Encoding Archives - IEEE Transactions on Quantum Engineering

Quantum Direct-Sequence Spread-Spectrum CDMA Communication Systems: Mathematical Foundations

April 15, 2025Mohammad Amir Dastgheib; Jawad A. Salehi; Mohammad RezaiQuantum InternetCommunication systems, Electro-optic modulators, Encoding, Interference, Modulation, Multiaccess communication, Photonics, Quantum communication, Quantum entanglement, Quantum mechanics

Abstract: This article describes the fundamental principles and mathematical foundations of quantum direct-sequence spread-spectrum code division multiple-access communication systems. The evolution of quantum signals through the quantum direct-sequence spread-spectrum multiple-access communication system is carefully characterized by a novel approach called the decomposition of creation operators. In this methodology, the creation operator of the transmitted quantum […]

Two-Step Quantum Search Algorithm for Solving Traveling Salesman Problems

March 6, 2025Rei Sato, Cui Gordon, Kazuhiro Saito, Hideyuki Kawashima, Tetsuro Nikuni, Shohei WatabeQuantum ComputingComplexity theory, Costs, Encoding, Heuristic algorithms, Optimization, Quantum algorithm, Quantum circuit, Search problems, Traveling salesman problems, Urban areas

Quantum search algorithms, such as Grover’s algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit presents a significant challenge. Existing quantum search algorithms for the TSP typically assume that an initial state—an equal superposition of all feasible solutions satisfying the […]

Explicit Quantum Circuit for Simulating the Advection–Diffusion–Reaction Dynamics

February 21, 2025Claudio Sanavio, Enea Mauri, Sauro SucciQuantum ComputingComputational fluid dynamics, Convergence, Encoding, Logic gates, Logistics, Mathematical models, Polynomials, Quantum algorithm, Quantum circuit, Qubit

We assess the convergence of the Carleman linearization of advection–diffusion–reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze […]

Variational Quantum Algorithms for Differential Equations on a Noisy Quantum Computer

January 20, 2025Niclas Schillo, Andreas SturmQuantum ComputingComputers, Differential equations, Encoding, Hardware, Logic gates, Noise measurement, Quantum algorithm, Quantum cascade lasers, Quantum circuit, Qubit

The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly interesting are algorithms that offer advantages […]

Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate

January 17, 2025Ryutaroh MatsumotoQuantum InformationCryptography, Encoding, Finite element analysis, Hands, Proposals, Quantum state, Reviews, Standards, Symbols, Teleportation

Abstract: In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the ramp quantum secret sharing schemes with the highest coding rate. This article […]

Quantum Two-Way Protocol Beyond Superdense Coding: Joint Transfer of Data and Entanglement

January 10, 2025Kristian S. Jensen, Lorenzo Valentini, René B. Christensen, Marco Chiani, Petar PopovskiQuantum InternetEncoding, Metadata, Photonics, Proposals, Protocols, Quantum channels, Quantum entanglement, Qubit, Repeaters, Throughput

In this article, we introduce a generalization of one-way superdense coding to two-way communication protocols for transmitting classical bits by using entangled quantum pairs. The proposed protocol jointly addresses the provision of entangled pairs and superdense coding, introducing an integrated approach for managing entanglement within the communication protocol. To assess the performance of the proposed […]

Noise Robustness of Quantum Relaxation for Combinatorial Optimization

August 6, 2024Kentaro Tamura, Yohichi Suzuki, Rudy Raymond, Hiroshi C. Watanabe, Yuki Sato, Ruho Kondo, Michihiko Sugawara, Naoki YamamotoQuantum ComputingApproximation algorithms, Decoding, Encoding, Noise, Optimization, Quantum state, Qubit

Relaxation is a common way for dealing with combinatorial optimization problems. Quantum random-access optimization (QRAO) is a quantum-relaxation-based optimizer that uses fewer qubits than the number of bits in the original problem by encoding multiple variables per qubit using quantum random-access code (QRAC). Reducing the number of qubits will alleviate physical noise (typically, decoherence), and […]

Noise Robustness of Quantum Relaxation for Combinatorial Optimization

August 6, 2024Kentaro Tamura, Yohichi Suzuki, Rudy Raymond, Hiroshi C. Watanabe, Yuki Sato, Ruho Kondo, Michihiko Sugawara, Naoki YamamotoQuantum Computer ArchitectureApproximation algorithms, Decoding, Encoding, Noise, Optimization, Quantum state, Qubit

Relaxation is a common way for dealing with combinatorial optimization problems.

Reliable Quantum Communications Based on Asymmetry in Distillation and Coding

May 10, 2024Lorenzo Valentini, René Bødker Christensen, Petar Popovski, Marco ChianiQuantum InternetEncoding, Protocols, Quantum computing, Quantum entanglement, Qubit, Reliability, Teleportation

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint […]

Accelerating Grover Adaptive Search: Qubit and Gate Count Reduction Strategies With Higher Order Formulations

April 25, 2024Yuki Sano, Kosuke Mitarai, Naoki Yamamoto, Naoki Ishikawa,Quantum ComputingEncoding, Logic gates, Optimization, Quantum computing, Qubit, Urban areas, Vectors

Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this article, we propose higher order binary formulations that can simultaneously reduce the numbers of qubits and gates required for GAS. Specifically, we consider two novel strategies: one that reduces the number of gates through polynomial factorization, and […]