Constructing the nearly deterministic Toffoli polarization gate with the spatial degree of freedom based on weak cross-Kerr nonlinearities

Xiu, Xiao‐Ming; Cui, Cen; Geng, Xue; Li, Qingyang; Dong, Hai-Kuan; Dong, Li; Gao, Yunzhi

doi:10.1016/j.optcom.2018.05.060

Cited by 11 publications

(9 citation statements)

References 69 publications

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“…[] and [], while

2^{n} - 1

and

n \cdot 2^{n - 1}

are needed for control‐path process and output process in the scheme of ref. []. Although the number of BS processes of the target photon in the present scheme (

2^{n} - 1

and

n \cdot 2^{n - 1}

for control‐path process and output process) is not less than the former three ones, the number of BSs applied in the present scheme ( n and n for control‐path process and output process) is reduced from exponential order to linear order of n .…”

Section: Discussion and Summarymentioning

confidence: 87%

“…In Table , we compare the physical resources and the optical elements needed in three schemes with the present one. Based on the spatial and polarization degrees of freedom, the number of spatial paths of the target photon is 2 n in the former three schemes, while it is 2 in the present scheme with the help of the temporal degree of freedom.…”

Section: Discussion and Summarymentioning

confidence: 99%

“…However, one BS and one BS process for coherent state interference process needs to be introduced in order to save one coherent state. Taking the two‐photon controlled one‐photon unitary gate as an example, four paths and seven BSs for the target photon are necessary if just the spatial degree of freedom as an assistance is exploited . However, only two paths and four BSs are needed to complete the same task when the spatial, temporal, and polarization degrees of freedom are applied …”

Section: Discussion and Summarymentioning

confidence: 99%

“…After measurement on the coherent state, such as X measurement, and appropriate feed‐forward operations (phase shift and swap gate operation illustrated in Figure b) need to be performed according to the measurement outcomes, the state of the control photon C 1 and the target photon T will become

\begin{matrix} true \\ right a_{1} {false| H false⟩}_{C_{1}} {false| ϕ false⟩}_{T_{1}, t} + b_{1} {false| V false⟩}_{C_{1}} {false| ϕ false⟩}_{T_{2}, t} \end{matrix}

which is a spatial and polarization entangled state of the control photon C 1 and the target photon T .…”

Section: A Polarization Multiphoton Controlled One‐photon Unitary Gatmentioning

confidence: 99%

“…Besides two‐photon quantum gates, some three‐photon quantum gates are also the reversible and universal logic gates for quantum computation, such as a Fredkin gate and a Toffoli gate . Assisted by strong and weak cross‐Kerr nonlinearities, the Fredkin gate and the Toffoli gate with high success probability can be constructed, where the spatial degree of freedom is applied to assist their construction. Relying on the assistance of the spatial degree of freedom, multiphoton polarization controlled logic gates attract much attention …”

Section: Introductionmentioning

confidence: 99%

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Construction of a Polarization Multiphoton Controlled One‐Photon Unitary Gate Assisted by the Spatial and Temporal Degrees of Freedom

et al. 2019

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In order to fulfill quantum information processing tasks such as quantum computation and scalable quantum networks, quantum logic gates are indispensable parts. A multiqubit logic gate can efficiently reduce the cost of physical resources and complicated operations that are necessary in the combination of fewer-qubit (e.g., two-qubit) logic gates to fulfill the same tasks. However, the construction of multiphoton quantum logic gates is a large challenge. Assisted by spatial and temporal degrees of freedom, a polarization multiphoton controlled one-photon unitary gate is proposed, which can be realized with three processes including the control-path process based on weak cross-Kerr nonlinearities, the unitary transformation process, and the output process. In the control-path process, the control-path modules are applied, where the entanglement between polarization, spatial and temporal degrees of freedom is generated by beam splitters, time delayers, and nonlinear interaction in cross-Kerr media. The scheme presented here, assisted by spatial and temporal degrees of freedom reduces the experimental complexity of the schemes assisted by only spatial degree of freedom. Moreover, it will also be a useful reference in optimally constructing multiqubit quantum logic gates with other multiple degrees of freedom in many physical systems.variety of physical systems in the theoretical aspect [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and experimental aspect. [21][22][23][24][25][26] Photons are the promising carriers of quantum information due to their advantages, fast propagation, low decoherence, ease to manipulate, etc. [27] However, owing to weak photon-photon interaction, quantum logic gates at the single-photon level had made slow progress. [22] The linear optics standard model proposed by Knill et al. [28] had changed this unclear situation, while its upper limitation of success probability is less than unity. [29] Furthermore, by using nonlinear optical interaction such as cross-Kerr interaction, the threshold on the success probability imposed by the linear optics standard model could be broken through. [30] Due to tiny strength of nonlinear interaction, the direct applications of cross-Kerr nonlinearities have not been easily realized. To achieve feasibility of deterministic quantum logic gates, weak cross-Kerr nonlinearities were applied first in the two-photon controllednot gate using an auxiliary photon, [31] which approaches the success probability nearly close to unity. After that, many construction schemes of twophoton logic gates based on weak cross-Kerr nonlinearities were proposed, for instance, the controlled-not gate with half unity success probability without an auxiliary photon, [32] the controllednot gate, [33] and the controlled-phase gate [34] with nearly unity success probability without the auxiliary photon, quantum logic gates [35] composed by control-path gate and merging gate. On the other hand, weak cross-Kerr nonlinearities were also used in the Bell states analys...

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“…[] and [], while

2^{n} - 1

and

n \cdot 2^{n - 1}

are needed for control‐path process and output process in the scheme of ref. []. Although the number of BS processes of the target photon in the present scheme (

2^{n} - 1

and

n \cdot 2^{n - 1}

Section: Discussion and Summarymentioning

confidence: 87%

Section: Discussion and Summarymentioning

confidence: 99%

Section: Discussion and Summarymentioning

confidence: 99%

\begin{matrix} true \\ right a_{1} {false| H false⟩}_{C_{1}} {false| ϕ false⟩}_{T_{1}, t} + b_{1} {false| V false⟩}_{C_{1}} {false| ϕ false⟩}_{T_{2}, t} \end{matrix}

which is a spatial and polarization entangled state of the control photon C 1 and the target photon T .…”

Section: A Polarization Multiphoton Controlled One‐photon Unitary Gatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Construction of a Polarization Multiphoton Controlled One‐Photon Unitary Gate Assisted by the Spatial and Temporal Degrees of Freedom

et al. 2019

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High‐Fidelity and Low‐Cost Hyperparallel Quantum Gates for Photon Systems via Λ‐Type Systems

Fan

et al. 2022

Annalen der Physik

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Quantum gates designed with minimized resources overhead have a crucial role in quantum information processing. Here, based on the degrees of freedom (DoFs) of photons and 𝚲-type atom systems, two high-fidelity and low-cost protocols are presented for realizing polarization-spatial hyperparallel controlled-not (CNOT) and Toffoli gates on photon systems with only two and four two-qubit polarization-polarization swap (P-P-SWAP) gates in each DoF, respectively. Moreover, the quantum gates can be extended feasibly to construct 2m-target-qubit hyperparallel CNOT and 2n-control-qubit Toffoli gates required only 4m and 4n P-P-SWAP gates on (m + 1)-and (n + 1)-photon systems, respectively, which dramatically lower the costs and bridge the divide between the theoretical lower bounds and the current optimal syntheses for the photonic quantum computing. Further, the unique auxiliary atom of these quantum gates can be regarded as a temporary quantum memory that requires no initialization and measurement, and is reused within the coherence time, as the state of the atom remains unchanged after the hyperparallel quantum computing.

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Refined Quantum Gates for Λ‐Type Atom‐Photon Hybrid Systems

Fan

2023

Adv Quantum Tech

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High‐efficiency quantum information processing is equivalent to the fewest quantum resources and simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three‐level Λ‐type atom‐cavity system, the authors present some refined protocols for realizing controlled‐not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of gates is encoded on a flying photon, and the remaining qubits are encoded on the atoms in the optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi‐qubit CNOT, Fredkin, and Toffoli gates with optical elements without auxiliary photons or atoms. Further, the simplest single‐qubit operations are applied to the photon only, which make these logic gates experimentally feasible with current technology.

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Constructing the nearly deterministic Toffoli polarization gate with the spatial degree of freedom based on weak cross-Kerr nonlinearities

Cited by 11 publications

References 69 publications

Construction of a Polarization Multiphoton Controlled One‐Photon Unitary Gate Assisted by the Spatial and Temporal Degrees of Freedom

Construction of a Polarization Multiphoton Controlled One‐Photon Unitary Gate Assisted by the Spatial and Temporal Degrees of Freedom

High‐Fidelity and Low‐Cost Hyperparallel Quantum Gates for Photon Systems via Λ‐Type Systems

Refined Quantum Gates for Λ‐Type Atom‐Photon Hybrid Systems

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