Quantum Variable Precision via Adaptive Register Dynamics
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Solution Overview
Problem
In digital computer systems, the precision of floating-point variables degrades significantly due to repeated arithmetic manipulations when the register size is fixed and a no-overflow requirement is guaranteed across all data points.
Innovation Solution
A method is introduced that uses a quantum register to represent random variables through a set of qubits, employing bijective affine transformations to map domain values to indexes, allowing for the generation of quantum variables by setting coefficients to the square root of probability distributions, and enabling operations like addition and multiplication without overflow by adjusting scaling and offset factors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a fixed register size is used for quantum floating-point arithmetic, then overflow is prevented, but precision degrades significantly due to repeated arithmetic manipulations
Solution Approach 1:
The patent applies dynamics by making the quantum register size adaptive rather than fixed. The system dynamically adjusts the number of qubits allocated to the significand based on the operation being performed and the precision requirements, allowing the register to expand when needed for arithmetic operations and contract afterward to maintain precision without permanent overflow risk
Solution Approach 2:
The patent changes the parameter of register size dynamically during computation. By adjusting the number of qubits in the significand register based on the operational context and precision requirements, the system can maintain both overflow protection and high precision simultaneously through parameter adaptation
2Measurement precision
If the register size is increased to maintain precision, then precision is improved, but overflow risk increases
Solution Approach 1:
The system dynamically adjusts register size based on operational needs. The quantum register expands to accommodate precision requirements during computation but contracts afterward, preventing permanent overflow while maintaining necessary precision temporarily during arithmetic operations
Solution Approach 2:
The quantum register is segmented into distinct components: a significand portion for precision and an exponent portion for range. This segmentation allows independent optimization of each component - the significand can be sized for precision while the exponent handles the range, preventing overflow through proper architectural division
3Productivity
If repeated arithmetic manipulations are performed, then computational capability is enhanced, but precision degrades significantly
Solution Approach 1:
The system discards excess precision temporarily during intermediate arithmetic operations by using expanded register sizes, then recovers full precision by contracting the register back to its optimal size after operations complete. This allows repeated manipulations without permanent precision loss
Solution Approach 2:
The system prepares for potential precision loss by having available qubit resources that can be temporarily allocated to cushion against precision degradation during repeated arithmetic operations, then recovered when no longer needed
Data Source
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AI summary
The present disclosure relates to a method comprising: providing a quantum register comprising a set of qubits defining a quantum system. The states of a computational basis of the quantum system may be represented by an ordered set of consecutive nonnegative integer numbers, referred to as a set of indexes. A random variable may be determined in accordance with a predefined classical-quantum format, wherein the random variable is valued in a finite domain of classical values such that each value of the domain is derived from a respective index of the set of indexes through an affine relationship, the affine relationship being defined by a scaling factor and an offset factor. The set of qubits may be encoded such that the probability of measuring a state of the quantum system in the computational basis is the probability of observing the domain value associated with the index representing said measured state when sampling the random variable.