Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

The exponential speed up of quantum algorithms and the fundamental limits of current CMOS process for future design technology have directed attentions toward quantum circuits. In this paper, the matrix specification of a broad category of quantum circuits, i.e. CNOT-based circuits, are investigated. We prove that the matrix elements of CNOT-based circuits can only be zeros or ones. In addition, the columns or rows of such a matrix have exactly one element with the value of 1.Furthermore, we show that these specifications can be used to synthesize CNOT-based quantum circuits. In other words, a new scheme is introduced to convert the matrix representation into its SOP equivalent using a novel quantum-based Karnaugh map extension. We then apply a search-based method to transform the obtained SOP into a CNOT-based circuit. Experimental results prove the correctness of the proposed concept. J n n n J n J n J n J n J n n J J J J J n n J J J J

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Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis

Saeedi

Zamani

Sedighi

2007

10th Euromicro Conference on Digital System Design Architectures, Methods and Tools (DSD 2007)

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Quantum Machine Learning Based on Minimizing Kronecker-Reed-Muller Forms and Grover Search Algorithm with Hybrid Oracles

Lee¹,

Perkowski

2016

2016 Euromicro Conference on Digital System Design (DSD)

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A quantum neural network computes its own relative phase

Behrman

Steck

2013

2013 IEEE Symposium on Swarm Intelligence (SIS)

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Complete characterization of the state of a quantum system made up of subsystems requires determination of relative phase, because of interference effects between the subsystems. For a system of qubits used as a quantum computer this is especially vital, because the entanglement, which is the basis for the quantum advantage in computing, depends intricately on phase. We present here a first step towards that determination, in which we use a two-qubit quantum system as a quantum neural network, which is trained to compute and output its own relative phase.

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Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Abstract: We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V)

Cited by 6 publications

References 12 publications

Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis

Algebraic Characterization of CNOT-Based Quantum Circuits with its Applications on Logic Synthesis

Quantum Machine Learning Based on Minimizing Kronecker-Reed-Muller Forms and Grover Search Algorithm with Hybrid Oracles

A quantum neural network computes its own relative phase

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