Quantum information processing in phase space: A modular variables approach

Ketterer, Andreas; Keller, A.; Walborn, S. P.; Coudreau, Thomas; Milman, P.

doi:10.1103/physreva.94.022325

Cited by 47 publications

(46 citation statements)

References 44 publications

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“…Evaluation of the quantum capacity, however, does not lend explicit encoding and decoding strategies achieving the capac- * kyungjoo.noh@yale.edu ity. In parallel with the characterization of quantum capacity, many bosonic quantum error-correcting codes have also been developed over the past two decades, using a few coherent states [20][21][22][23][24][25], position/momentum eigenstates [26][27][28][29][30][31], finite superpositions of the Fock states [32][33][34][35][36][37][38] of the bosonic modes. Hybrid CV-DV schemes have also been proposed [39,40].…”

Section: Introductionmentioning

confidence: 99%

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Noh

Albert

Jiang

2019

IEEE Trans. Inform. Theory

158

146

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Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide improved upper bounds of Gaussian loss channel capacity, both in the energy-constrained and unconstrained scenarios. We briefly review the Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energy-unconstrained case, that the GKP codes achieve the quantum capacity of Gaussian loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize the entanglement fidelity. The biconvex optimization is solved by an alternating semidefinite programming (SDP) method and we report that, starting from random initial codes, our numerical optimization yields GKP codes as the optimal encoding in a practically relevant regime. arXiv:1801.07271v2 [quant-ph]

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Section: Introductionmentioning

confidence: 99%

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Noh

Albert

Jiang

2019

IEEE Trans. Inform. Theory

158

146

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“…Each popular encoding, for which the computational basis states could be Fock states, coherent states, Cat states, superpositions of squeezed states, or else [8][9][10][11][12][13][14][15][16][17][18][19], has its own strength in, e.g., efficiency of initialisation, error-tolerance, or measurement accuracy. Conventionally, implementing the computing logical processes requires the engineering of dedicated interactions according to the characteristics of the encoding basis, which may require a specific physical setup, i.e.…”

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confidence: 99%

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding

Lau

Plenio

2016

Phys. Rev. Lett.

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Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap-tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the 'hardware' problem of engineering quantum-computing-universal interactions, from the 'software' problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.Introduction-In a wide range of quantum computational tasks, the basic quantity of quantum information is a two-level system that can be prepared in an arbitrary superposition state (qubit) [1]. If the quantum system consists of individually addressable energy eigenstates, such as the internal levels in trapped atoms or the polarisation states of electron spins [2], the qubit bases are most trivially represented by two of such states. On the other hand, there are also quantum systems, such as optical modes [3], mechanical oscillators [4], quantised motion of trapped ions [5], and spin ensembles [6,7], that consist of an abundance of evenly-spaced energy levels. In these systems, usually referred to as continuous-variable (CV) systems, addressing a particular energy eigenstate is usually challenging. There is thus no trivial CV representation of a qubit.

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“…Beginning with the two-mode "dual-rail" encoding in 1995 [5], there are currently several CV codes on the market. One can characterize them by the oscillator basis states that most conveniently expresses the code: Fock/number states {|n } ∞ n=0 [6][7][8][9][10][11][12], position and momentum eigenstates {|x } x∈R and {|p } p∈R [13][14][15][16][17][18], or a few coherent states {|α } α∈S (for some finite set S) [19][20][21][22]. There also exist hybrid schemes which couple an oscillator to other systems [23,24].…”

Section: A Motivation and Outlinementioning

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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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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Quantum information processing in phase space: A modular variables approach

Cited by 47 publications

References 44 publications

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding

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

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