Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them efficient for studying complex quantum phenomena. However, unlike their digital counterparts, analog quantum simulations face significant limitations due to the absence of effective error mitigation techniques. This work introduces two novel error mitigation strategies—Hamiltonian reshaping and Hamiltonian rescaling—in analog quantum simulation for tasks like eigen-energy evaluation. Hamiltonian reshaping uses random unitary transformations to generate new Hamiltonians with identical eigenvalues but varied eigenstates, allowing error reduction through averaging. Hamiltonian rescaling mitigates errors by comparing eigenvalue estimates from energy-scaled Hamiltonians. Numerical calculations validate both methods, demonstrating their significant practical effectiveness in enhancing the accuracy and reliability of analog quantum simulators.
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them efficient for studying complex quantum phenomena. However, unlike their digital counterparts, analog quantum simulations face significant limitations due to the absence of effective error mitigation techniques. This work introduces two novel error mitigation strategies—Hamiltonian reshaping and Hamiltonian rescaling—in analog quantum simulation for tasks like eigen-energy evaluation. Hamiltonian reshaping uses random unitary transformations to generate new Hamiltonians with identical eigenvalues but varied eigenstates, allowing error reduction through averaging. Hamiltonian rescaling mitigates errors by comparing eigenvalue estimates from energy-scaled Hamiltonians. Numerical calculations validate both methods, demonstrating their significant practical effectiveness in enhancing the accuracy and reliability of analog quantum simulators.
Analog quantum simulation has been proposed as an efficient approach for
probing classically intractable many-body physics. In contrast to digital,
gate-based quantum simulation, the analog approach involves configuring the
quantum hardware to directly mimic the physics of the target system. This
reduces the level of control required and can offer a degree of inherent
robustness, but it comes at the cost that known error-handling techniques may
be inapplicable. Accumulation of error is thus a major challenge facing
medium-scale and large-scale analog quantum simulation with current and
near-term noisy quantum (NISQ) devices. Here we propose a hybrid error
mitigation scheme that can suppress general local Markovian noise in analog
quantum simulators. We employ stochastic error mitigation for physical noise
and use Richardson extrapolation to compensate for model estimation error. We
numerically test the error mitigation scheme for an Ising-type Hamiltonian with
energy relaxation and dephasing noise, and show an improvement of simulation
accuracy by two orders. We assess the resource cost of our error mitigation
scheme and conclude that analog quantum simulation at scale is feasible with
NISQ hardware.
Quantum computing has emerged as a revolutionary paradigm with the potential to solve computationally intractable problems. However, the practical realization of quantum al-gorithms faces significant challenges due to noise and errors inherent in quantum systems. Hamiltonian simulations serve as a cornerstone in quantum computing, providing insights into quantum dynamics and enabling the study of quantum algorithms. This paper studies error mitigation in analog-based Hamiltonian simulations as they have native support for generating Hamiltonians as opposed to digital-based simulations, which results in shorter pulse schedules to simulate the Hamiltonians. We further aim to enhance the accuracy and reliability of these simulations through error mitigation techniques. This research explores several error mitigation techniques tailored for analog-based Hamiltonian simulations. Among them, Zero-Noise Extrapolation (ZNE) mitigates errors by extrapolating simulation results to the ideal noise-free scenario. Building upon ZNE, Folding-Free ZNE (FFZNE) introduces novel use of the infinite error point to address the challenges posed by folding techniques. Additionally, Reliability-Based ZNE (RBZNE) leverages a mix of both techniques, utilizing the folding method and the infinite error point. Through empirical studies and rigorous analysis, this paper evaluates the efficacy and limitations of these error mitigation techniques in analog-based Hamiltonian simulations on both noise simulator and real quantum hardware. The experimental results shed light on the comparative performance of ZNE, FFZNE, and RBZNE, understanding their strengths and weak-nesses in mitigating errors across different quantum systems and noise conditions. By providing the understanding of these techniques, this research contributes to the advancement of error mitigation strategies in quantum computing, paving the way for more reliable and accurate quantum simulations.
Analog quantum simulators have provided key insights into quantum many-body dynamics. However, in such systems, both coherent and incoherent errors limit their scalability, hindering simulations in regimes that challenge classical simulations. In this work, we introduce an error mitigation technique that addresses and effectively suppresses a key source of error in leading simulator platforms: shot-to-shot fluctuations in the parameters for the Hamiltonian governing the system dynamics. We rigorously prove that amplifying this shot-to-shot noise and extrapolating to the zero-noise limit recovers noiseless results for realistic noise distributions. Experimentally, we demonstrate this technique on a 27-ion trapped-ion quantum simulator, extending the two-qubit exchange oscillation lifetime threefold. Numerically, we predict a significant enhancement in the effective many-body coherence time for Rydberg atom arrays under realistic conditions. Our scheme provides a possible route towards extending the effective coherence time in analog quantum experiments, enabling deeper explorations of quantum many-body dynamics.
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated into their performance analysis, despite the non-negligible noise levels of quantum devices. We present an end-to-end complexity analysis of noisy Hamiltonian simulation combined with quantum error mitigation (QEM) to answer how many circuit runs are required to reach a given target accuracy. Because the QEM sampling overhead grows exponentially with the circuit depth while the algorithmic error decreases with it, the circuit depth becomes an optimization variable, and we derive an analytic depth-selection rule for two algorithm families. For the order-k Suzuki--Trotter formula, the optimized cost exhibits a critical error εc, below which the required number of circuit runs grows exponentially. QEM improves the noise dependence of εc from sublinear to kth-power scaling, an exponent improvement by a factor of k+1. For randomized-LCU-based simulation, optimizing the repetition number yields a square-root improvement in the simulation-time dependence of the sampling-overhead exponent over the standard parameter choice. We further quantify the noise-characterization cost required for error mitigation via gate set tomography and the recently proposed space-time noise inversion method, showing that the latter can significantly reduce this cost.
Quantum computing is emerging as a transformative paradigm for molecular-level modeling in process engineering, offering the potential to perform large-scale, high-accuracy simulations that surpass the computational limits of classical methods. However, the inherent noise and decoherence in quantum systems present major obstacles to reliable molecular interaction predictions. This research conducts a qualitative investigation of error-mitigation strategies designed to improve the accuracy and stability of quantum simulations for modeling molecular interactions relevant to chemical and process engineering. By reviewing scientific literature and analyzing case studies across quantum mechanics, computational chemistry, and industrial process modeling, the study identifies the principal challenges associated with quantum noise, gate fidelity, and algorithmic scalability. A conceptual framework was developed to evaluate how quantum error correction (QEC) techniques, zero-noise extrapolation, and hybrid quantum–classical algorithms enhance predictive precision in molecular simulations. The findings suggest that combining these methods not only mitigates computational noise but also improves convergence efficiency in modeling reaction pathways and intermolecular potentials. This research synthesizes interdisciplinary insights to propose a roadmap for integrating quantum-enhanced molecular simulations into sustainable process engineering. It underscores how advances in error mitigation will be essential for achieving trustworthy, energy-efficient, and scalable industrial applications of quantum computation in the coming decade.
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