A Hybrid Quantum-Classical Approach to Mitigating Measurement Errors in Quantum Algorithms
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Abstract
When noisy intermediate scalable quantum (NISQ) devices are applied in information processing, all of the stages through preparation, manipulation, and measurement of multipartite qubit states contain various types of noise that are generally hard to be verified in practice. In this article, we present a scheme to deal with unknown quantum noise and show that it can be used to mitigate errors in measurement readout with NISQ devices. Quantum detector tomography that identifies a type of noise in a measurement can be circumvented. The scheme applies single-qubit operations only, that are with relatively higher precision than measurement readout or two-qubit gates. A classical post-processing is then performed with measurement outcomes. The scheme is implemented in quantum algorithms with NISQ devices: the Bernstein-Vazirani algorithm and a quantum amplitude estimation algorithm in <inline-formula><tex-math notation="LaTeX">$\mathrm{IBMQ\_yorktown}$</tex-math><alternatives><mml:math><mml:mrow><mml:mi> IBMQ </mml:mi><mml:mo>_</mml:mo><mml:mi> yorktown </mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="bae-ieq1-3009664.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mathrm{IBMQ\_essex}$</tex-math><alternatives><mml:math><mml:mrow><mml:mi> IBMQ </mml:mi><mml:mo>_</mml:mo><mml:mi> essex </mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="bae-ieq2-3009664.gif"/></alternatives></inline-formula>. The enhancement in the statistics of the measurement outcomes is presented for both of the algorithms with NISQ devices.