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Continuous variables error correction with integrated biphoton frequency combs

Nicolas Fabre, G. Maltese, Félicien Appas, Simone Felicetti, Andreas Ketterer, Arne Keller, T. Coudreau, F. Baboux, Maria I. Amanti, S. Ducci, P. Milman

Published Apr 2, 2019• 2 citations
OpenAlex

Abstract

Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman, Kitaev and Preskill in Phys. Rev. A \textbf{64} 012310, (2001). We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We experimentally illustrate our results using an integrated AlGaAs photon pairs source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.

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Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman, Kitaev and Preskill in Phys. Rev. A \textbf{64} 012310, (2001). We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We experimentally illustrate our results using an integrated AlGaAs photon pairs source. We show how single qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed by Gottesman et al. [Phys. Rev. A 64 012310 (2001)]. We show how to experimentally implement this encoding using time-frequency continuous degrees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how single-qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in circuit-like and measurement-based architectures.
Encoding quantum information in continuous variables is intrinsically faulty. Nevertheless, redundant qubits can be used for error correction, as proposed in [1]. We show how to experimentally implement this encoding using time-frequency continuous de- grees of freedom of photon pairs produced by spontaneous parametric down conversion. We illustrate our results using an integrated AlGaAs photon-pair source. We show how sin- gle qubit gates can be implemented and finally propose a theoretical scheme for correcting errors in a circuit-like and in a measurement-based architecture.
Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.
On the physical level, digital computers are not error free. However, by adding the redundancy and using the error-correction technique, the errors on the computational level can be mitigated to the point that the probability of error occurring is negligible for most tasks. In quantum computation, a similar strategy can be employed. Here, a main difference between classical computer and quantum computer is that the quantum error correction needs to mitigate the errors, while maintaining the quantum coherence. In this chapter, we will first discuss the conceptual ideas of how to implement quantum error correction and achieve fault tolerance in the continuous-variable system. In the case of the continuous-variable system, we need to first encode the information using a logical qubit which, in a sense, digitize the broad Hilbert space. We will give some examples of the logical qubits and then discuss a particular type of encoding called Gottesman-Kitaev-Preskill (GKP) qubit, which is one of the currently most promising encoding.
Recently it has been proposed to construct quantum error-correcting codes that embed a finite-dimensional Hilbert space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables [D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001)]. The main difficulty of this continuous variable encoding relies on the physical generation of the quantum codewords. We show that ponderomotive interaction suffices to this end. As a matter of fact, this kind of interaction between a system and a meter causes a frequency change on the meter proportional to the position quadrature of the system. Then, a phase measurement of the meter leaves the system in an eigenstate of the stabilizer generators, provided that system and meter's initial states are suitably prepared. Here we show how to implement this interaction using either travelling or trapped atoms, and how the encoding can be performed on their motional degrees of freedom. The robustness of the codes with respect to the various experimental imperfections is then carefully analyzed.
GKP states, introduced by Gottesman, Kitaev, and Preskill, are continuous variable logical qubits that can be corrected for errors caused by phase space displacements. Their experimental realization is challenging, in particular, using propagating fields, where quantum information is encoded in the quadratures of the electromagnetic field. However, traveling photons are essential in many applications of GKP codes involving the long-distance transmission of quantum information. We introduce a new method for encoding GKP states in propagating fields using single photons, each occupying a distinct auxiliary mode given by the propagation direction. The GKP states are defined as highly correlated states described by collective continuous modes, as time and frequency. We analyze how the error detection and correction protocol scales with the total photon number and the spectral width. We show that the obtained code can be corrected for displacements in time-frequency phase space, which correspond to dephasing, or rotations, in the quadrature phase space and to photon losses. Most importantly, we show that generating two-photon GKP states is relatively simple, and that such states are currently produced and manipulated in several photonic platforms where frequency and time-bin biphoton entangled states can be engineered.