Efficient quantum modular multiplier and quantum modular multiplication method
AssigneeIndustry-University Cooperation Foundation Hanyang University Erica Campus
InventorsSeung Hyun Seo, Seong Min Cho, Ae Young Kim
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Abstract
Provided are an efficient quantum modular multiplier using characteristics of a modular operation, that is, a quantum modular multiplier having low quantum circuit complexity, and a quantum modular multiplication method. A quantum modular multiplier according to one embodiment of the present invention is a quantum modular multiplier for multiplying first qubits having N digits by second qubits having N digits (N is a natural number that is greater than or equal to 2) and includes a first auxiliary register setting unit, a second auxiliary register setting unit, an addition unit, and an auxiliary register initialization unit.
Claims16
A quantum modular multiplication circuit for multiplying first qubits having N digits by second qubits having N digits, wherein N is a natural number that is greater than or equal to 2, the quantum modular multiplication circuit comprising:
- a first auxiliary register configured to store partial products of a lowest first qubit among the first qubits and the second qubits in first auxiliary qubits;
- a second auxiliary register configured to left-shift partial products of a pth first qubit among the first qubits and the second qubits (p−1) times and store the left-shifted partial products in second auxiliary qubits, wherein p is a natural number that is greater than or equal to 2 and less than or equal to N;
- an addition unit including a modular 2N quantum adder circuit and configured to perform modular addition on the first auxiliary qubits and the second auxiliary qubits and store a modular addition result in the first auxiliary qubits;
- and
- a third auxiliary register configured to initialize the second auxiliary qubits,
- wherein, while p increases from 2 to N, the second auxiliary register, the addition unit, and the third auxiliary register are repeatedly operated.
A quantum modular multiplication circuit for multiplying first qubits having N digits by second qubits having N digits, wherein N is a natural number that is greater than or equal to 2, the quantum modular multiplication circuit comprising:
- a plurality of auxiliary registers configured to left-shift partial products of an fth first qubit among the first qubits and the second qubits (f−1) times and store the left-shifted partial products in an fth auxiliary register among the plurality of auxiliary registers, wherein f is a natural number that is less than or equal to N;
- and
- an addition unit including a plurality of modular 2N quantum adder circuits and configured to perform modular addition on the plurality of auxiliary registers and store a modular addition result in one of the plurality of auxiliary registers.
A quantum modular multiplication circuit for multiplying first qubits having N digits by second qubits having N digits, wherein N is a natural number that is greater than or equal to 2, the quantum modular multiplication circuit comprising:
- a first auxiliary register configured to store partial products of a lowest first qubit among the first qubits and the second qubits in first auxiliary qubits;
- a second auxiliary register configured to left-circular-shift partial products of a pth first qubit among the first qubits and the second qubits (p−1) times and store the left-circular-shifted partial products in second auxiliary qubits, wherein p is a natural number that is greater than or equal to 2 and less than or equal to N;
- an addition unit including a modular 2N−1 quantum adder circuit and configured to perform modular 2N−1 addition on the first auxiliary qubits and the second auxiliary qubits and store a modular addition result in the first auxiliary qubits;
- and
- a third auxiliary register configured to initialize the second auxiliary qubits,
- wherein, while p increases from 2 to N, the second auxiliary register, the addition unit, and the third auxiliary register are repeatedly operated.
A quantum modular multiplication circuit for multiplying first qubits having N digits by second qubits having N digits, wherein N is a natural number that is greater than or equal to 2, the quantum modular multiplication circuit comprising:
- a plurality of auxiliary registers configured to left-circular-shift partial products of an fth first qubit among the first qubits and the second qubits (f−1) times and store the left-circular-shifted partial products in an fth auxiliary register among a plurality of auxiliary registers, wherein f is a natural number that is less than or equal to N;
- and
- an addition unit including a plurality of modular 2N−1 quantum adder circuits and configured to perform modular addition on the plurality of auxiliary registers and store a modular addition result in one of the plurality of auxiliary registers.
Dependencies are inferred from the claim text.