As quantum devices continue to improve in scale and precision, a central challenge is how to effectively utilize noisy hardware for meaningful computation. Most existing approaches aim to recover noiseless circuit outputs from noisy ones through error mitigation or correction. Here, we show that noisy quantum devices can be directly leveraged as computational resources to enhance the classical simulation of quantum circuits. We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based classical Monte Carlo simulation methods by incorporating data obtained from noisy quantum hardware. Specifically, NDE-CS uses noisy executions of a target circuit together with noisy Clifford circuits to learn how the target circuit can be expressed in terms of Clifford circuits under realistic noise. The same learned relation can then be reused in the noiseless Clifford limit, enabling accurate estimation of ideal expectation values with substantially reduced sampling cost. Numerical simulations on Trotterized Ising circuits demonstrate that NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches from which it is derived, while maintaining the same accuracy. We also compare NDE-CS with Sparse Pauli Dynamics (SPD), a powerful classical framework capable of simulating quantum circuits at previously inaccessible scales, and provide an example where the cost of SPD scales exponentially with system size, while NDE-CS scales much more favorably. These results establish NDE-CS as a scalable hybrid simulation approach for quantum circuits, where noise can be harnessed as a computational asset.
As quantum devices continue to improve in scale and precision, a central challenge is how to effectively utilize noisy hardware for meaningful computation. Most existing approaches aim to recover noiseless circuit outputs from noisy ones through error mitigation or correction. Here, we show that noisy quantum devices can be directly leveraged as computational resources to enhance the classical simulation of quantum circuits. We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based classical Monte Carlo simulation methods by incorporating data obtained from noisy quantum hardware. Specifically, NDE-CS uses noisy executions of a target circuit together with noisy Clifford circuits to learn how the target circuit can be expressed in terms of Clifford circuits under realistic noise. The same learned relation can then be reused in the noiseless Clifford limit, enabling accurate estimation of ideal expectation values with substantially reduced sampling cost. Numerical simulations on Trotterized Ising circuits demonstrate that NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches from which it is derived, while maintaining the same accuracy. We also compare NDE-CS with Sparse Pauli Dynamics (SPD), a powerful classical framework capable of simulating quantum circuits at previously inaccessible scales, and provide an example where the cost of SPD scales exponentially with system size, while NDE-CS scales much more favorably. These results establish NDE-CS as a scalable hybrid simulation approach for quantum circuits, where noise can be harnessed as a computational asset.
Accurately estimating observables on noisy quantum devices remains a central challenge for near-term quantum algorithms. While quantum error mitigation techniques can reduce noise-induced bias, they often rely on unverifiable assumptions about the circuit noise, and cannot guarantee the magnitude of residual bias error. Here, rather than using classical resources to mitigate a noisy quantum circuit execution, we propose a hybrid algorithm that uses quantum resources to improve the accuracy of approximate classical Pauli-path simulation. Our protocol, Quantum Enhanced Pauli Propagation (QuEPP), uses Clifford perturbation theory (CPT) to construct a classically simulable ensemble of Clifford circuits from the low-order terms in CPT, which directly provide the approximate classical Pauli-path simulation of the target circuit. Noisy quantum expectation values of this ensemble are then used to infer a global rescaling factor that corrects quantum execution of the target circuit, providing higher-order contributions absent from the truncated low-order classical simulation. This approach requires no noise characterization, applies to arbitrary circuits, and provides a provable route to asymptotically unbiased estimates. Using IBM Heron hardware, we demonstrate QuEPP on 2D random mirror circuits of up to 49 qubits and circuit depth 80, as well as Trotterized Hamiltonian evolution, showing consistent improvements beyond classical CPT and unmitigated quantum results. QuEPP offers a simple, scalable, and model-free framework for enabling accurate quantum computation in the pre-fault-tolerant era.
Noise is usually treated as an obstacle to reliable quantum computation. Here, we show that noisy quantum data can instead enhance classical simulation by introducing the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol. NDE-CS decomposes the expectation value of a target non-Clifford parameterized quantum circuit into a linear combination of expectation values of Clifford circuits. These Clifford circuits are sampled by replacing the rotation gates in the target circuit with Clifford analogs, while preserving the original gate layout and connectivity. The protocol learns highly efficient linear combinations from noisy expectation values on quantum hardware and uses them to reconstruct the noiseless target expectation value. Numerical simulations show that NDE-CS outperforms layer-wise stabilizer Monte Carlo baselines and, for two specific circuit families, requires substantially fewer resources than Sparse Pauli Dynamics (SPD), highlighting its complementary role to SPD. Lastly, we experimentally implement NDE-CS on a superconducting quantum processor, demonstrating that the protocol remains effective on real-world quantum hardware.
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data { X i noisy , X i exact } via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where X i noisy and X i exact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.
Achieving near-term quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. Here, we obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.
Quantum error mitigation (QEM) is critical for harnessing the potential of near-term quantum devices. Particularly, QEM protocols can be designed based on machine learning, where the mapping between noisy computational outputs and ideal ones can be learned on a training set consisting of Clifford circuits or near-Clifford circuits that contain only a limited number of non-Clifford gates. This learned mapping is then applied to noisy target circuits to estimate the ideal computational output. In this work, we propose a learning-based error mitigation framework called Clifford Perturbation Data Regression (CPDR), which constructs training sets by Clifford circuits with small perturbations. Specifically, these circuits are parameterized quantum circuits, where the rotation angles of the gates are restricted to a narrow range, ensuring that the gates remain close to Clifford gates. This design enables the efficient simulation of the training circuits using the Sparse Pauli Dynamics method. As a result, CPDR is able to utilize training sets with a better diversity to train the model, compared with previous learning-based QEM models that construct training sets with only Clifford or near-Clifford circuits. Numerical simulations on small-scale Ising model circuits demonstrate that the performance of CPDR dramatically outperforms that of existing methods such as Zero-Noise Extrapolation and learning-based Probabilistic Error Cancellation. Furthermore, using the experimental data from IBM's 127-qubit Eagle processor, our findings suggest that CPDR demonstrates improved accuracy compared to the original mitigation results reported in [Nature 618, 500 (2023)].
Classical simulability of quantum circuits plays a central role in characterizing and quantifying quantum computational advantage. Typically, the presence of non-Clifford gates introduces an exponential runtime overhead for classically estimating expectation values of observables. In this work, we introduce an efficient simulation framework that integrates the sum-over-Clifford method with quasi-probability-based stabilizer simulation to directly estimate expectation values. To optimize efficiency, we incorporate a circuit-adaptive reduction via variance estimation protocol, which terminates simulations once an empirical confidence bound is sufficient to guarantee the prescribed error tolerance. Our method circumvents overly conservative Hoeffding's inequality, thereby reducing the dependence on the gate-wise stabilizer extent from quadratic to linear in the low-variance regime, while maintaining the same space complexity as previous approaches. We explicitly prove the sample-complexity reduction for random quantum circuits and T-doped Clifford circuits and also empirically validate these advantages in the quantum approximate optimization algorithm and quantum kernel method.