Mitigation of quantum errors is critical for current NISQ devices. In the present work, we address this task by treating the execution of quantum algorithms as the time evolution of an idealized physical system. We use knowledge of its physics to assist the mitigation of the quantum noise produced on the real device. In particular, the time evolution of the idealized system obeys a corresponding Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. This is the basis for the novel error mitigation scheme that we propose. Specifically, we employ a subset of the BBGKY hierarchy as supplementary constraints in the zero-noise extrapolation (ZNE) method for error mitigation. We ensure that the computational cost of the scheme scales polynomially with the system size. We test our method on digital quantum simulations of the lattice Schwinger model under noise levels mimicking realistic quantum hardware. We demonstrate that our scheme systematically improves the error mitigation for the measurements of the particle number and the charge within this system. Relative to ZNE, we obtain an average reduction of the error by $(18.2\ifmmode\pm\else\textpm\fi{}0.5)%$ and $(52.8\ifmmode\pm\else\textpm\fi{}6.3)%$ for the respective above observables. We propose further applications of the BBGKY hierarchy for quantum error mitigation.
Mitigation of quantum errors is critical for current NISQ devices. In the present work, we address this task by treating the execution of quantum algorithms as the time evolution of an idealized physical system. We use knowledge of its physics to assist the mitigation of the quantum noise produced on the real device. In particular, the time evolution of the idealized system obeys a corresponding Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. This is the basis for the novel error mitigation scheme that we propose. Specifically, we employ a subset of the BBGKY hierarchy as supplementary constraints in the zero-noise extrapolation (ZNE) method for error mitigation. We ensure that the computational cost of the scheme scales polynomially with the system size. We test our method on digital quantum simulations of the lattice Schwinger model under noise levels mimicking realistic quantum hardware. We demonstrate that our scheme systematically improves the error mitigation for the measurements of the particle number and the charge within this system. Relative to ZNE, we obtain an average reduction of the error by (18.2\ifmmode±\else\textpm\fi0.5) and (52.8\ifmmode±\else\textpm\fi6.3) for the respective above observables. We propose further applications of the BBGKY hierarchy for quantum error mitigation.
Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum simulations of time-dependent Hamiltonian dynamics on NISQ devices. The scheme uses a polynomial subset of extended qubit Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations as a sampling criterion of possible mitigated candidates for the quantum observables. We show that for favorable Hamiltonians the polynomial subset of BBGKY hierarchy equations leads to a polynomial overhead in both classical and quantum resources. We employ the method to mitigate simulations of the chiral magnetic effect (CME), a chiral feature of the Schwinger model. We empirically show the effectiveness of our scheme at recovering the real-time dynamics of the CME from noisy quantum simulations of the Schwinger model, for a range of different parameter values of the model. We numerically demonstrate a systematic reduction of quantum noise, together with an increasing noise reduction capability as the amount of BBGKY constraints grows.
Near-term physical implementations of quantum algorithms require efficient quantum error mitigation schemes to reduce quantum noise. In this letter we propose a new mitigation technique, by extending the applicability of our BBGKY-ISM scheme from quantum simulations of spin chains to arbitrary quantum circuits. We map executions of quantum circuits using Feynman's clock Hamiltonian to the Hamiltonian dynamics of a corresponding quantum system, whose time evolution obeys a BBGKY-like hierarchy of equations informing the BBGKY-ISM mitigation. We show that the method's classical and quantum overheads are polynomial in the circuit size and in the number of qubits. We apply our method to numerical simulations of tunable Bell state preparation circuits under state-of-the-art quantum noise, and numerically demonstrate its systematic and controllable quantum error reduction capability.
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a stochastic QEM method. Since our method assumes only accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by 2 orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
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.
Abstract Hardware Error Outputs of Quantum Computing Not Reliable because of Hardware Calibration Drift, Measurement Noise, Gate Errors on NISQ Systems. Even though MEMs, ZNEs, and CDRs slightly increase output accuracy, they operate under the assumption of static noise, therefore they do not account for changing output of the NISQ devices in real-time. The limitations of MEMs, ZNEs, and CDRs can be overcome by using the Hybrid Adaptive Error Mitigation (HAEM) method proposed in this article that has the capability to combine baseline measurement-error mitigation with Real-time Calibration Circuits and Lightweight-Machine-learning algorithms for adaptive error-correcting and increasing the overall output integrity of quantum devices affected by fluctuations in noise. The application of the HAEM method will utilize Qiskit Runtime to develop, implement, and validate the Hybrid Adaptive Error Mitigation method through testing using controlled noisy simulated environments based on the characteristics of current advanced NISQ quantum computers. The results of the tests demonstrate the HAEM architecture provides a higher level of accuracy and fidelity than static and non-mitigated executions ("mitigated execution vs. HAEM execution"), providing an increase of up to thirty-four percent in fidelity under high-noise conditions with minimal computational overhead. The results demonstrate that the use of adaptive and data-driven mitigation techniques, like those used in the Hybrid Adaptive Error Mitigation method, are an efficient way to increase the accuracy of quantum computations.