Quantum Normal Distribution Preparation Using QFT and Qubit Scaling
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Solution Overview
Problem
Existing quantum algorithms for tasks like amplitude estimation, option pricing, principal-component analysis, and machine learning face computational bottlenecks due to inefficient generation of initial distributions.
Innovation Solution
A method for preparing normal distributions on quantum computers using a series of quantum operations, including Hadamard gates, quantum Fourier transforms, and controlled gates, with optional qubit scaling and post-selection to achieve precise distribution generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum algorithms use standard initialization methods, then implementation is simple, but computational bottlenecks occur due to inefficient distribution generation
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing lookup tables of normal distribution values before quantum computation. The classical computer generates these distributions in advance, stores them in memory, and retrieves them during quantum algorithm execution, thereby eliminating the computational bottleneck of generating normal distributions during quantum processing while maintaining algorithmic efficiency
Solution Approach 2:
The patent introduces an intermediary classical computing system that bridges the quantum and classical domains. The classical computer generates normal distributions using standard algorithms, transfers them to quantum memory registers, and facilitates their use in quantum algorithms. This intermediary approach allows efficient distribution generation without requiring complex quantum circuitry for the generation process itself
2Measurement precision
If quantum algorithms require high precision normal distributions, then accuracy improves, but computational overhead increases
Solution Approach 1:
The patent pre-generates high-precision normal distribution values using classical computers with sufficient computational resources, storing them in lookup tables before quantum execution. This preliminary high-precision generation avoids the need for time-consuming quantum computations during algorithm execution, achieving both high accuracy and efficient runtime performance
Solution Approach 2:
The patent creates classical copies of normal distributions in the form of lookup tables that can be rapidly retrieved and loaded into quantum registers. These classical copies serve as pre-computed references that eliminate the need for repeated quantum computation of distribution values, maintaining precision while reducing computational time overhead
Data Source
AI summary
A quantum computer program may receive a mean, a standard deviation, and a discretization for a target normal distribution; determine a number of iterations t based on the mean and standard deviation; identify a value n from the discretization and value X0 from the mean; initialize n qubits in register q and an ancilla; apply a quantum Fourier transform and a +X0 gate to q; apply a Y-Rotation with angle π/2 to the ancilla; apply a controlled +1 gate to q controlled by the ancilla; apply a Hadamard gate to the ancilla; measure the ancilla; set a value C to a value of the measured ancilla; repeat from the Y-Rotation t times; apply an inverse quantum Fourier transform to q; and output amplitudes of basis states of q as the normal distribution. The program may use qubit-scaling to reduce the number of iterations needed.