Quantum Variable Encoding for Floating-Point Precision
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Solution Overview
Problem
The precision of floating-point variables degrades significantly due to repeated arithmetic manipulations in digital computer systems, especially when the register size is fixed and a no-overflow requirement is guaranteed on all data points.
Innovation Solution
A method for determining quantum variables is provided, which involves representing states of a quantum system in a computational basis using an ordered set of consecutive nonnegative integer numbers, and encoding qubits to represent random variables in a classical-quantum format, ensuring that the probability of measuring a state corresponds to the probability of observing a domain value associated with that state.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If floating-point variables are used in digital computer systems with fixed register size, then the system can guarantee no-overflow on all data points, but the precision of the variables degrades significantly due to repeated arithmetic manipulations
Solution Approach 1:
The patent introduces an intermediary representation called quantum floating-point format that acts as a mediator between classical fixed-register arithmetic and high-precision computation. This intermediary uses a quantum register to store the significand while maintaining a classical exponent, allowing repeated arithmetic operations without the precision degradation that occurs in classical floating-point systems, while still guaranteeing no-overflow through the quantum representation.
2Device complexity
If the register size is fixed in digital computer systems, then overflow can be prevented, but the precision of arithmetic operations deteriorates with repeated manipulations
Solution Approach 1:
The patent transitions from a purely classical register system to a hybrid quantum-classical system by introducing a quantum register for the significand. This dimensional change allows the system to maintain fixed physical register size while achieving arbitrary precision through the quantum superposition states, effectively adding a new dimension (quantum state space) to the computational architecture.
Data Source
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.