Exact and approximate continuous-variable gate decompositions

Kalajdzievski, Timjan; Quesada, Nicolás

doi:10.22331/q-2021-02-08-394

Cited by 18 publications

(16 citation statements)

References 53 publications

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“…1 A related decomposition in terms of local squeezing between beam splitters is given in Ref. [35]. That decomposition is related to ours through Eq.…”

Section: Teleporation-based Gkp Error Correctionmentioning

confidence: 92%

Streamlined quantum computing with macronode cluster states

Walshe,

Alexander,

Menicucci

et al. 2021

Preprint

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Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster states, whose construction is defined by a fixed, low-depth beam splitter network, we show that a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. We give explicit recipes to realize the Clifford generating set, and we calculate the logical gate-error rates given finite squeezing in the cluster-state and GKP resources. We find that logical error rates of 10 −2 -10 −3 , compatible with the thresholds of topological codes, can be achieved with squeezing of 11.9-13.7 dB. The protocol presented eliminates noise present in prior schemes and puts the required squeezing for fault tolerance in the range of current state-of-the-art optical experiments. Finally, we show how to produce distillable GKP magic states directly within the cluster state.

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“…1 A related decomposition in terms of local squeezing between beam splitters is given in Ref. [35]. That decomposition is related to ours through Eq.…”

Section: Teleporation-based Gkp Error Correctionmentioning

confidence: 92%

Streamlined quantum computing with macronode cluster states

Walshe,

Alexander,

Menicucci

et al. 2021

Preprint

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“…The concept of Boson Sampling holds the potential of experimentally extracting the permanent of a matrix instead of calculating it, by sampling boson-based quantum states, according to Equation 1. This, however, presents some practical problems in the case of Boson Sampling, namely (1) the difficulty of generating and manipulating single photon distributions [11] and (2) the practical complexity of significantly sampling high-dimensional quantum states [12][13][14].…”

Section: The Permanent Of a Matrixmentioning

confidence: 99%

Gaussian Boson Sampling Compilation

Alarcon

Rueda

2022

Preprint

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Gaussian Boson Sampling is gaining relevance among the multiple technologies currently implementing quantum computing. The problem of sampling out of a boson distribution across multiple modes has a strong mathematical connection with combinatorics problems, with multiple practical applications that would classically be unfeasible to solve within reasonable time. The software stack that accompanies this GBS approach, and that takes the application from its high level description to the hardware implementation, is the main focus of this paper. The general compilation process of Gaussian Boson Samplers is described in detail. The specifics of the Strawberry Fields (Xanadu) compilation and simulation framework are discussed, along with its time profiling, and time implications on computationally significant problem sizes. Last, a compilation step to reduce the hardware description complexity is presented, demonstrating a linear reduction on the overall number of operators when the number of Gaussian operators increases.

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“…Phase gate The CV quadratic phase gate P (s) is just a squeezing gate Ŝ(re iφ ) composed with a rotation gate R(θ). The ideal decomposition is given by [19,83] P (s) = R(θ) Ŝ(re iφ ), θ = tan −1 s 2 , φ = −sign(s)…”

Section: Gates That Employ Inline Squeezingmentioning

confidence: 99%

Fast Simulation of Bosonic Qubits via Gaussian Functions in Phase Space

et al. 2021

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Bosonic qubits are a promising route to building fault-tolerant quantum computers on a variety of physical platforms. Studying the performance of bosonic qubits under realistic gates and measurements is challenging with existing analytical and numerical tools. We present a novel formalism for simulating classes of states that can be represented as linear combinations of Gaussian functions in phase space. This formalism allows us to analyze and simulate a wide class of non-Gaussian states, transformations and measurements. We demonstrate how useful classes of bosonic qubits-Gottesman-Kitaev-Preskill (GKP), cat, and Fock states-can be simulated using this formalism, opening the door to investigating the behaviour of bosonic qubits under Gaussian channels and measurements, non-Gaussian transformations such as those achieved via gate teleportation, and important non-Gaussian measurements such as threshold and photon-number detection. Our formalism enables simulating these situations with levels of accuracy that are not feasible with existing methods. Finally, we use a method informed by our formalism to simulate circuits critical to the study of fault-tolerant quantum computing with bosonic qubits but beyond the reach of existing techniques. Specifically, we examine how finite-energy GKP states transform under realistic qubit phase gates; interface with a CV cluster state; and transform under non-Clifford T gate teleportation using magic states. We implement our simulation method as a part of the open-source Strawberry Fields Python library.

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Exact and approximate continuous-variable gate decompositions

Cited by 18 publications

References 53 publications

Streamlined quantum computing with macronode cluster states

Streamlined quantum computing with macronode cluster states

Gaussian Boson Sampling Compilation

Fast Simulation of Bosonic Qubits via Gaussian Functions in Phase Space

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