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IEEE International Conference on Solid-State and Integrated Circuit Technology

A novel optimization methodology based on Genetic Algorithm for gain-boosted OPAMP

Xiaomu Wang, Zhaohua Zhang, Litian Liu, Tian‐Ling Ren

Published Oct 1, 2008• 0 citations
Publisher

Abstract

Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (w-input parity check) gate plus at most 2 m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.

DOI
10.1109/icsict.2008.4734891

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Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (w-input parity check) gate plus at most 2 m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.
The Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (n-input parity check) gate plus at most 2m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.
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.
Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the two-qubit controlled-sign [or controlled NOT (CNOT)] gate, we provide numerical evidence that the maximum success rate is S=2/27S=2/27S=2/27 using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the three-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons---less than in any existing scheme---with a maximum S=0.003 40S=0.003\text{ }40S=0.003 40. This compares well to $S={(2/27)}^{2}/2\ensuremath{\approx}0.002\text{ }74$, obtainable by combining two CNOT gates and a passive quantum filter [T. C. Ralph, K. J. Resch, and A. Gilchrist, Phys. Rev. A 75, 022313 (2007)]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [M. M. Wilde and D. B. Uskov, Phys. Rev. A 79, 022305 (2009); G. A. Durkin and J. P. Dowling, Phys. Rev. Lett. 99, 070801 (2007)].
Multi-bit Toffoli gates form an essential quantum gate class for quantum algorithms. They should be efficiently decomposed into elementary single- or multi-qubit quantum gates, such as CNOT, T, and Hadarmard, for a scalable implementation of a quantum algorithm. We propose an engineering method for the practical synthesis of a multi-bit Toffoli gate. Two optimization models and their closed-form solutions are presented for optimal decomposition of the multi-bit Toffoli gate. These models are based on linearized multi-objective integer programming with parameters such as the number of target ancillae, ancillae states, and basis gates. The proposed method supports the systematic handling of quantum circuit constraints, including the total number of available qubits and maximum circuit depth, which depend on various quantum hardware specifications. Our approach exhibits promise in the noisy intermediate-scale quantum environment by providing a rapid and optimal method for synthesizing multi-bit Toffoli gates in diverse and unpredictable quantum hardware specifications.
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.