Quantifying the magic of quantum channels

Journal Article · 01 October 2019 · New Journal of Physics

DOI: https://doi.org/10.1088/1367-2630/ab451d · OSTI ID:1569302

Wang, Xin ; Wilde, Mark M. ; Su, Yuan

Abstract To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d , it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.

• Sponsoring Organization: USDOE
• OSTI ID: 1569302
• Journal Information: New Journal of Physics, Journal Name: New Journal of Physics Journal Issue: 10 Vol. 21; ISSN 1367-2630
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United Kingdom
• Language: English