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Efficient Construction of a Control Modular Adder on a Carry-Lookahead Adder Using Relative-Phase Toffoli Gates
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- Kento Oonishi
- Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan
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- Tomoki Tanaka
- Mitsubishi UFJ Financial Group (MUFG), Inc. and MUFG Bank, Ltd., Tokyo, Japan
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- Shumpei Uno
- Quantum Computing Center, Keio University, Yokohama, Japan
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- Takahiko Satoh
- Quantum Computing Center, Keio University, Yokohama, Japan
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- Rodney Van Meter
- Quantum Computing Center, Keio University, Yokohama, Japan
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- Noboru Kunihiro
- University of Tsukuba, Tsukuba, Japan
Description
Control modular addition is a core arithmetic function, and we must consider the computational cost for actual quantum computers to realize efficient implementation. To achieve a low computational cost in a control modular adder, we focus on minimizing KQ, defined by the product of the number of qubits and the depth of the circuit. In this paper, we construct an efficient control modular adder with small KQ by using relative-phase Toffoli gates in two major types of quantum computers: Fault-Tolerant Quantum Computers (FTQ) on the Logical layer and Noisy Intermediate-Scale Quantum Computers (NISQ). We give a more efficient construction compared to Van Meter and Itoh's, based on a carry-lookahead adder. In FTQ, $T$ gates incur heavy cost due to distillation, which fabricates ancilla for running $T$ gates with high accuracy but consumes a lot of specially prepared ancilla qubits and a lot of time. Thus, we must reduce the number of $T$ gates. We propose a new control modular adder that uses only 20% of the number of $T$ gates of the original. Moreover, when we take distillation into consideration, we find that we minimize $\text{KQ}_{T}$ (the product of the number of qubits and $T$-depth) by running $��\left(n / \sqrt{\log n} \right)$ $T$ gates simultaneously. In NISQ, CNOT gates are the major error source. We propose a new control modular adder that uses only 35% of the number of CNOT gates of the original. Moreover, we show that the $\text{KQ}_{\text{CX}}$ (the product of the number of qubits and CNOT-depth) of our circuit is 38% of the original. Thus, we realize an efficient control modular adder, improving prospects for the efficient execution of arithmetic in quantum computers.
Journal
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- IEEE Transactions on Quantum Engineering
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IEEE Transactions on Quantum Engineering 3 1-18, 2022
Institute of Electrical and Electronics Engineers (IEEE)
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Keywords
- Quantum Physics
- FOS: Physical sciences
- control modular adder
- fault-tolerant quantum computers (FTQ)
- Shor’s algorithm
- TA401-492
- Carry-lookahead adder
- Atomic physics. Constitution and properties of matter
- Quantum Physics (quant-ph)
- Materials of engineering and construction. Mechanics of materials
- noisy intermediate-scale quantum computers (NISQ)
- QC170-197
Details 詳細情報について
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- CRID
- 1360298754845027456
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- ISSN
- 26891808
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- Article Type
- journal article
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- Data Source
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- Crossref
- KAKEN
- OpenAIRE