Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps

Ghose, Shohini; Sanders, Barry C.

doi:10.1080/09500340601101575

Cited by 94 publications

(90 citation statements)

References 30 publications

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“…For our first protocol, we exploit the idea that it is possible to induce a non-Gaussian evolution on an input state by coupling it with a non-Gaussian resource [7,8,17,23,24]. For instance, the cubic phase gate may be implemented with the help of the so-called cubic phase state…”

Section: Methods 1: Photon Subtracted Ancillamentioning

confidence: 99%

“…(8). However, the vectors m span a continuous space, hence it is not possible to post-select on a single vector, as the probability of a realization of a single vector is zero.…”

Section: A Derivation Of the Effective Transformationmentioning

confidence: 99%

“…Non-Gaussian gates are the most challenging to implement. Former experimental proposals for their implementation [7] require resources currently out of technological reach [8]. Yet, it has been proven that the use of at least one non-Gaussian operation is necessary in order to build algorithms that could not be efficiently simulated on a classical computer [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

2017

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In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.

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Section: Methods 1: Photon Subtracted Ancillamentioning

confidence: 99%

“…(8). However, the vectors m span a continuous space, hence it is not possible to post-select on a single vector, as the probability of a realization of a single vector is zero.…”

Section: A Derivation Of the Effective Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

2017

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“…The quality of the cubic phase state depends on the photon number measured. This is investigated further in [34]. 4.…”

Section: Types Of Encodings Into Optical Statesmentioning

confidence: 99%

Models of optical quantum computing

Krovi

2017

Nanophotonics

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I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

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“…More recently, however, there has emerged considerable interest in non-Gaussian states [22][23][24][25][26][27][28][29][30][31][32][33]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and nonclassicality for multimode radiation-field states

et al. 2011

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Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multi-mode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beamsplitters, in a transparent manner.For single mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beamsplitter, these conditions turn exactly into signatures of NPT entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beamsplitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beamsplitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

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Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps

Cited by 94 publications

References 30 publications

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

Models of optical quantum computing

Entanglement and nonclassicality for multimode radiation-field states

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