Abstract
It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localised Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a `SWAP test' circuit. Our optimised methods dramatically reduce the circuit's output error without increasing the qubit count or time requirements.
Highlights
Controlling noise in quantum systems is crucial for the development of practical technologies
The theory of quantum fault tolerance (QFT) reveals that the introduction of logical qubits, composed of numerous physical qubits, can allow one to detect and correct errors at the physical level; this capacity comes at an enormous multiplicative cost in resources
A recent estimate suggests that a Shor algorithm operating on a few thousand logical qubits would require several million physical qubits [1]
Summary
Controlling noise in quantum systems is crucial for the development of practical technologies. The authors explained that by replacing operations in the quantum circuit and assigning parity Æ1 to each operation following a certain probability distribution dependent on the noise, an experimentalist can obtain the unbiased estimator, at the cost of an increase in the variance Their method was shown to be applicable to specific noise types, including homogeneous depolarizing errors and damping errors. For the extrapolation method, which is a relatively straightforward technique, our optimization is to observe that typically for the classes of noise most common in experiments it is appropriate to assume that the expected value of the observable will decay exponentially with the severity of the circuit noise Adopting this underlying assumption, rather than a polynomial (e.g., linear) fit, proves to be quite advantageous. We perform at least 103 repetitions so that the distribution becomes clear; at least 107 individual numerical experiments are performed for each of the curves that we presently report
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