Table 1 The comparisons of our CNOT gates with previous photonic implementations.

From: Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity

Type

n i

n p

n QND

|ϕa〉

L

Ps

CNOTp,p in ref. 22

4

2

2

XPM

≈1

CNOTp,p in ref. 23

2

0

1

|α〉

XPM

1/2

CNOTp,s in ref. 51

4

0

1

DXPM

≈1

CNOTp,p in ref. 52

12

1

9

DXPM

≈1

CNOTp,p in ref. 53

5

0

2

DXPM

≈1

CNOTp,p in Fig. 1

8

0

2

DXPM

≈1

CNOTs,s in Fig. 2

8

0

2

DXPM

≈1

CNOTs,p in Fig. 3

10

0

2

DXPM

≈1

CNOTp,s in Fig. 4

8

0

2

DXPM

≈1

CNOTp,s,1 in Fig. 5

10

0

2

DXPM

≈1

  1. Ps denotes the success probability. CNOTp,p denotes the CNOT gate on the polarization DoF of two photons. CNOTp,s,1 denotes the polarization DoF and spatial mode of one photon. CNOTp,s denotes the polarization DoF of one photon and the spatial mode of the other photon. CNOTs,p denotes the spatial DoF of one photon and the polarization DoF of the other photon. CNOTs,s denotes the spatial DoFs of two photons. ni denotes the number of the interaction between the input photon and a coherent state with the cross-Kerr nonlinearities. np denotes the number of ancillary photons. nQND denotes the number of the QND. |ϕa〉 denotes the auxiliary coherent state. L ∈ {DXPM, XPM} denotes the double cross-phase modulation technique or cross-phase modulation technique. CNOTp,p is easily followed by combining with the C-path gate and Merging gate53.
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