Optical quantum devices are promoting the development not only of communication but also of quantum computation using optical quantum gates. We will explain how to replace circuits consisting of gates such as NOT and AND used in classical logic calculations with quantum calculation gates. These classical gates can be expressed as NOT and CNOT of quantum computing gates. We show how to express these quantum gates as optical devices using the behavior of the polarization of discrete photons. Next, we describe the backtracking method of quantum circuits utilizing the reversibility of quantum gates. As classical gates are not unitary, we use probabilistic methods that rely on measurements. In a typical classical gate, there are multiple inputs corresponding to a certain output, so backtracking requires tracing multiple states. The quantum bit representation, which can represent superposition states, is suitable for this purpose. As an application example, we explain how to backtrack integer multipliers and perform factorization. In a configuration using quantum gates, one measurement quantum bit is required for each element, resulting in a large number of state bits. However, by reusing bits that are no longer needed, it was possible to construct a circuit with a number of state bits proportional to the number of bits for the integer multiplicand. We simulated an integer multiplier circuit by combining classical gates and backtracked the circuit to derive two factors from a composite number represented by quantum bits. By performing a simulation on a PC, we succeeded in factorizing a 100-bit composite number, subject to the condition that it is a product of two prime numbers close to less than 2m1−1 and 2m2−1, where m1 and m2 are integers. We compare our method with the calculation using satisfiability (SAT) for the factoring problem.
Optical quantum devices are promoting the development not only of communication but also of quantum computation using optical quantum gates. We will explain how to replace circuits consisting of gates such as NOT and AND used in classical logic calculations with quantum calculation gates. These classical gates can be expressed as NOT and CNOT of quantum computing gates. We show how to express these quantum gates as optical devices using the behavior of the polarization of discrete photons. Next, we describe the backtracking method of quantum circuits utilizing the reversibility of quantum gates. As classical gates are not unitary, we use probabilistic methods that rely on measurements. In a typical classical gate, there are multiple inputs corresponding to a certain output, so backtracking requires tracing multiple states. The quantum bit representation, which can represent superposition states, is suitable for this purpose. As an application example, we explain how to backtrack integer multipliers and perform factorization. In a configuration using quantum gates, one measurement quantum bit is required for each element, resulting in a large number of state bits. However, by reusing bits that are no longer needed, it was possible to construct a circuit with a number of state bits proportional to the number of bits for the integer multiplicand. We simulated an integer multiplier circuit by combining classical gates and backtracked the circuit to derive two factors from a composite number represented by quantum bits. By performing a simulation on a PC, we succeeded in factorizing a 100-bit composite number, subject to the condition that it is a product of two prime numbers close to less than 2m1−1 and 2m2−1, where m1 and m2 are integers. We compare our method with the calculation using satisfiability (SAT) for the factoring problem.
Optical quantum devices are promoting the development not only of communication but also of quantum computation using optical quantum gates. Here, we will explain how to replace circuits consisting of gates such as NOT, AND, etc. used in classical logic calculations with quantum calculation gates. These classical gates can be expressed as NOT and CNOT of quantum computing gates. We show how to express these quantum gates as optical devices using the behavior of the polarization of discrete photons. Next, we describe the backtracking method of quantum circuits utilizing the reversibility of quantum gates. Since classical gates are not unitary, we use probabilistic methods that rely on measurements. In a typical classical gate, there are multiple inputs corresponding to a certain output, so backtracking requires tracing multiple states. The quantum bit representation, which can represent superposition states, is suitable for this purpose. As an application example, we explain how to backtrack integer multipliers and perform factorization. In configuration using quantum gates, one measurement quantum bit is required for each element, resulting in a large number of state bits. However, by reusing bits that are no longer needed, it was possible to construct a circuit with a number of state bits proportional to the number of bits for the integer multiplicand. We simulated an integer multiplier circuit by combining classical gates, and backtrack the circuit to derive two factors from a composite number represented by quantum bits. We performed simulations on a PC and succeeded in factorizing a 100-bit composite number.
This Spotlight aims to provide a general introduction to linear and nonlinear optical components that are frequently used to implement the protocols for quantum computation and communication. The role of each optical element is described briefly, and it is shown that these optical elements can be combined to constitute quantum circuits for performing various quantum computing and communication tasks. Present challenges and future scopes are also mentioned briefly. Specifically, after introducing the qubit, it is stated that a quantum gate is a device that transforms a quantum state into another quantum state. Thus, most of the optical components (e.g., a beamsplitter, a wave plate, a mirror, a polarizing beamsplitter) can be viewed as quantum gates because each of these optical elements can transform a quantum state into another quantum state. This fact is the basis for constructing useful quantum circuits using optical elements. Finally, a few proposals for optical realizations of schemes for quantum communication and computation are described.
In classical computation and communication, we use classical gates and bits. Similarly, in quantum computation and communication, we use their quantum analogs, i.e., quantum gates and qubit(s) [quantum bit(s)]. We have already mentioned that a bit can be realized in various ways. In the same way, a qubit can also be realized in various ways, and accordingly, corresponding quantum gates that would operate on qubits can also be realized in various ways. Here, we focus on a specific implementation: optical implementation, where qubits are realized using photons and quantum gates, and circuits are realized using various optical components. Specific merits of this realization lie in the following facts: (i) in quantum communication we need to transmit qubits from one location to the other, and transmission of photons is easier than any other realization of qubits; (ii) the effect of the environment (e.g., external electric and magnetic fields) on photons is less compared to any other implementations of qubits; and (iii) integrated optics are already a well-developed field. Keeping these points in mind, this Spotlight describes basic optical elements and how to use those elements to implement various schemes of quantum computation and communication. We will mostly describe realizations using bulk optics. However, in most cases, it is not difficult to transform these bulk-optics-based realizations into integrated optics. To begin with, in Section 1.1, we formally define a qubit and describe two alternative ways of realizing a qubit using a photon.
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.
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.
A quantum computer is a device for computation that makes direct use of distinctively quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. In a classical (or conventional) computer, the amount of data is measured by bits, in a quantum computer; it is measured by quantum of bits (qubits). This work describes, and implements the universal quantum logic gates, the terminology is introduced with two well known quantum gates, the quantum NOT, and the quantum XOR gates. The NOT and XOR gates have already been described in classical reversible logic. This work gives the implementation of the quantum circuits, such as the Quantum Half-Adder Circuits, which consists of quantum control control not gate (CCNot) and quantum control not gate (CNot). Also, it describes and implements the Quantum Full-Adder Circuits, which consists of two Quantum Half-Adder Circuits and one control not gate (CNot). Depending on the quantum circuits, one can implement the quantum basic arithmetic operations such as (addition, subtraction, multiplication and division). After each implementation, the computational complexity of each step is calculated. Key words:
Purpose The purpose of this paper is to introduce an approach form‐valued classical and non‐classical (reversible and quantum) optical computing. The developed approach utilizes new multiplexer‐based optical devices and circuits within switch logic to perform the required optical computing. The implementation of the new optical devices and circuits in the optical regular logic synthesis using new lattice and systolic architectures is introduced, and the extensions to quantum optical computing are also presented. Design/methodology/approach The new linear optical circuits and systems utilize coherent light beams to perform the functionality of the basic logic multiplexer. The 2‐to‐1 multiplexer is a basic building block in switch logic, where in switch logic a logic circuit is implemented as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less‐costly in synthesizing wide variety of logic circuits and systems. The extensions to quantum optical computing using photon spins and the collision of Manakov solitons are also presented. Findings New circuits for the optical realizations ofm‐valued classical and reversible logic functions are introduced. Optical computing extensions to linear quantum computing using photon spins and nonlinear quantum computing using Manakov solitons are also presented. Three new multiplexer‐based linear optical devices are introduced that utilize the properties of frequency, polarization and incident angle that are associated with any light‐matter interaction. The hierarchical implementation of the new optical primitives is used to synthesize regular optical reversible circuits such as them‐valued regular optical reversible lattice and systolic circuits. The concept of parallel optical processing of an array of input laser beams using the new multiplexer‐based optical devices is also introduced. The design of regular quantum optical systems using regular quantum lattice and systolic circuits is introduced. New graph‐based quantum optical representations using various types of quantum decision trees are also presented to efficiently represent quantum optical circuits and systems. Originality/value The introduced methods for classical and non‐classical (reversible and quantum) optical regular circuits and systems are new and interesting for the design of several future technologies that require optimal design specifications such as super‐high speed, minimum power consumption and minimum size such as in quantum computing and nanotechnology.