Abstract
Quantum error mitigation (QEM) has been proposed as an alternative method of quantum error correction to compensate errors in quantum systems without qubit overhead. While Markovian gate errors on digital quantum computers have been mainly considered previously, it is indispensable to discuss a relationship between QEM and non-Markovian errors because non-Markovian noise effects inevitably exist in most of the solid-state systems. In this work, we investigate the QEM for non-Markovian noise, and show that there is a clear relationship between costs for QEM and non-Markovian measures. As examples, we show several non-Markovian noise models to bridge a gap between our theoretical framework and concrete physical systems. This discovery may help in designing better QEM strategies for realistic quantum devices with non-Markovian environments.
Highlights
It is widely accepted that quantum computing will enable us to perform classically intractable tasks such as Shor’s algorithm for prime factorization [1], quantum simulation for quantum many-body systems [2], and the Harrow-HassidimLloyd (HHL) algorithm for solving linear equations [3]
Quantum error mitigation (QEM) methods have been proposed to mitigate errors in digital quantum computing, which is compatible with near-term quantum computers with the restricted number of qubits and gate operations as it does not rely on the encoding required in fault-tolerant quantum computing [8,9,10,11,12]
We show that QEM costs reduce in the non-Markovian region
Summary
It is widely accepted that quantum computing will enable us to perform classically intractable tasks such as Shor’s algorithm for prime factorization [1], quantum simulation for quantum many-body systems [2], and the Harrow-HassidimLloyd (HHL) algorithm for solving linear equations [3]. There are many applications to utilize nonMarkovianity in a positive way for quantum information processing, including quantum Zeno effects [27,28], dynamical decoupling [29], Loschmidt echo and criticality [30], continuous-variable quantum key distribution [31], timeinvariant discord [32], quantum chaos [33], quantum resource theory [34], and quantum metrology [35,36] These motivate researchers to investigate the properties of non-Markovianity. We calculate QEM costs for two experimental setups showing non-Markovianity as examples: One is a controllable open quantum system, which consists of a long-lived qubit coupled with a short-lived qubit This system has been realized in NMR experiments [38,39].
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