{"title":"Designs of the divider and special multiplier optimizing T and CNOT gates","authors":"Ping Fan, Hai-Sheng Li","doi":"10.1140/epjqt/s40507-024-00222-4","DOIUrl":null,"url":null,"abstract":"<div><p>Quantum circuits for multiplication and division are necessary for scientific computing on quantum computers. Clifford + T circuits are widely used in fault-tolerant realizations. T gates are more expensive than other gates in Clifford + T circuits. But neglecting the cost of CNOT gates may lead to a significant underestimation. Moreover, the small number of qubits available in existing quantum devices is another constraint on quantum circuits. As a result, reducing T-count, T-depth, CNOT-count, CNOT-depth, and circuit width has become the important optimization goal. We use 3-bit Hermitian gates to design basic arithmetic operations. Then, we present a special multiplier and a divider using basic arithmetic operations, where ‘special’ means that one of the two operands of multiplication is non-zero. Next, we use new rules to optimize the Clifford + T circuits of the special multiplier and divider in terms of T-count, T-depth, CNOT-count, CNOT-depth, and circuit width. Comparative analysis shows that the proposed multiplier and divider have lower T-count, T-depth, CNOT-count, and CNOT-depth than the current works. For instance, the proposed 32-bit divider achieves improvement ratios of 40.41 percent, 31.64 percent, 45.27 percent, and 65.93 percent in terms of T-count, T-depth, CNOT-count, and CNOT-depth compared to the best current work. Further, the circuit widths of the proposed <i>n</i>-bit multiplier and divider are 3<i>n</i>. I.e., our multiplier and divider reach the minimum width of multipliers and dividers, keeping an operand unchanged.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"11 1","pages":""},"PeriodicalIF":5.8000,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-024-00222-4","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-024-00222-4","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
Quantum circuits for multiplication and division are necessary for scientific computing on quantum computers. Clifford + T circuits are widely used in fault-tolerant realizations. T gates are more expensive than other gates in Clifford + T circuits. But neglecting the cost of CNOT gates may lead to a significant underestimation. Moreover, the small number of qubits available in existing quantum devices is another constraint on quantum circuits. As a result, reducing T-count, T-depth, CNOT-count, CNOT-depth, and circuit width has become the important optimization goal. We use 3-bit Hermitian gates to design basic arithmetic operations. Then, we present a special multiplier and a divider using basic arithmetic operations, where ‘special’ means that one of the two operands of multiplication is non-zero. Next, we use new rules to optimize the Clifford + T circuits of the special multiplier and divider in terms of T-count, T-depth, CNOT-count, CNOT-depth, and circuit width. Comparative analysis shows that the proposed multiplier and divider have lower T-count, T-depth, CNOT-count, and CNOT-depth than the current works. For instance, the proposed 32-bit divider achieves improvement ratios of 40.41 percent, 31.64 percent, 45.27 percent, and 65.93 percent in terms of T-count, T-depth, CNOT-count, and CNOT-depth compared to the best current work. Further, the circuit widths of the proposed n-bit multiplier and divider are 3n. I.e., our multiplier and divider reach the minimum width of multipliers and dividers, keeping an operand unchanged.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following:
Quantum measurement, metrology and lithography
Quantum complex systems, networks and cellular automata
Quantum electromechanical systems
Quantum optomechanical systems
Quantum machines, engineering and nanorobotics
Quantum control theory
Quantum information, communication and computation
Quantum thermodynamics
Quantum metamaterials
The effect of Casimir forces on micro- and nano-electromechanical systems
Quantum biology
Quantum sensing
Hybrid quantum systems
Quantum simulations.