Abstract

The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which is a subset of the symmetric group, where the NCT library is considered as the generators of the permutation group.

Highlights

  • One of the problems in classical computers is heat dissipation and energy loss

  • The paper has two aims: the first aim of this paper is to propose an algorithm that optimizes the quantum cost of 3-bit reversible circuits based on a modified version of the NCT library; the second aim is to propose a new gate library by modifying the NCT library to replace positive control with negative control, which shows less quantum cost compared with the NCT library

  • The modified circuit optimization algorithm is applied to the Negative NCT library with an average quantum cost of 11.209 in cost115 metric and 10.078 in cost015 metric without using any ancillary qubits

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Summary

Introduction

One of the problems in classical computers is heat dissipation and energy loss. The amount of energy dissipated for any lost bit of information is calculated by R. Reversible computing has one of many features, where no heat dissipation is produced by the system [1]; no information is destroyed This feature has many applications [2], such as low-power CMOS [3], nanotechnology [4], DNA-based logic circuit with self error recovery capability employing massive parallelism [5] and many more [6]. Different Toffoli decompositions are proposed in [21] to reduce the quantum cost of reversible circuits. The paper has two aims: the first aim of this paper is to propose an algorithm that optimizes the quantum cost of 3-bit reversible circuits based on a modified version of the NCT library; the second aim is to propose a new gate library by modifying the NCT library to replace positive control with negative control, which shows less quantum cost compared with the NCT library.

Reversible Boolean Function
Reversible Quantum Logic
One-Qubit Gates
Condition on Control Qubits
Two-Qubit Gates
Three-Qubit Gate
Quantum Cost of a Reversible Circuit
Optimization Rules of Quantum Gates
Gate Decomposition
Basic Pairs
Choosing the Basic Pair
Build a Circuit with Basic Pairs
Conclusions
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