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Register a new userModel-free readout-error mitigation for quantum expectation values
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Measurements on current quantum-hardware are subject to hardware imperfections that lead to readout-errors. These errors manifest themselves as a bias in quantum expectation values. Here, we propose a method to remove this bias from the expectation values of Pauli observables. No specific form of the noise is assumed, other than requiring that it is `weak. We apply a method that forces the bias in the expectation value to appear as a multiplicative factor irrespective of the actual noise process. This factor can be measured directly and removed, at the cost of an increase in the sampling complexity for the observable. A bound relating the error in the expectation value to the sample complexity is derived.
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Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale experimental demonstrations. However, the practical scaling of these methods to larger system sizes remains unknown. Here, we demonstrate the utility of zero-noise extrapolation for relevant quantum circuits using up to 26 qubits, circuit depths of 60, and 1080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to the quench dynamics of 2-D Ising spin lattices with varying couplings. We show that the efficacy of the error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, we demonstrate an accuracy in the approximate quantum simulation of the quench dynamics that surpasses the classical approximations obtained from a state-of-the-art 2-D tensor network method. These results reveal a path to a relevant quantum advantage with noisy, digital, quantum processors.
Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental emph{response matrix} that describes the error associated with measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially in the number of qubits $n$. In this work, we modify standard matrix inversion techniques using two perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high order bitflip events is strongly suppressed. Given a characteristic error rate $q$, our first method recovers the probability of the all-zeros bitstring $p_0$ by sampling only a small subspace of the response matrix before inverting readout error resulting in a relative speedup of $text{poly}left(2^{n} / big(begin{smallmatrix} n w end{smallmatrix}big)right)$, which we motivate using a simplified error model for which the approximation incurs only $O(q^w)$ error for some integer $w$. We then provide a generalized technique to efficiently recover full output distributions with $O(q^w)$ error in the perturbative limit. These approximate techniques for readout error correction may greatly accelerate near term quantum computing applications.
A general method to mitigate the effect of errors in quantum circuits is outlined. The method is developed in sight of characteristics that an ideal method should possess and to ameliorate an existing method which only mitigates state preparation and measurement errors. The method is tested on different IBM Q quantum devices, using randomly generated circuits with up to four qubits. A large majority of results show significant error mitigation.
Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring $M$ copies of a noisy state $rho$. This enables us to estimate expectation values with respect to a state with dramatically reduced error, $rho^M/ mathrm{Tr}(rho^M)$, without explicitly preparing it, hence the name virtual distillation. As $M$ increases, this state approaches the closest pure state to $rho$, exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of $rho$). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.
Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal with noise that can be applied to these algorithms. Recent work introduced a technique for mitigating expectation values against correlated measurement errors that can be applied to measurements of 10s of qubits. We apply these techniques to VQAs and demonstrate its effectiveness in improving estimates to the cost function. Moreover, we use the data resulting from this technique to experimentally characterize measurement errors in terms of the device connectivity on devices of up to 20 qubits. These results should be useful for better understanding the near-term potential of VQAs as well as understanding the correlations in measurement errors on large, near-term devices.
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