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Communications Physics

Scalable set of reversible parity gates for integer factorization

Martin Lanthaler, Benjamin E. Niehoff, Wolfgang Lechner

Published Apr 17, 2023• 4 citations
Publisher

Abstract

Classical microprocessors operate on irreversible gates, that, when combined with AND, half-adder and full-adder operations, execute complex tasks such as multiplication of integers. We introduce parity versions of all components of a multiplication circuit. The parity gates are reversible quantum gates based on the recently introduced parity transformation and build on ground-space encoding of the corresponding gate logic. Using a quantum optimization heuristic, e.g., an adiabatic quantum computing protocol, allows one to quantum mechanically reverse the process of multiplication and thus factor integers, which has applications in cryptography. Our parity approach builds on nearest-neighbor constraints equipped with local fields, able to encode the logic of a binary multiplication circuit in a modular and scalable way.

DOI
10.1038/s42005-023-01191-3

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•Jan 29, 2014•66 citations
Classical microprocessors operate on irreversible gates, that, when combined with AND, half-adder and full-adder operations, execute complex tasks such as multiplication of integers. We introduce parity versions of all components of a multiplication circuit. The parity gates are reversible quantum gates based on the recently introduced parity transformation and build on ground-space encoding of the corresponding gate logic. Using a quantum optimization heuristic, e.g., an adiabatic quantum computing protocol, allows one to quantum mechanically reverse the process of multiplication and thus factor integers, which has applications in cryptography. Our parity approach builds on nearest-neighbor constraints equipped with local fields, able to encode the logic of a binary multiplication circuit in a modular and scalable way.
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Quantum computing represents a paradigm shift in computation by leveraging the principles of quantum mechanics such as superposition, entanglement, and interference to perform operations beyond classical limitations. Unlike classical computing systems that rely on irreversible logic operations and suffer from energy dissipation due to information loss, quantum systems utilize reversible unitary transformations that preserve information and improve computational efficiency. This paper presents a comprehensive framework for the design, simulation, and validation of quantum gates and reversible arithmetic circuits, including half adders and half subtractors. The proposed approach systematically maps classical arithmetic logic into quantum circuits using fundamental quantum gates such as Pauli-X, Hadamard, Controlled-NOT (CNOT), and Toffoli gates. The circuits are implemented and simulated using the Qiskit Aer framework, enabling detailed analysis of quantum state evolution and measurement outputs. The results obtained from simulation include program-level outputs, state vector representations, measurement counts, and probability distributions, all of which demonstrate strong agreement with classical truth tables. The analysis confirms the correctness, reversibility, and scalability of the proposed designs. Furthermore, a comparative performance evaluation highlights the advantages of quantum computing over classical approaches in terms of parallelism and energy efficiency. The proposed framework establishes a robust foundation for future implementation of complex Boolean logic and arithmetic operations in quantum systems.
Reversible logic is gaining importance in recent years largely due to its property of low power consumption.It has a wide range of applications which include advance computing, low power CMOS, optical information processing, quantum computing, DNA cryptography and nanotechnology.Reversible gates are the building blocks of quantum computation.This paper presents an optimized parallel binary adder/subtractor using existing reversible gates which is further used to implement a novel circuit capable of performing modulo operation.All circuits have been modeled and verified using Verilog and Modelsim.An overall analysis of the modulo circuit and a comparative study of the proposed parallel adder/subtractor with respect to previous designs in terms of the number of gates, number of garbage outputs and quantum costs is presented.
The futuristic computing is desired to be more power full with low-power consumption.That is why quantum computing has been a key area of research for quite some time and is getting more and more attention.Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times.Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance.In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer.The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations.The quantum costs of these designs are comparable.Many of the implemented micro-operations are not seen in previous literatures.The performances of the proposed circuits are compared with existing designs wherever available.
Abstract — Reversible logic is one of the most vital issue at present time and it has different areas for its application, those are low power CMOS, quantum computing, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, computer graphics. It is not possible to realize quantum computing without implementation of reversible logic. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. This paper provides the basic reversible logic gates, which in designing of more complex system having reversible circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. This paper presents the data relating to the primitive reversible gates which are available in literature and helps researches in designing higher complex computing circuits using reversible gates.