Quantum Processor Factor Graph Mapping for Integer Factoring
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Solution Overview
Problem
Current methods for factoring large integer numbers, particularly biprimes, are inefficient and require substantial computational power, making them unsuitable for secure encryption schemes as they can be decrypted with significant effort, compromising data security over time.
Innovation Solution
A method utilizing a quantum processor to factor numbers by creating a factor graph, mapping it onto an analog processor, initializing it to an initial state, evolving it to a final state, and measuring the output to obtain the prime factors, leveraging quantum mechanics for efficient computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical computing devices are used to factor large numbers, then the computational process becomes intractable, but the security of encryption schemes is compromised over time
Solution Approach 1:
The patent replaces classical mechanical computing systems with a quantum processor that utilizes quantum mechanical effects (superposition, entanglement, interference) to perform factorization. The quantum processor implements a quantum circuit that computes the period of a function, enabling efficient factorization of large numbers and thereby maintaining encryption security against quantum attacks.
2Reliability
If larger numbers are used for encryption, then security increases, but the computational difficulty of factoring increases exponentially
Solution Approach 1:
The patent changes the fundamental parameters of the computational system by transitioning from classical to quantum computing. The quantum processor uses quantum states with exponentially larger state spaces to represent and manipulate factorization problems, allowing it to handle larger encrypted numbers efficiently without exponential increases in computational complexity.
3Productivity
If more computational power is allocated to factoring, then the speed of factorization increases, but the cost and resource requirements increase substantially
Solution Approach 1:
The patent substitutes quantum mechanical computation for classical computational resources. The quantum processor achieves high factoring speed not by allocating more classical computational resources, but by fundamentally changing the computation mechanism to exploit quantum parallelism and interference, thereby achieving exponential speedup with relatively few qubits.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces the time required for factoring large numbers, enhancing the security of encryption schemes by making it computationally infeasible for unauthorized parties to decrypt, thus ensuring secure data transmission.
Implementation Method 1
A method utilizing a quantum processor to factor numbers by creating a factor graph, mapping it onto an analog processor, initializing it to an initial state, evolving it to a final state, and measuring the output to obtain the prime factors, leveraging quantum mechanics for efficient computation.
Data Source
AI summary
Systems, methods and apparatus for factoring numbers are provided. The factoring may be accomplished by creating a factor graph, mapping the factor graph onto an analog processor, initializing the analog processor to an initial state, evolving the analog processor to a final state, and receiving an output from the analog processor, the output comprising a set of factors of the number. The factoring may be accomplished by generating a logic circuit representation of the factoring problem, such as a multiplication circuit, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s).