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arXiv:2105.10631 · Advanced Quantum Technologies

Universal Quantum Multi‐Qubit Entangling Gates with Auxiliary Spaces

Wen‐Qiang Liu, Hai‐Rui Wei, L. C. Kwek

Published Mar 18, 2022• 30 citations
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Abstract

Abstract Universal quantum entangling gates are a crucial building block in the large‐scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled‐NOT (CNOT) gate is constructed by introducing a non‐computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n ‐control‐qubit Toffoli gate with qubit–qudit gates and single‐qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.

DOI
10.1002/qute.202100136

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Minimizing the number of necessary two-qubit gates is an important task in quantum information processing. By introducing non-computational quantum states in auxiliary spaces, we construct effective circuits for the controlled-NOT (CNOT) gate and the n-control-qubit Toffoli gate with (2n-1) qubit-qudit gates and (2n-2) single-qudit gates. We propose the polarization CNOT and Toffoli gates based on the designed quantum circuits in linear optics by operating on the spatial-mode degree of freedom of photons. Our optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.
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Abstract Quantum gates are the essential block for quantum computers. High‐dimensional quantum gates exhibit remarkable advantages over their 2D counterparts for some quantum information processing tasks. Here, a family of entanglement‐based optical controlled‐SWAP gates on is presented. With the hybrid encoding, the control qubits and target qudits are encoded in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only () linear optics, beating an earlier result of 14 linear optics with . The circuit depth five is much lower than an earlier result of 11 with . Besides, the fidelity of the presented circuit can reach 99.4%, and it is higher than the previous counterpart with . The scheme is constructed in a deterministic way without any borrowed ancillary photons or measurement‐induced nonlinearities. Moreover, the approach allows .
Quantum gates are the essential block for quantum computer. High-dimensional quantum gates exhibit remarkable advantages over their two-dimensional counterparts for some quantum information processing tasks. Here we present a family of entanglement-based optical controlled-SWAP gates on C2⊗Cd⊗Cd\mathbb{C}^{2}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}C2⊗Cd⊗Cd. With the hybrid encoding, we encode the control qubits and target qudits in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only (2+3d)(2+3d)(2+3d) (d≥2d\geq 2d≥2) linear optics, beating an earlier result of 14 linear optics with d=2d=2d=2. The circuit depth 5 is much lower than an earlier result of 11 with d=2d=2d=2. Besides, the fidelity of the presented circuit can reach 99.4\%, and it is higher than the previous counterpart with d=2d=2d=2. Our scheme are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Moreover, our approach allows d>2d>2d>2.
Abstract 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 ‐ and ‐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.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to their relatively easy manipulation and realization. We present efficient schemes to implement controlled-not (cnot) gates and controlled-swap (Fredkin) gates by using solely linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd level), respectively. On the basis of the hybrid encoding, cnot and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a cnot gate has been reduced to one polarizing beam splitter, while only ddd polarizing beam splitters are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to 1 and and are dimension independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7% under realistic conditions, which is higher than in previous schemes.