Efficiently improving the performance of noisy quantum computers
Samuele Ferracin, Akel Hashim, Jean-Loup Ville, Ravi Naik, Arnaud Carignan-Dugas, Hammam Qassim, Alexis Morvan, David Santiago, Irfan A. Siddiqi, Joel J. Wallman
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named Noiseless Output Extrapolation" and Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
Quantum computers have enabled solving problems beyond the current machines' capabilities. However, this requires handling noise arising from unwanted interactions in these systems. Several protocols have been proposed to address efficient and accurate quantum noise profiling and mitigation. In this work, we propose a novel protocol that efficiently estimates the average output of a noisy quantum device to be used for quantum noise mitigation. The multi-qubit system average behavior is approximated as a special form of a Pauli Channel where Clifford gates are used to estimate the average output for circuits of different depths. The characterized Pauli channel error rates, and state preparation and measurement errors are then used to construct the outputs for different depths thereby eliminating the need for large simulations and enabling efficient mitigation. We demonstrate the efficiency of the proposed protocol on four IBM Q 5-qubit quantum devices. Our method demonstrates improved accuracy with efficient noise characterization. We report up to 88% and 69% improvement for the proposed approach compared to the unmitigated, and pure measurement error mitigation approaches, respectively.
Quantum error mitigation techniques mimic noiseless quantum circuits by running several related noisy circuits and combining their outputs in particular ways. How well such techniques work is thought to depend strongly on how noisy the underlying gates are. Weakly-entangling gates, like R Z Z ( θ ) for small angles θ , can be much less noisy than entangling Clifford gates, like CNOT and CZ, and they arise naturally in circuits used to simulate quantum dynamics. However, such weakly-entangling gates are non-Clifford, and are therefore incompatible with two of the most prominent error mitigation techniques to date: probabilistic error cancellation (PEC) and the related form of zero-noise extrapolation (ZNE). This paper generalizes these techniques to non-Clifford gates, and comprises two complementary parts. The first part shows how to effectively transform any given quantum channel into (almost) any desired channel, at the cost of a sampling overhead, by adding random Pauli gates and processing the measurement outcomes. This enables us to cancel or properly amplify noise in non-Clifford gates, provided we can first characterize such gates in detail. The second part therefore introduces techniques to do so for noisy R Z Z ( θ ) gates. These techniques are robust to state preparation and measurement (SPAM) errors, and exhibit concentration and sensitivity—crucial statistical properties for many experiments. They are related to randomized benchmarking, and may also be of interest beyond the context of error mitigation. We find that while non-Clifford gates can be less noisy than related Cliffords, their noise is fundamentally more complex, which can lead to surprising and sometimes unwanted effects in error mitigation. Whether this trade-off can be broadly advantageous remains to be seen.
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits efficiently classically simulable, thereby destroying any quantum advantage potentially offered by an ideal (noiseless) implementation of these circuits. Although the technique of quantum error correction (QEC) allows correcting these errors very accurately, QEC usually requires a large overhead of physical qubits which is not reachable with currently available quantum hardware. This has been the motivation behind the field of quantum error mitigation, which aims at developing techniques to correct an important part of the errors in quantum circuits, while also being compatible with current and near-term quantum hardware. In this work, we present a technique for quantum error mitigation which is based on a technique from quantum verification, the so-called accreditation protocol, together with postselection. Our technique allows for correcting the expectation value of an observable O, which is the output of multiple runs of noisy quantum circuits, where the noise in these circuits is at the level of preparations, gates, and measurements. We discuss the sample complexity of our procedure and provide rigorous guarantees of errors being mitigated under some realistic assumptions on the noise. Our technique is tailored to time-dependent behaviors, as we allow for the output states to be different between different runs of the accreditation protocol. We validate our findings by running our technique on currently available quantum hardware.
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.
As quantum devices grow in size while remaining affected by noise, a key challenge is to determine when and how they can surpass classical computation on practical tasks. This requires the development of highly efficient classical simulation algorithms. Pauli backpropagation algorithms are among the most promising, having shown efficiency in simulating certain classes of parameterized quantum circuits, strong candidates for near‑term quantum advantage, under random circuit assumptions and depolarizing noise. However, their efficiency had not been demonstrated for more realistic nonunital noise models, such as amplitude damping, which better capture the behaviour of current hardware. We close this gap by adapting Pauli backpropagation to most single‑qubit noise channels, including nonunital noise, and proving that it remains efficient under these conditions. Our algorithm is parallelizable, memory‑efficient, and requires no assumptions on the locality of the observable, the geometry of the hardware, or the depth of the circuit. While hardware noise can strongly affect computational power in highly structured, fault‑tolerant circuits, our findings indicate little difference for most near‑term variational architectures. This establishes Pauli backpropagation as an efficient method for simulating noisy quantum devices under realistic noise assumptions.While these advances improve our ability to reproduce noisy expectation values of observables, many practical applications, including combinatorial optimization, require direct access to the bitstrings output by quantum circuits, as these encode candidate solutions. Classical replication of such noisy samples has so far been limited beyond the random circuit setting. To bridge this gap, we first focus on problems whose objective functions depend only on two‑body correlations, such as Max‑Cut, and apply Gaussian randomized rounding to the circuit's two‑qubit marginals. This produces classical samples whose expected cost is provably close to that of the noisy quantum device. Large‑scale simulations and experiments on IBMQ hardware confirm that the rounded samples reproduce the full energy distribution, with similar behaviour under various noise models. Coupled with Pauli backpropagation for efficiently estimating noisy marginals, this yields an end‑to‑end classical sampler operating in polynomial time for a broad class of variational circuits. Our results therefore show that sufficiently noisy quantum circuits for combinatorial optimization can be sampled from classically, clarifying where near‑term hardware may or may not outperform classical algorithms.Finally , we go beyond one and two‑body marginals and present an algorithm that samples valid bitstrings directly from a maximum‑entropy distribution matching the given expectation values of the quantum circuit. This method does not rely on the locality or sparsity of the problem's Hamiltonian and performs well across a variety of quantum circuits, including deep circuits on many qubits. When combined with Pauli propagation or error mitigation, it provides a practical pipeline for obtaining samples from quantum circuits in the near term, where full error correction might not yet be available.
As quantum computing advances towards practical applications, reducing errors remains a crucial frontier for developing near-term devices. Errors in the quantum gates and quantum state readout could result in noisy circuits, which would prevent the acquisition of the exact expectation values of the observables. Although ultimate robustness to errors is known to be achievable by quantum error correction-based fault-tolerant quantum computing, its successful implementation demands large-scale quantum processors with low average error rates that are not yet widely available. In contrast, quantum error mitigation (QEM) offers more immediate and practical techniques, which do not require extensive resources and can be readily applied to existing quantum devices to improve the accuracy of the expectation values. Here, we report the implementation of a zero-noise extrapolation-based error mitigation technique on a silicon spin qubit platform. This technique has recently been successfully demonstrated for other platforms such as superconducting qubits, trapped-ion qubits, and photonic processors. We first explore three methods for amplifying noise on a silicon spin qubit: global folding, local folding, and pulse stretching, using a standard randomized benchmarking protocol. We then apply global folding-based zero-noise extrapolation to the state tomography and achieve a state fidelity of 99.96% (98.52%), compared to the unmitigated fidelity of 75.82% (82.16%) for different preparation states. The results show that the zero-noise extrapolation technique is a versatile approach that is generally adaptable to quantum computing platforms with different noise characteristics through appropriate noise amplification methods.