arXiv subjects

Shanyan Chen

Publications and source records attributed to Shanyan Chen.

5 recordsLinked to original sources

arXiv2025

Solving Segment Display Problems Using Quantum Grover's Search Algorithm

This paper introduces a new Boolean-based methodology for constructing Segment Display Problems (SDPs) in the quantum domain and solving them using Grover's quantum search algorithm. In the classical domain, the SDPs are typically solved using various techniques, such as human deduction, heuristic search, and methods for solving Boolean satisfiability (SAT) and constraint satisfaction problems (CSPs) that are based on different problem design models. In this paper, our newly introduced methodology proposes a quantum-based approach for solving such SDPs, by building their quantum oracle using binary reversible circuits and our previously proposed step-decreasing structures shaped operators (Stesso). To demonstrate the usability of this proposed method, we experimentally solve an SDP instance of the matchstick problem using Grover's algorithm with a noisy simulated quantum computer implemented in Qiskit.

quant-ph↗

arXiv2025

Stesso: A reconfigurable decomposition of $n$-bit Toffoli gates using symmetrical logical structures and adjustable support qubits

An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to decompose $(n+1)$-bit Toffoli gates in a quantum circuit into a set of standard 3-bit Toffoli gates or a set of elementary quantum gates, such as single-qubit and two-qubit gates. However, these methods are not effectively reconfigurable for linearly connected symmetrical structures (layouts) of contemporary quantum computers, usually utilizing more ancilla qubits. This paper introduces a new structural design method to effectively decompose $(n+1)$-bit Toffoli gates by utilizing configurable ancilla qubits, which we named the ``support qubits". Collectively, we call our decomposition method for symmetrical structures using support qubits the ``step-decreasing structures shaped operators (Stesso)". The main advantage of Stesso is to configurable construct different decomposed operators of various polarities and intermediate sub-circuits, such as Positive Polarity-Stesso, Mixed Polarity-Stesso, and Generalized-Stesso. With Stesso, it has been experimentally proven that $(n+1)$-bit Toffoli gates always have lower quantum costs than using conventional composition methods.

quant-ph↗

arXiv2025

Visualizing the state space and transformations of higher order quantum logics via toric geometry

We propose some new uses of toric variety structures in the study of quantum computation for small radices. In particular, we observe the concurrence of the equivalence classes of quantum states under quantum measurement and the orbits of the toric geometric structure of the state space. Visualizations of these state spaces and of certain fundamental unitary transformations in binary and ternary quantum logic and a method to develop new transformations based on these visualization techniques are presented. Transformations discussed included minimal universal sets for permutative ternary quantum circuits. In addition, general structures and synthesis methods based on quantum multiplexers are presented. A general framework for the design of optimal ternary quantum transformations and circuits is additionally presented. Finally, a number of open research areas that are extensions of the work presented herein are given.

quant-ph↗

arXiv2025

A Cost-Effective Quantum Boolean-Phase SWAP Gate with Only Two CNOT Gates

A new Boolean-Phase swapping gate is presented with improved quantum generality and cost-effectiveness. Our swapping gate is termed the "p-SWAP gate", where p is the phase difference selected for a set of swapped qubits. The phase p is expressed in radians and $-π~{\leq}$ p ${\leq}~+π$. The generality of p-SWAP gate is demonstrated for Phase applications for selected values of p and for Boolean applications when the value of p is ignored. The cost-effectiveness of p-SWAP gate follows from the lower quantum cost and depth of its final realized (transpiled) quantum circuit, when compared to the standard SWAP gate composed of three Feynman (CNOT) gates. Specifically, our presented p-SWAP gate utilizes only two CNOT gates. The quantum circuit of the p-SWAP gate is visually designed using our previously developed Bloch sphere approach. Experimentally, after transpilation for an IBM quantum computer, the transpiled p-SWAP gate shows an approximate 23% quantum cost reduction and an approximate 26% depth minimization compared to the transpiled standard SWAP gate.

quant-ph↗

arXiv2023

Formalization of Robot Collision Detection Method based on Conformal Geometric Algebra

Cooperative robots can significantly assist people in their productive activities, improving the quality of their works. Collision detection is vital to ensure the safe and stable operation of cooperative robots in productive activities. As an advanced geometric language, conformal geometric algebra can simplify the construction of the robot collision model and the calculation of collision distance. Compared with the formal method based on conformal geometric algebra, the traditional method may have some defects which are difficult to find in the modelling and calculation. We use the formal method based on conformal geometric algebra to study the collision detection problem of cooperative robots. This paper builds formal models of geometric primitives and the robot body based on the conformal geometric algebra library in HOL Light. We analyse the shortest distance between geometric primitives and prove their collision determination conditions. Based on the above contents, we construct a formal verification framework for the robot collision detection method. By the end of this paper, we apply the proposed framework to collision detection between two single-arm industrial cooperative robots. The flexibility and reliability of the proposed framework are verified by constructing a general collision model and a special collision model for two single-arm industrial cooperative robots.

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