Encoding qubits into harmonic-oscillator modes via quantum walks in phase space
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Encoding qubits into harmonic-oscillator modes via quantum walks in phase space Chai-Yu Lin1 · Wang-Chang Su1 · Shin-Tza Wu1 Received: 9 August 2019 / Accepted: 17 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We provide a theoretical framework for encoding arbitrary logical states of a quantum bit (qubit) into a continuous-variable quantum mode through quantum walks. Starting with a squeezed vacuum state of the quantum mode, we show that quantum walks of the state in phase space can generate output states that are variants of codeword states originally put forward by Gottesman, Kitaev and Preskill (GKP) (Phys Rev A 64:012310, 2001). In particular, with a coin-toss transformation that projects the quantum coin onto the diagonal coin state, we show that the resulting dissipative quantum walks can generate qubit encoding akin to the prototypical GKP encoding. We analyze the performance of these codewords for error corrections and find that even without optimization our codewords outperform the GKP ones by a narrow margin. Using the circuit representation, we provide a general architecture for the implementation of this encoding scheme and discuss its possible realization through circuit quantum-electrodynamics systems. Keywords Quantum walk · Quantum error correction · Continuous-variable quantum computing · Gottesman–Kitaev–Preskill encoding · Circuit quantum-electrodynamics
1 Introduction Computing based on quantum mechanical principles (i.e., quantum computing) requires exquisite control of quantum systems [1]. Thanks to advancements in experimental techniques, tremendous progress has been made for achieving this goal during the past few years [2]. For large-scale quantum computing, it is indispensable to have an architecture that enables efficient detection and correction of errors during the computing [3]. Recently, there has been significant progress toward this direction in
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Shin-Tza Wu [email protected] Department of Physics, National Chung Cheng University, Chiayi 621, Taiwan 0123456789().: V,-vol
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the field of continuous-variable (CV) measurement-based quantum computing, which seeks to achieve quantum computing by sequence of adaptive local measurements over highly entangled resource states in a state space with continuous spectrum [4,5]. In particular, Menicucci has shown that fault-tolerant quantum computing can be achieved in this scheme provided resource states with squeezing above 20.5 dB are available [6]. Recently, with the aid of topological codes, this squeezing threshold has been reduced to less than 10 dB [7,8]. Essential to these breakthroughs is a quantum errorcorrecting scheme due to Gottesman, Kitaev and Preskill (GKP) [9]. In this approach, quantum information is encoded through a “hybrid” quantum bit (qubit) embedded in the (quantum mechanical) phase space of a quantum harmonic oscillator. Despite the importance of the GKP scheme, existing proposals for the experimental generation of GKP qubits remain
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