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On construction of quantum logical gates with a general beam splitting by Fichtner-Freudenberg expression

Keita Kohira, Noboru Watanabe

Published Jul 6, 2015• 0 citations
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In usual computer, there is an upper bound of computational speed because of irreversibility of logical gate.In order to avoid this demerit, Fredkin and Tof- foli [3] proposed a conservative logical gate.After that, Milburn [4] constructed a physical model of reversible quantum gate with beam splittings and a Kerr medium.This model is called FTM (Fredkin $-$ Toffoli $-$ Milburn gate) in this paper.This FTM gate was described by the quantum channel and the efficiency of information transmission of the FTM gate was discussed in [10].FTM gate is using a photon number state as an input state for control gate.The photon number state might be difficult to realize physically.In this paper, we introduced a new device on symmetric Fock space in order to avoid this difficulty.In Section 1, we briefly review noisy quantum channels and generalized beam splittings.In Section 2, we explain the quantum channel for FTM gate based on the notation of Section 1.In Section 3, we intruduced a new operator on symmetric Fock space and discuss the truth table for our new gate.

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Note on Logical Gates by Gauge Field Formalism of Quantum Error Correction

Junichi Haruna

The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank-Shor-Steane (CSS) codes. In this work, we extend this framework to construct a broad class of logical gates for general CSS codes, including the S, Hadamard, T, and (multi)controlled-Z gates, under the condition where fault-tolerance or circuit-depth optimality is not necessarily imposed. We show that these logical gates can be expressed as exponentials of polynomial functions of the electric and magnetic gauge fields, which allows us to derive explicit decompositions into physical gates. We further prove that their logical action depends only on the (co)homology classes of the corresponding logical qubits, establishing consistency as logical operations. Our results provide a systematic method for formulating logical gates for general CSS codes, offering new insights into the interplay between quantum error correction, algebraic topology, and quantum field theory.

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QUANTUM LOGICAL GATES REALIZED BY BEAM SPLITTINGS

Wolfgang Freudenberg, Masanori Ohya, NATALIYA TURCHINA +1 more

•Mar 1, 2006•0 citations
In usual computer, there is an upper bound of computational speed because of irreversibility of logical gate.In order to avoid this demerit, Fredkin and Tof- foli [3] proposed a conservative logical gate.After that, Milburn [4] constructed a physical model of reversible quantum gate with beam splittings and a Kerr medium.This model is called FTM (Fredkin −-− Toffoli −-− Milburn gate) in this paper.This FTM gate was described by the quantum channel and the efficiency of information transmission of the FTM gate was discussed in [10].FTM gate is using a photon number state as an input state for control gate.The photon number state might be difficult to realize physically.In this paper, we introduced a new device on symmetric Fock space in order to avoid this difficulty.In Section 1, we briefly review noisy quantum channels and generalized beam splittings.In Section 2, we explain the quantum channel for FTM gate based on the notation of Section 1.In Section 3, we intruduced a new operator on symmetric Fock space and discuss the truth table for our new gate.
The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank-Shor-Steane (CSS) codes. In this work, we extend this framework to construct a broad class of logical gates for general CSS codes, including the S, Hadamard, T, and (multi)controlled-Z gates, under the condition where fault-tolerance or circuit-depth optimality is not necessarily imposed. We show that these logical gates can be expressed as exponentials of polynomial functions of the electric and magnetic gauge fields, which allows us to derive explicit decompositions into physical gates. We further prove that their logical action depends only on the (co)homology classes of the corresponding logical qubits, establishing consistency as logical operations. Our results provide a systematic method for formulating logical gates for general CSS codes, offering new insights into the interplay between quantum error correction, algebraic topology, and quantum field theory.