Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Continuous variable encoding by ponderomotive interaction

Stefano Pirandola, Mancini, S, Vitali, D, Tombesi, P

Published Mar 1, 2005• 17 citations
OpenAlex

Abstract

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.

Related papers

Preparing encoded states in an oscillator

B. C. Travaglione, Gerard J Milburn

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

arXiv:quant-ph/0205114•Physical Review A•Nov 22, 2002•68 citations

Generating continuous variable quantum codewords in the near-field atomic lithography

Stefano Pirandola, Stefano Mancini, David Vitali +1 more

Recently, D. Gottesman et al. [Phys. Rev. A 64, 012310 (2001)] showed how to encode a qubit into a continuous variable quantum system. This encoding was realized by using non-normalizable quantum codewords, which therefore can only be approximated in any real physical setup. Here we show how a neutral atom, falling through an optical cavity and interacting with a single mode of the intracavity electromagnetic field, can be used to safely encode a qubit into its external degrees of freedom. In fact, the localization induced by a homodyne detection of the cavity field is able to project the near-field atomic motional state into an approximate quantum codeword. The performance of this encoding process is then analyzed by evaluating the intrinsic errors induced in the recovery process by the approximated form of the generated codeword.

arXiv:quant-ph/0510053•Journal of Physics B Atomic Molecular and Optical Physics•Feb 1, 2006•33 citations

Encoding a qubit in an oscillator

Daniel Gottesman, Alexei Kitaev, John P. Preskill

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.

arXiv:quant-ph/0008040•Physical Review A•Jun 11, 2001•1,525 citations

Continuous variables error correction with integrated biphoton frequency combs

Nicolas Fabre, G. Maltese, Félicien Appas +8 more

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.

•Apr 2, 2019•2 citations

Quantum Error Correction in Continuous-Variable System

Warit Asavanant, Akira Furusawa

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.

•Jan 25, 2022•1 citation

Constructing finite-dimensional codes with optical continuous variables

Stefano Pirandola, Stefano Mancini, David Vitali +1 more

We show how a qubit can be fault-tolerantly encoded in the infinite-dimensional Hilbert space of an optical mode. The scheme is efficient and realizable with present technologies. In fact, it involves two travelling optical modes coupled by a cross-Kerr interaction, initially prepared in coherent states, one of which is much more intense than the other. At the exit of the Kerr medium, the weak mode is subject to a homodyne measurement and a quantum codeword is conditionally generated in the quantum fluctuations of the intense mode.

arXiv:quant-ph/0402202•Europhysics Letters (EPL)•Oct 19, 2004•69 citations
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.
Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.
Recently, D. Gottesman et al. [Phys. Rev. A 64, 012310 (2001)] showed how to encode a qubit into a continuous variable quantum system. This encoding was realized by using non-normalizable quantum codewords, which therefore can only be approximated in any real physical setup. Here we show how a neutral atom, falling through an optical cavity and interacting with a single mode of the intracavity electromagnetic field, can be used to safely encode a qubit into its external degrees of freedom. In fact, the localization induced by a homodyne detection of the cavity field is able to project the near-field atomic motional state into an approximate quantum codeword. The performance of this encoding process is then analyzed by evaluating the intrinsic errors induced in the recovery process by the approximated form of the generated codeword.
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.
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.
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.
We show how a qubit can be fault-tolerantly encoded in the infinite-dimensional Hilbert space of an optical mode. The scheme is efficient and realizable with present technologies. In fact, it involves two travelling optical modes coupled by a cross-Kerr interaction, initially prepared in coherent states, one of which is much more intense than the other. At the exit of the Kerr medium, the weak mode is subject to a homodyne measurement and a quantum codeword is conditionally generated in the quantum fluctuations of the intense mode.