Photonic reversible computing: a proposal for a Toffoli gate using QND for polarization-based qubits and their applications

Samy C. Policarpo

Published Jan 1, 2023• 0 citations

Abstract

Reversible photonic computing is a promising research field that seeks to develop computers that can perform calculations without loss of information by means of the controlled manipulation of light. Reversibility is an important property of a computational system, as it allows the system to be restored to its initial state after the calculation. This can be useful for applications such as cryptography, security, and image processing. This work presents a theoretical optical apparatus (cS) for polarization qubits based on quantum nondemolition measurements (QND) which through analytical and comparable calculations, presented an efficiency greater than 90% that is capable of performing the Toffoli gate function. The proposed optical system is configurable, based on prior configuration and combination, and reversible AND, NAND, Toffoli, CNOT, Peres, Fredkin, HNG, and ALG gates can be obtained, as well as any other reversible gate based on C n+1 -NOT gates. The cS system can be configured to function as a sequential binary comparator and the same can be used as a Bell state generator.

Related papers

Design Exploration and Application of Reversible Circuits in Emerging Technologies

Saurabh Kotiyal

The reversible logic has promising applications in emerging computing paradigms, such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates, there is a unique one-to-one mapping between the inputs and outputs. To generate a useful gate function, the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred to as the garbage outputs. The number of ancilla inputs, the number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Reversible circuits are of highest interest in optical computing, quantum dot cellular automata and quantum computing. The quantum gates perform an elementary unitary operation on one, two or more two-state quantum systems called qubits. Any unitary operation is reversible in nature, and hence, quantum networks are also reversible, to conclude the quantum computers must be built from reversible logic components. The main contribution of this dissertation is the design exploration and application of reversible circuits in emerging nanotechnologies. The emerging technologies explored in this work are 1) Optical quantum computing 2) Quantum computing. The first contribution of this dissertation is Mach-Zehnder interferometer based design of all optical reversible binary adder. The all optical reversible adder design is based on two new optical reversible gates referred as optical reversible gate I (ORG-I) and optical reversible gate II (ORG-II) and the existing all optical Feynman gate. The two new reversible gates ORG-I and ORGI-II have been proposed and can implement a reversible adder with a reduced optical cost which is equal to the number of MZI switches required, less propagation delay, and with zero overhead in terms of number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder design based on the ORG-I and ORG-II reversible gates are compared and shown to be better than the other existing designs of reversible adder proposed in the non-optical domain in terms of number of MZI switches, delay, the number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder will be a key component of an all optical reversible arithmetic logical unit (ALU), that is a quite essential component in a wide variety of optical signal processing applications. In the existing literature, the NAND logic based implementation is the only known implementation available for reversible gates and its functions. There is a lack of research in the direction of NOR logic based implementation of reversible gates and functions. The second contribution of this dissertation is the design of NOR logic based n-input and n-output reversible gates, one of which can be efficiently mapped into optical computing using the Mach-Zehnder interferometer (MZI), while the other can be mapped efficiently in optical computing using the linear optical quantum gates. The proposed reversible NOR gates work as a corresponding NOR counterpart of NAND logic based Toffoli gates. The proposed optical reversible NOR logic gates can implement the reversible boolean logic functions with less number of linear optical quantum logic gates with reduced optical cost and propagation delay compared to the implementation using existing optical reversible NAND gates. It is illustrated that an optical reversible gate library having both optical Toffoli gate and the proposed optical reversible NOR gate is superior compared to the library containing only the optical Toffoli gate: (i) in terms of number of linear optical quantum gates when implemented using linear optical quantum computing (LOQC), (ii) in terms of optical cost and delay when implemented using the Mach-Zehnder interferometer. The third contribution of this dissertation is a binary tree-based design methodology for a NxN reversible multiplier. The proposed binary tree-based design methodology for a NxN reversible multiplier performs the addition of partial products in parallel using the reversible ripple adders with zero ancilla bit and zero garbage bit; thereby, minimizing the number of ancilla and garbage bits used in the design. The proposed design methodology shows improvements in terms of number of ancilla inputs and garbage outputs compared to all the existing reversible multiplier designs. The methodology is also extended to the design of NxN reversible signed multiplier based on modified Baugh-Wooley multiplication methodology.

Jan 1, 20162 citations

The Fredkin gate in reversible and quantum environments

Claudio Moraga, Fatima Zohra Hadjam

Reversible Computing circuits are characterized by low power consumption and their proximity to circuits for quantum computing. The Fredkin gate was one of the earliest proposed controlled reversible circuits, which however, was soon superseded by the Toffoli gate, the NOT, and CNOT gates, which constituting a flexible functionally complete set could also realize the Fredkin gate as a building block. In quantum computing circuits, the Fredkin gate (under the name controlled SWAP) plays an important role regarding the superposition of states. The present paper studies extensions of the Fredkin gate in terms of mixed polarity in the reversible domain and an application in quantum computing.

Facta universitatis - series Electronics and EnergeticsJan 1, 20234 citations

Implementation of CNOT and Toffoli gates with higher-dimensional spaces

Wen‐Qiang Liu, Hai‐Rui Wei, L. C. Kwek

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.

Jul 20, 20211 citation

Aspects of Reversible and Quantum Computing in a -Valued Domain

Claudio Moraga

This paper presents basic aspects of non-binary reversible and quantum computing in a p-valued environment, since there are no physical reasons for quantum computing to be necessarily binary. A “quantum technology” is not yet available, but different alternatives at the level of laboratory experiments are promising. A theoretical background is needed to face the challenge of designing circuits for quantum computing. Pauli matrices are introduced in the p-valued domain and their properties are explained. The Vilenkin-Chrestenson matrix is shown to produce superposition of states. Entanglement of quantum states in the p-valued environment is introduced and its measurement effect is illustrated. It is shown that in the p-valued domain, the binary Toffoli gate may be given different generalizations with different functionalities. An ancillary-free realization of a new generalized p-valued Toffoli gate based on Muthukrishnan-Stroud elementary gates is presented, its functionality is extended to two kinds of control, and a proof of its performance is given.

IEEE Journal on Emerging and Selected Topics in Circuits and SystemsMar 1, 20164 citations

Reversible Logic Gates for Efficient Circuit Construction and Quantum Computing

R Manaswini, J Silamboli, Kalyandurg Rafeeq Ahmed +2 more

Reversible logic, also known as information lossless logic, is a promising technology that allows embedded data within circuits to be retrieved in case of failure.This study explores the use of reversible gates, such as Feynman gates, Toffoli gates, Fredkin gates, Peres gates, Double Feynman gates, NFT gates, DKG gates, and DFT gates, to construct logic circuits.These reversible logic gates can be effectively used for the implementation of any higher logic circuits-based applications.In the proposed paper the Arithmetic logic unit based on reversible logic hates is implemented in Verilog as well as IBM quantum software.The major applications of reversible logic gates include quantum computing, low power circuits, nano and CMOS technologies, photonics.In the last part of the paper the circuits implemented using Verilog and IBM quantum a chip level design using Cadance layout is implemented.

International Conference on Computer, Computation and Communication (IC3C)Jan 1, 20250 citations

Implementation of frequency encoded all optical reversible logic

Nikhlesh Kumar Mishra, Upendra Chaurasiya, Saumya Srivastava +2 more

Abstract Reversible gate has been one of the emerging research areas that ensure continual process of innovation trends that explore and utilizes the resources. Due to the increasing power consumption of electronic circuits, it has been observed that quantum computing is one of its latest applications. This technology can be utilized by reducing the energy consumption by preserving the bits of information that are still useful. A photon has zero rest mass, while an electron has a nonzero rest mass. These characteristics inspired the researchers to develop an all-optical Fredkin gate. The proposed gate design overcomes the shortcomings of conventional Fredkin gates and provides better performance.

Journal of Optical CommunicationsNov 8, 20213 citations