Quantum Prime-Factorization Circuits With Variable Control Qubits
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Solution Overview
Problem
The existing Shor's algorithm for quantum prime factorization requires a large number of control qubits, leading to increased circuit depth and execution time, with limited studies on reducing this depth using intermediate values between the maximum and minimum number of qubits.
Innovation Solution
An information processing program and system that determine the optimal number of control qubits based on the relationship between modular exponentiation calculation and measurement/classical conditional arithmetic operation times, generating a quantum circuit pattern to minimize execution time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of control qubits is increased to maximize computational capability, then the arithmetic operation can be performed with standard quantum circuits, but the circuit depth increases and execution time increases
Solution Approach 1:
The patent changes the parameter of number of control qubits from fixed values (1 or 2L+1) to variable intermediate values. By determining the optimal number of control qubits based on the relationship between modular exponentiation calculation time and measurement/classical conditional arithmetic operation time, the system achieves reduced circuit depth and execution time while maintaining computational capability.
2Quantity of substance
If the number of control qubits is reduced to minimize qubit usage, then the circuit depth can be reduced, but the arithmetic operation time for modular exponentiation increases
Solution Approach 1:
The patent optimizes the parameter of number of control qubits by determining it based on the relationship between modular exponentiation calculation time and measurement/classical conditional arithmetic operation time. This allows finding the optimal balance point where both qubit quantity and operation time are minimized.
Solution Approach 2:
The patent makes the number of control qubits dynamic rather than fixed. By determining the optimal number based on actual execution time relationships, the system adapts the qubit configuration to achieve minimum execution time, allowing the parameter to vary based on computational requirements.
3Loss of time
If intermediate values between minimum and maximum number of control qubits are used, then the circuit depth can be optimized, but this requires determining the optimal value based on execution time relationships
Solution Approach 1:
The patent introduces feedback by determining the optimal number of control qubits based on the relationship between modular exponentiation calculation time and measurement/classical conditional arithmetic operation time. This feedback mechanism allows the system to iteratively find the optimal configuration that minimizes circuit depth while managing the determination process complexity.
Data Source
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AI summary
An information processing program for causing a computer to execute: determining a number of control qubits using a relationship between a first arithmetic operation time for each of multiple kinds of modular exponentiation calculation processing in an arithmetic operation of prime factorization and a second arithmetic operation time for each of a plurality of measurement and classical conditional arithmetic operations in inverse quantum Fourier transform processing on results of the multiple kinds of modular exponentiation calculation processing in the arithmetic operation of the prime factorization; determining a circuit pattern for performing the arithmetic operation of the prime factorization by executing the multiple kinds of modular exponentiation calculation processing and the inverse quantum Fourier transform processing, based on the number of control qubits; generating a quantum circuit using the circuit pattern; and performing the arithmetic operation of the prime factorization by using the quantum circuit.