Cat Codes with Optimal Decoherence Suppression for a Lossy Bosonic Channel

Li, Linshu; Zou, Chang‐Ling; Albert, Victor V.; Muralidharan, Sreraman; Girvin, S. M.; Jiang, Liang

doi:10.1103/physrevlett.119.030502

Cited by 108 publications

(108 citation statements)

References 66 publications

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“…For even d, instead of utilizing the entire d-dimensional space for each ∆ to store information, one can define the twodimensional subspace µ ∈ {0, d /2} as the new logical qubit and use the complementary subspace to protect said qubit from higher-weight errors. (In the single mode case, a more judicious choice of qubit suppresses errors even more [30]; the same is likely true here, but this is outside the scope of this paper.) For example, the generalized states for M = 2, obtained by taking |µ γ,∆ (3.12) and substituting 2n + µ −→ (S + 1)(2n + µ) , (5.11) (a) (b) Figure 4.…”

Section: B Multimode Generalizationmentioning

confidence: 71%

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Pair-cat codes: autonomous error-correction with low-order nonlinearity

Albert

Mundhada

Grimm

et al. 2019

Quantum Sci. Technol.

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We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode cat-qubit counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a twodimensional complex plane, instead of the full four-dimensional two-mode phase space. The twomode codes are generalized to multiple modes in an extension of the stabilizer formalism to nondiagonalizable stabilizers. The M -mode codes can protect against either arbitrary photon losses in up to M − 1 modes or arbitrary losses and gains in any one mode.

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Section: B Multimode Generalizationmentioning

confidence: 71%

“…In an alternative scenario, the recovery channel in Ref. [30] can be implemented after the state has evolved under photon loss for finite κ a t. Such a channel can be implemented continuously via the procedure in Sec. III.D of Ref.…”

Section: Loss Errorsmentioning

confidence: 99%

Pair-cat codes: autonomous error-correction with low-order nonlinearity

Albert

Mundhada

Grimm

et al. 2019

Quantum Sci. Technol.

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“…If a quantum error correction code allows reduction of the order of this error to γ t+1 , we say that the quantum code corrects t AD errors. Unsurprisingly, there has been extensive work on quantum error correction codes specialized against correcting amplitude damping errors [15,12,16,17,18,19,20,21,22]. Of special note are some previously constructed constant-excitation quantum codes that do offer immunity against the natural dynamics of quantum harmonic oscillators [12,23,24].…”

Section: Introductionmentioning

confidence: 99%

Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping

Ouyang

Chao

2020

IEEE Trans. Inform. Theory

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The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors which model photon loss. Although considerable research has been devoted to quantum error correcting codes for amplitude damping, not so much attention has been paid to having these codes simultaneously lie within the decoherence free subspace of their underlying physical system. One common physical system comprises of quantum harmonic oscillators, and constantexcitation quantum codes can be naturally stabilized within them. The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes. To construct such quantum codes, we use the nullspace of a specially constructed matrix based on integer partitions. arXiv:1809.09801v3 [quant-ph]

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“…Production of multicomponent states of the first class has been proposed for cavity field [26], but not yet reported. These states are highly important for studying decoherence [29], and for application in quantum computation with qudits, quantum systems with the number of levels higher than two [30,31].…”

Section: Introductionmentioning

confidence: 99%

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

Horoshko

Patera

Kolobov

2019

Optics Communications

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Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schrödinger cat" state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. We show that these states are generalizations of Bell states of two qubits to the case of N-level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that using a state of this class as a shared resource, one can teleport a superposition of coherent states on the circle (a qudit). Differently from some other existing protocols of quantum teleportation, the proposed protocol provides the unit fidelity for all input states of the qudit. We calculate the probability of success for this type of teleportation and show that it approaches unity for the average number of photons in one component above N 2 . Thus, the teleportation protocol can be made unit-fidelity and deterministic at finite resources.

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Cat Codes with Optimal Decoherence Suppression for a Lossy Bosonic Channel

Cited by 108 publications

References 66 publications

Pair-cat codes: autonomous error-correction with low-order nonlinearity

Pair-cat codes: autonomous error-correction with low-order nonlinearity

Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

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