantum algorithms and their potential applications.
Dynamic quantum circuits integrate mid-circuit measurements and feed-forward operations to enable real-time classical processing and conditional quantum logic. These capabilities are central to key quantum protocols such as quantum error correction, and have recently demonstrated significant potential for reducing quantum resources, including circuit depth and gate count, across a range of applications. However, executing dynamic circuits on real quantum hardware introduces a critical trade-off: while resource requirements decrease, circuit fidelity degrades due to high error rates of mid-circuit measurements, as well as the decoherence errors accumulated during the extended idle periods introduced by both mid-circuit measurements and feed-forward operations. In this paper, we systematically investigate the impact of standard error mitigation techniques on dynamic circuit applications pertaining to Hamiltonian simulation and ground state estimation of physically relevant systems like the Heisenberg model. We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). Through experiments conducted on IBM quantum hardware, we benchmark effective combinations of these strategies that maximize the practical benefits of dynamic quantum circuits in these applications. We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.
Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.
The real-time simulation of large many-body quantum systems is a formidable task, that may only be achievable with a genuine quantum computational platform. Currently, quantum hardware with a number of qubits sufficient to make classical emulation challenging is available. This condition is necessary for the pursuit of a so-called quantum advantage, but it also makes verifying the results very difficult. In this paper, we flip the perspective and utilize known theoretical results about many-body quantum critical dynamics to qualitatively benchmark digital quantum hardware and various error mitigation techniques. In particular, we benchmark against known universal scaling laws in the Hamiltonian simulation of a time-dependent transverse-field Ising Hamiltonian of up to 133 qubits. Incorporating only basic error mitigation and suppression methods, our study shows reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates, before noise becomes prevalent. These results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning. We demonstrate this on the example of digitized quantum annealing for optimization and identify an optimal working point in terms of both circuit depth and time step on a 133-site optimization problem. Published by the American Physical Society 2024