In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.

arXiv:quant-ph/0602009Feb 1, 20060 citations

Reversible arithmetic logic unit

Rigui zhou, Yang shi, Manqun Zhang

Quantum computer requires quantum arithmetic. The sophisticated design of a reversible arithmetic logic unit (reversible ALU) for quantum arithmetic has been investigated in this letter. We provide explicit construction of reversible ALU effecting basic arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the classical arithmetic and logic operation in a reversible integrated system. This letter provides actual evidence to prove the possibility of the realization of reversible Programmable Logic Device (RPLD) using reversible ALU.Quantum computer requires quantum arithmetic. The sophisticated design of a reversible arithmetic logic unit (reversible ALU) for quantum arithmetic has been investigated in this letter. We provide explicit construction of reversible ALU effecting basic arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the classical arithmetic and logic operation in a reversible integrated system. This letter provides actual evidence to prove the possibility of the realization of reversible Programmable Logic Device (RPLD) using reversible ALU.

arXiv:1107.3924Jul 20, 20110 citations

Quantum Arithmetic Circuits

Hafiz Md. Hasan Babu

Springer eBooksJan 1, 20250 citations

A Feasible Design of Elementary Quantum Arithmetic Logic Units for Near-Term Quantum Computers

Junxu Li

Quantum arithmetic logic units (QALUs) constitute a fundamental component of quantum computing. However, the implementation of QALUs on near-term quantum computers remains a substantial challenge, largely due to the limited connectivity of qubits. In this paper, we propose feasible QALUs, including quantum binary adders, subtractors, multipliers, and dividers, which are designed for near-term quantum computers with qubits arranged in two-dimensional arrays. Additionally, we introduce a feasible quantum arithmetic operation to compute the two's complement representation of signed integers. The proposed QALUs utilize only Pauli-X gates, CNOT gates, and $C\sqrt{X}$ (CSX) gates, and all two-qubit gates are operated between nearest neighbor qubits. Our work demonstrates a viable implementation of QALUs on near-term quantum computers, advancing towards scalable and resource-efficient quantum arithmetic operations.Quantum arithmetic logic units (QALUs) constitute a fundamental component of quantum computing. However, the implementation of QALUs on near-term quantum computers remains a substantial challenge, largely due to the limited connectivity of qubits. In this paper, we propose feasible QALUs, including quantum binary adders, subtractors, multipliers, and dividers, which are designed for near-term quantum computers with qubits arranged in two-dimensional arrays. Additionally, we introduce a feasible quantum arithmetic operation to compute the two's complement representation of signed integers. The proposed QALUs utilize only Pauli-X gates, CNOT gates, and $C\sqrt{X}$ (CSX) gates, and all two-qubit gates are operated between nearest neighbor qubits. Our work demonstrates a viable implementation of QALUs on near-term quantum computers, advancing towards scalable and resource-efficient quantum arithmetic operations.

arXiv:2408.06561Aug 13, 20240 citations

Quantum Mathematics Findings

Manahel Thabet

Jan 1, 20131 citation

C\sqrt{X}

(CSX) gates, and all two-qubit gates are operated between nearest neighbor qubits. Our work demonstrates a viable implementation of QALUs on near-term quantum computers, advancing towards scalable and resource-efficient quantum arithmetic operations.