Subsystem analysis of continuous-variable resource states

Pantaleoni, Giacomo; Baragiola, Ben Q.; Menicucci, Nicolas C.

doi:10.1103/physreva.104.012430

“…Notable exceptions are positionor momentum-squeezed vacuum states, which are often used in combination with GKP states to produce hybrid cluster states for use in fault-tolerant architectures [20,26,33]. These Gaussian states instead yield undistillable encoded states that are close to Pauli eigenstates [44], so a different type of Gaussian state must be used instead.…”

Section: Magic Statesmentioning

confidence: 99%

Streamlined quantum computing with macronode cluster states

Walshe

¹

,

Alexander

²

,

Menicucci

³

et al. 2021

Self Cite

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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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“…We can evaluate the PDF of a rotated and squeezed realistic GKP state using similar techniques to the case of the ideal GKP states. We know that it is possible to write the wave function of the realistic GKP states in the form [56,57]…”

Section: F1 Pdf Of a Rotated And Squeezed Realistic Gkp Statementioning

confidence: 99%

Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits

Calcluth

¹

,

Ferraro

²

,

Ferrini

³

2022

Quantum

9

0

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We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable.

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“…Notable exceptions are positionor momentum-squeezed vacuum states, which are often used in combination with GKP states to produce hybrid cluster states for use in fault-tolerant architectures [20,26,41]. These Gaussian states instead yield undistillable encoded states that are close to Pauli eigenstates [42], so a different type of Gaussian state must be used instead.…”

Section: Magic Statesmentioning

confidence: 99%

Streamlined quantum computing with macronode cluster states

Walshe,

Alexander,

Menicucci

et al. 2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

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.

show abstract

Subsystem analysis of continuous-variable resource states

Cited by 13 publications

References 51 publications

Streamlined quantum computing with macronode cluster states

Streamlined quantum computing with macronode cluster states

Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits

Streamlined quantum computing with macronode cluster states

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