Quanton representation for emulating quantum-like computation on classical processors
First Claim
1. A method of emulating an evolution of a quantum system, the method being performed by circuitry, the method comprising:
- storing in memory a Quanton virtual machine data structure (QVM) by configuring in the memory a permutation data structure representing a quantum state, configuring in the memory a second data structure representing an evolution operator of the quantum state as directional displacements on a manifold, and configuring in the memory a relational table relating permutations to lattice points on the manifold;
receiving training data representing a plurality of input quantum states respectively associated with a plurality of output quantum states of the plurality of input quantum states after having evolved according to the quantum system;
training, using the received training data, the QVM byinitializing a distribution of the QVM, anditeratively updating the distribution of the QVM based on results of a fitness function applied to randomly selected QVMs to generate a trained QVM representing a convergence of the distribution of the QVM, whereinthe results of the fitness function applied to a QVM of the randomly selected QVMs include a distance measure between respective states of the output quantum states and corresponding states of the plurality of input quantum states after having applied the QVM of the randomly selected QVMs; and
emulating the quantum system by applying the trained QVM to a quantum input representing an initial state of the quantum system and thereby generating, in polynomial time, a quantum output representing an initial state of the quantum system and corresponding to the quantum input evolved according to the quantum system, whereinthe permutation data structure is an array representing a permutation matrix, andeach of the randomly selected QVMs are determined using respective random numbers generated by the circuitry according to the distribution of the QVM.
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Abstract
The Quanton virtual machine approximates solutions to NP-Hard problems in factorial spaces in polynomial time. The data representation and methods emulate quantum computing on classical hardware but also implement quantum computing if run on quantum hardware. The Quanton uses permutations indexed by Lehmer codes and permutation-operators to represent quantum gates and operations. A generating function embeds the indexes into a geometric object for efficient compressed representation. A nonlinear directional probability distribution is embedded to the manifold and at the tangent space to each index point is also a linear probability distribution. Simple vector operations on the distributions correspond to quantum gate operations. The Quanton provides features of quantum computing: superpositioning, quantization and entanglement surrogates. Populations of Quantons are evolved as local evolving gate operations solving problems or as solution candidates in an Estimation of Distribution algorithm. The Quanton representation and methods are fully parallel on any hardware.
18 Citations
56 Claims
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1. A method of emulating an evolution of a quantum system, the method being performed by circuitry, the method comprising:
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storing in memory a Quanton virtual machine data structure (QVM) by configuring in the memory a permutation data structure representing a quantum state, configuring in the memory a second data structure representing an evolution operator of the quantum state as directional displacements on a manifold, and configuring in the memory a relational table relating permutations to lattice points on the manifold; receiving training data representing a plurality of input quantum states respectively associated with a plurality of output quantum states of the plurality of input quantum states after having evolved according to the quantum system; training, using the received training data, the QVM by initializing a distribution of the QVM, and iteratively updating the distribution of the QVM based on results of a fitness function applied to randomly selected QVMs to generate a trained QVM representing a convergence of the distribution of the QVM, wherein the results of the fitness function applied to a QVM of the randomly selected QVMs include a distance measure between respective states of the output quantum states and corresponding states of the plurality of input quantum states after having applied the QVM of the randomly selected QVMs; and emulating the quantum system by applying the trained QVM to a quantum input representing an initial state of the quantum system and thereby generating, in polynomial time, a quantum output representing an initial state of the quantum system and corresponding to the quantum input evolved according to the quantum system, wherein the permutation data structure is an array representing a permutation matrix, and each of the randomly selected QVMs are determined using respective random numbers generated by the circuitry according to the distribution of the QVM. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29)
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30. An apparatus comprising:
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a memory storing a Quanton virtual machine data structure (QVM), the QVM including a permutation data structure representing a quantum state, a second data structure representing an evolution operator of the quantum state as directional displacements on a manifold, and a relational table relating the permutation data structure to lattice points embedded in the manifold corresponding to the second data structure; and circuitry configured to generate random number according a predefined distribution, receive training data representing a plurality of input quantum states respectively associated with a plurality of output quantum states of the plurality of input quantum states after having evolved according to the quantum system, and train, using the received training data, the QVM by initializing a distribution of the QVM, and iteratively updating the distribution of the QVM based on results of a fitness function applied to randomly selected QVMs to generate a trained QVM representing a convergence of the distribution of the QVM, wherein the results of the fitness function applied to a QVM of the randomly selected QVMs include a distance measure between respective states of the output quantum states and corresponding states of the plurality of input quantum states after having applied the QVM of the randomly selected QVMs, and emulate the quantum system by applying the trained QVM to a quantum input and thereby generating, in polynomial time, a quantum output corresponding to the quantum input evolved according to the quantum system, wherein the permutation data structure is an array representing a permutation matrix, and each of the randomly selected QVMs are determined using respective random numbers generated by the circuitry according to the distribution of the QVM. - View Dependent Claims (31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56)
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Specification