Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection

doi:10.1007/s11467-022-1172-3

Front. Phys.

2022, Vol. 17

Issue (5) : 51502 https://doi.org/10.1007/s11467-022-1172-3

RESEARCH ARTICLE

Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection

Yi-Ming Wu, Gang Fan, Fang-Fang Du(

)

Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan 030051, China

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Abstract

We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy (NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are transformed into the detectable failures rather than infidelity based on the heralding mechanism of detectors, a near-unit fidelity of the quantum hyper-Toffoli gate can be implemented. By recycling the procedures, the efficiency of our protocol for the hyper-Toffoli gate is improved further. Meanwhile, the evaluation of gate performance with achieved experiment parameters shows that it is feasible with current experimental technology and provides a promising building block for quantum compute.

Keywords hyperparallel Toffoli gate photon system quantum information processing

Corresponding Author(s): Fang-Fang Du

Issue Date: 30 June 2022

Cite this article:

Yi-Ming Wu,Gang Fan,Fang-Fang Du. Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection[J]. Front. Phys. , 2022, 17(5): 51502.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1172-3
https://academic.hep.com.cn/fop/EN/Y2022/V17/I5/51502

Fig.1 A cavity-NV center system consists of the negatively charged NV center confined in an optical one-sided cavity. The optical transitions from the spin-ground states

| ± 1 ?

to the excited state

| A 2 ?

are coupled by the

| σ ? ?

circularly polarized photons.

Fig.2 Schematic diagram for the hyper-parallel Toffoli gate for a three-photon system in polarized DoF assisted by two NV-cavity systems. CPBS

j

(

j

= 1, 2, 3, 4) represents a circularly polarized beam splitter, which completes the reflection of state

| 0 ? p

and the transmission of state

| 1 ? p

. H

k

(

k

= 1, 2, 3, 4, 5) is a half-wave plate inclined at

22.5 °

, which performs the polarized Hadamard operation, i.e.,

| 0 ? p → (| 0 ? p +

| 1 ? p) / 2, | 1 ? p → (| 0 ? p ? | 1 ? p) / 2

. X performs a qubit-flip operation on the polarized DoF of a photon

[| 0 ? p ? | 1 ? p]

by tilting the half-wave plate at

45 °

. VBS

1

is an adjustable beam splitter with transmission coefficient

(r 1 ? r 0) / 2

and reflection coefficient

1 ? [(r 1 ? r 0) / 2] 2

. Similarly, the transmission and reflection coefficient of VBS

2

are

[(r 1 ? r 0) / 2] 3

and

1 ? [(r 1 ? r 0) / 2] 6

, respectively. D represents a single-photon detector. DL is a delay line, which makes the two wave packets confluent at the same time.

Fig.3 Schematic diagram for the hyper-parallel Toffoli gate for a three-photon system in spatial DoF assisted by two NV-microcavity systems. BS

1

and BS

4

denote 50:50 beam splitter which completes the Hadamard operation of the photon in spatial DoF, i.e.,

| 1 ? c s ? (| 0 ? d s + | 1 ? d s) / 2

. BS

2

and BS

3

complete the operation, i.e.,

| 0 ? d s ? (| 0 ? d s + | 1 ? d s) /

2, | 1 ? d s ? (| 0 ? d s ? | 1 ? d s) / 2

Measurement results	Single-qubit operations

$\| + 1 ? 1 \| + 1 ? 2$	$I a ? I b ? I c$
$\| + 1 ? 1 \| ? 1 ? 2$	$(σ z p) a ? I b ? I c$
$\| ? 1 ? 1 \| + 1 ? 2$	$I a ? (σ z p) b ? I c$
$\| ? 1 ? 1 \| ? 1 ? 2$	$(σ z p) a ? (σ z p) b ? I c$

Tab.1 The measurement results of the two-electron-spin states in NV

1

and NV

2

, and the corresponding feed-forward single-qubit operations on polarized DoF of three photons.

Measurement results	Single-qubit operations

$\| + 1 ? 3 \| + 1 ? 4$	$I a ? I b ? I c$
$\| + 1 ? 3 \| ? 1 ? 4$	$e i π \| 0 ? a s ? I b ? I c$
$\| ? 1 ? 3 \| + 1 ? 4$	$I a ? e i π \| 1 ? b s ? I c$
$\| ? 1 ? 3 \| ? 1 ? 4$	$e i π \| 0 ? a s ? e i π \| 1 ? b s ? I c$

Tab.2 The measurement results of the two-electron-spin states in NV

3

and NV

4

, and the corresponding feed-forward single-qubit operations on polarized DoF of three photons.

Fig.4 Schematic diagram of a hybrid hyper-Toffoli gate.

	$g / κ = 0.5$	$g / κ = 1.5$	$g / κ = 2.4$

$η T$	90.53 $%$	98.90 $%$	99.57 $%$
$η D$	0.01 $%$	$0$	$0$

Tab.3 The efficiency

η T

of the hyper-Toffoli gates and the probability

η D

of D triggered in the block

1

or block

2

vs. the ratio of

g / κ

when

ω c = ω p = ω c

γ = 0.01 κ

Fig.5 The efficiency

η T

of the hyper-Toffoli gates and the probability

η D

of D triggered in the block

1

vs the ratio of

g / κ

when

ω c = ω p = ω c

γ = 0.01 κ

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