Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime

Minimizing the effect of noise is essential for quantum computers. The conventional method to protect qubits against noise is through quantum error correction. However, for current quantum hardware in the so-called noisy intermediate-scale quantum (NISQ) era, noise presents in these systems and is too high for error correction to be beneficial. Quantum error mitigation is a set of alternative methods for minimizing errors, including error extrapolation, probabilistic error cancellation, measurement error mitigation, subspace expansion, symmetry verification, virtual distillation, etc. The requirement for these methods is usually less demanding than error correction. Quantum error mitigation is a promising way of reducing errors on NISQ quantum computers. This paper gives a comprehensive introduction to quantum error mitigation. The state-of-art error mitigation methods are covered and formulated in a general form, which provides a basis for comparing, combining and optimizing different methods in future work.

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“…Meanwhile, QEM could be used in part of QEC to reduce the qubit cost when fault-tolerant technology becomes available. [76][77][78][79]…”

Section: Discussionmentioning

confidence: 99%

An overview of quantum error mitigation formulas

Qin

Xu²,

Liu³

2022

Chinese Phys. B

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“…The overhead at ξ = 0 after 15 Trotter steps is γ (0) = 7.25, while it is only γ (0.5) = 2.69 at ξ = 0.5. quantum advantage when full quantum error correction is not available. The use of quantum error mitigation is also expected to extend into the era of fault-tolerant quantum computing with logical qubits as it can lower the overhead for quantum error correction [20]- [22]. While hardware improvements that reduce gate error rates are crucial, the development of controlled and automated error mitigation software provides progress towards performing more complex quantum calculations.…”

Section: Discussionmentioning

confidence: 99%

Automated quantum error mitigation based on probabilistic error reduction

McDonough¹,

Mari²,

Shammah³

et al. 2022

Preprint

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Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the computation, which experiences a bias in the presence of hardware noise. A systematic way to remove such bias is probabilistic error cancellation (PEC). PEC requires a full characterization of the noise and introduces a sampling overhead that increases exponentially with circuit depth, prohibiting high-depth circuits at realistic noise levels. Probabilistic error reduction (PER) is a related quantum error mitigation method that systematically reduces the sampling overhead at the cost of reintroducing bias. In combination with zero-noise extrapolation, PER can yield expectation values with an accuracy comparable to PEC. Noise reduction through PER is broadly applicable to nearterm algorithms, and the automated implementation of PER is thus desirable for facilitating its widespread use. To this end, we present an automated quantum error mitigation software framework that includes noise tomography and application of PER to user-specified circuits. We provide a multi-platform Python package that implements a recently developed Pauli noise tomography (PNT) technique for learning a sparse Pauli noise model and exploits a Pauli noise scaling method to carry out PER. We also provide software tools that leverage a previously

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“…Now recall the retrieving cost, which quantifies the resources required to recover a certain piece of shadow information. The corresponding retrieving protocol can be considered as a method to mitigate errors, endowing the retrieving cost with a practical meaning in quantum error mitigation [23][24][25][26][27][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. In probabilistic error cancellation (PEC) (see, e.g., [23][24][25][26][27]), the sampling cost is used to depict the resource to be consumed, which has the same meaning as retrieving cost.…”

Section: (Data Processing Inequalitymentioning

confidence: 99%

Information recoverability of noisy quantum states

Zhao¹,

Zhao²,

Xia³

et al. 2022

Preprint

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Classical information, also known as shadow information, carried by quantum states could be corrupted as they undergo undesirable noises modelled by quantum channels. Due to quantum channels' destructive nature, a fundamental problem in quantum information theory is how well we can retrieve information from noisy quantum states. In this work, we introduce a systematic framework to quantitatively study this problem. First, we prove that classical information can be retrieved if and only if the querying observable is in the image of the whole observable space under the channel's adjoint. Second, we further define the dimension of the evolved observable space as the quantum channel's effective shadow dimension that quantifies the information recoverability of the channel. This quantity can be computed as the rank of a matrix derived from the channel's Kraus operators, and it induces the shadow destructivity as a measure with meaningful properties. Third, we resolve the minimum cost of retrieving a piece of shadow information from the required number of copies of a noisy state. We in particular show that the optimal cost and the corresponding protocol are efficiently computable by semidefinite programming. As applications, we derive the ultimate limits on shadow retrieving costs for generalized amplitude damping channels and mixed Pauli channels and employ the corresponding protocol to mitigate errors in tasks of ground state energy estimation.

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Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime

Cited by 27 publications

References 34 publications

An overview of quantum error mitigation formulas

An overview of quantum error mitigation formulas

Automated quantum error mitigation based on probabilistic error reduction

Information recoverability of noisy quantum states

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