METHODS AND SYSTEMS FOR QUANTUM SEARCH, COMPUTATION AND MEMORY

• US 20090164435A1
• Filed: 12/17/2008
• Published: 06/25/2009
• Est. Priority Date: 12/20/2007
• Status: Active Grant

• Current Assignee: Telean Technologies Limited
• Original Assignee: Thomas J. Routt
• Inventors: Routt, Thomas J.
• Granted Patent: US 8,190,553 B2
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: B82Y 10/00 Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
• CPC Class Codes: G06F 16/951 Indexing; Web crawling techniques
• CPC Class Codes: G06N 10/00 Quantum computing, i.e. information processing based on quantum-mechanical phenomena
• CPC Class Codes: H04L 9/0852 Quantum cryptography transmission systems employing electromagnetic waves other than radio waves, e.g. light, infrared H04B10/00; wavelength-division multiplex systems H04J14/02; WDM arrangements H04J14/03

Abstract

A system for performing multi-dimensional quantum search, quantum computation, quantum memory, quantum storage, and quantum retrieval includes a structure and method for: enabling components and systems for quantum search, and more particularly to improved local and remote quantum computing and search components and systems; quantum memory component and systems; quantum storage components and systems; quantum retrieval components and systems; quantum logic gates; classical (non-quantum) search components and systems; integrated quantum-classical search components and systems; and integrated quantum-classical cryptosystems.

Claims

1. A system for quantum search and retrieval in multiple dimensions comprising:

a Quantum search query module;

a Quantum oracle index;

a Mapping index including;

a quantum search index with rotation operators and spin matrices components;

an addressable absolute memory index with rotation matrices, quantum number, world sheet, root systems, and root memory cells components; and

an encryption index with quantum, classical, and steganographic components;

a Content mapping module; and

a Quantum application programming interface.

2. A system as recited in claim 1, incorporating a classical application programming interface and a quantum-classical application programming interface to a classical (non-quantum) search and retrieval system including:

a classical crawler module;

a classical page repository;

a plurality of classical indexes and modules; and

a plurality of classical query and ranking modules.

3. A system as recited in claim 1, wherein the system initializes to a superposition:

[(|0+|00+ . . . +|0 . . . 0+|1+|11+ . . . +|1 . . . 1)/n√

2],

the superposition obtained within an nth root of A number of steps, where A is any complex number of the form a+bi, where a and b are real numbers, and where i is an imaginary unit, with the property i²=−

1;

where such a superposed intialization provides a basis for massively parallel quantum computation, enabling combined sequential and simultaneous processing, generating a conditional basis for massively parallel calculation of a plurality of computational trajectories, pathways, and outcomes.

4. A system as recited in claim 1 for calculating a quantum addressable absolute memory index (AAMI) in the form:

5. A system as recited in claim 4 for:

identifying quantum numbers of spin-polarized electrons;

identifying fermionic quantum numbers, where fermions include any of electrons, protons, neutrons, neutrinos, quarks, or certain atomic structures;

storing quantum numbers of spin-polarized electrons;

storing fermionic quantum numbers, where fermions include any of electrons, protons, neutrons, neutrinos, quarks, or certain atomic structures;

associating a plurality of quantum numbers to a plurality of particles, at a plurality of scales, to a plurality of quantum memory cells, where the set of quantum numbers specifies the complete and unique quantum state of each particle functioning as a particular quantum memory cell, and where the combination of any given particle quantum number set associated with any given unique quantum memory cell; and

associating particle states to wave functions.

6. A quantum search oracle comprising:

zero-point quantum computation, search, storage and retrieval logic within a plurality of superposed quantum gaps, or computational singularities;

remains internally state-continuous while stationed between and among any 2-to-n instances of a plurality of observable system states; and

marks a plurality of solutions to a plurality of quantum search query requests by phase-shifting search request solutions utilizing zero-point, self-referral computations in quantum gap logic that approach infinite root (→

∞

√

N/M) search iterations at hyper-exponentially convergent calculation velocities, where the search problem contains a plurality of possible items and a plurality of possible solutions.

7. A quantum search, computation, and retrieval system comprising:

a plurality of mapping indices between and among a plurality of real-, complex-, and quaternion-based computations and representations.

8. A quantum search, computation and retrieval system comprising:

a source of spin-polarized particles;

a Wavefunction Ψ

(x) initialization at uniform superposition, with equal amplitudes in all basis states and where sums of entries in initialization matrix columns are unity;

a Quantum logic initialization for a named search sets wavefunction time to zero, where [(t=0)Ψ

(x)] is an eigenstate of a Hamiltonian (H), a self-adjoint operator acting on a state space to initialize computational energy as a physically observable (real number-based) quantity=N which is associated with a named computational search set=S_n;

a plurality of computational and search arguments and parameters that propel a quantum, massively parallel search along n-dimensional, massively interlinked computational pathways;

a quantum search query module that formats and presents a plurality of quantum search query requests to a quantum oracle index;

a quantum oracle index that invokes a quantum search oracle;

a plurality of E₈ roots and cells mapped to a plurality of quantum root memory cells;

a rotation operator module to associate a plurality of basis state phase shift rotations by π

to a plurality of root memory cells;

phase-shiftmarked basis state search matches by rotations of 2π

;

phase-shift unmarked basis state search matches by rotations of 3π

/2;

phase-shift a plurality of marked and unmarked basis state computational and search matches by a plurality of infinitesimal increments of rotations of [−

∞

≦

π

≦

∞

];

associate a plurality of marked rotations (2π

-to-nπ

-radians) and unmarked rotations (3π

/2-to-nπ

/n-radians), with a plurality of quantum search indices utilizing an nth root algorithm, where a plurality of radicands is enabled, approaching infinite root at exponentially or hyper-exponentially convergent calculation velocities;

associate a plurality of marked rotations (2π

-to-nπ

-radians) and unmarked rotations (3π

/2-to-nπ

/n-radians), with a plurality of locations on an absolute addressable memoiy index;

associate a plurality of infinitesimal increments of phase-shifted rotations of [−

∞

≦

π

≦

∞

] to a plurality of locations on an addressable absolute memory index;

initialize subsequent named computational search sets [S_n+1→

S_∞

] on E₈ roots and cells that are directly mapped to a plurality of root memoiy cells;

a spin matrices module where spin-polarized particle results from marked and unmarked rotations generate and apply n-vector extensions to a plurality of spin matrices;

a rotation matrices module that generates a plurality of spin-polarized particle rotation matrices;

a quantum number module that initializes root memory cell map index matrices, calculates a plurality of root system, principal, azimuthal, magnetic, and spin quantum numbers;

an integrated world sheet root system and root memory cells module that initializes nth-root search logic approaching infinite root a hyper-exponentially convergent calculation velocities;

initializes cartan sub-algebra generators;

generates a strong G2 root system;

rotates and scales in n-dimensions;

matches on parallel world lines;

collapses a G₂ root system to lower dimensional embedded space;

generates a plurality of graviweak F₄ vertices a quantum number;

generates a plurality of gravitation and electroweak D₂ vertices;

calculates a plurality of E₈ polytope vertices;

calculates an E₈ quantum number;

combines a plurality of E₈ root in eight dimensions;

collapses an E₈ root system along matched parallel world lines and lattices to lower dimensional embedded space;

calculates a plurality of E₈ root systems along mapped world lines;

calculates collapsed n-dimensional E₈ root system projections;

maps to a plurality of root memory cells;

a quantum encryption module that performs quantum encryption and decryption;

a classical encryption module that performs industry-standard classical (non-quantum) encryption, decryption and interfaces;

a steganographic encryption module that performs steganographic encoding of a plurality of quantum and classical encryption operations;

a content mapping module that formats, maps, and returns a plurality of quantum search query request indexes into a quantum search results list across a quantum application programming interface;

an integrated classical crawler module, classical page repository, classical search indexes, and classical search query ranking module that processes a plurality of search query requests and formats a plurality of search results within a classical search system and via interface to a quantum search system.

9. A quantum search, computation, and retrieval system as recited in claim 8 that generates a quantum search index of the form 0≦

element index≦

N−

1 to N search elements, N=2ⁿ;

where the quantum search index can be stored in n qubits, an associated quantum search problem has M solutions with 1≦

M≦

N, the quantum search index obtains a search solution utilizing an exponentially or hyper-exponentially converging nth root algorithm for finding an nth root of A, where A is any complex number of the form a+bi, where a and b are real numbers, where i is an imaginary unit with the property i²=−

1, and where a radical or root may be encoded by an infinite series;

10. A quantum search, computation, and retrieval system as recited in claim 8 that associates with, and encodes to, a plurality of Lie groups, the Lie groups being differentiable manifolds with the property that group operations are compatible with a continuous-symmetry smooth structure, i.e., continuous symmetries of differential equations;

associating a plurality of spin states with local or linearized, versions of a global quantum computational object with its infinitesimal group, based on Lie algebra;

comprising a plurality of root vectors and a plurality of Cartan subalgebra generators that span the Lie algebra and, in so doing, can function as generators—

the Cartan-Weyl basis of the Lie algebra, where the Lie bracket between root vectors corresponds to vector addition between their roots, and to interactions between quantum memory address locations;

where eigenvectors function as weight vectors of the Cartan subalgebra, with eigenvalues that correspond to the generalized roots (weights) that describe a plurality of representations;

comprising a plurality of canonical forms for the commutation relations of a Lie algebra, where resulting equations are invariant under the nonsingular transformation U, and where the canonical form is a polynomial in λ

of order η

, with real coefficients φ

_j(rⁱ), depending on the choice of Lie algebra element; and

comprising a means to generate and store a plurality of Lie brackets within a plurality of Lie groups as a function of equivalent operators of a subgroup of vectors in fundamental representation spaces, based upon a plurality of superposed quantum gaps, or computational singularities, stationed between and among any 2-to-n instances of a plurality of observable system states.

11. A quantum search, computation, and retrieval system as recited in claim 8 further comprising a means to cross-associate and cross-integrate quantum search and retrieval initialization, time-series evolution, and results, within and among a plurality of classical, non-quantum systems as a function of a plurality of addressable classical memory components existing within a quantum memory system.

12. A quantum search, computation, and retrieval system as recited in claim 8 further comprising:

a plurality of spin-polarized electrons or spin-polarized photons generated and expressed as a plurality of spin slopes and spin slope fields;

a first means to achieve long storage times of representations of spin polarization, based upon construction of a plurality of slope fields associated with a plurality of spin-polarized states, expressed as differentiable functions computed at n-dimensional cartesian coordinate-based points of spin-polarized near-tangency;

a second means to generate autonomous differential equations, yielding horizontal-shift-invariant slope fields;

a third means to generate nonautonomous differential equations yielding horizontal- and vertical-shift-variant slope fields;

a fourth means to associate a plurality of nonautonomous differential equation-based slope fields to a plurality of spin-polarized electronic, and to a plurality of spin-polarized photonic states;

a fifth means to represent a plurality spin-polarized electronic and a plurality of spin-polarized photonic states, to a plurality of autonomous and nonautonomous differential equation-based slope fields;

a sixth means to generate a plurality of solution curves to a plurality of autonomous and non-autonomous differential equation-based representations of spin-polarized electronic and photonic states, where convergence regions generate addressable and reusable quantum search index identifiers; and

a seventh means to associate a plurality of quantum numbers to a plurality of quantum memory cells, where the associated set of quantum numbers specifies the complete and unique quantum state of each particle functioning as a particular quantum memory cell.

13. A quantum search, computation, and retrieval system as recited in claim 12, further comprising a plurality of spin state-vectors imparted with n-dimensional components via operators on n-directional photonic oscillating magnetic field and electric field parallel and perpendicular alignments, where spin decoherence is contained by minimizing duration of optical pulse and storage times, and

wherein the first through seventh means are a quantum computer.

14. A quantum cryptosystem of the quantum search, computation, and retrieval system as recited in claim 8,

wherein qubits are established via the oscillating polarization generated as a function of the time-varying electric field of a light wave where the relationship between the polarization and applied electric field is linear, with the resulting time-varying polarization sinusoidal at frequency ω

₁ through ω

_n;

wherein sinusoidally-varying fields are generated for any medium in which induced polarization is a nonlinear function of any electric field, inducing polarizations that incorporate frequency components at 1-to-n higher harmonics of the original (first-order, or linear) frequency, generating the basis for 1-to-n qubit encryption;

where Σ

-frequencies of second-to-nth-order harmonic waves expressing as qubits are calculated using perturbations of Maxwell'"'"'s equations for static and time-varying electric and magnetic fields, and where computational reversibility may be calculated through an Inverse Fourier Transform on any classical (non-quantum) function ƒ

(x).

15. A quantum cryptosystem of the quantum search, computation, and retrieval system as recited in claim 8, wherein computational reversibility can be calculated through a Quantum Fourier Transform as the discrete Fourier transform with a specified decomposition into a product of simpler unitary matrices, and where the decomposition and associated decryption can be implemented as a quantum logic gate.

16. A quantum cryptosystem of the quantum search, computation, and retrieval system as recited in claim 8, wherein the relationship between induced polarization P and the electric field E is not linear;

qubits are established as a result of the generated polarization not being the same for a given applied field of magnitude +E₀, in the same fashion as for an applied field of magnitude −

E₀; and

the polarization response to any given applied sinusoidal field is not purely sinusoidal, generating a distortion reflecting the presence of polarization components at frequencies ≠

ω

₁, and therefore providing the basis state for a strong component at the second-harmonic frequency 2ω

₁ or nth-harmonic frequencies 2ω

_n.

17. A quantum cryptosystem of the quantum search, computation, and retrieval system as recited in claim 8, wherein sender-receiver parties rotate Einstein-Podolsky-Rosen (EPR) quantum key-generating pairs [(|00+|11)√

2)] by 1-to-n spin-polarized phase angles (θ

) throughout the integer and/or sub-integer range 0≦

θ

≦

360.

18. A quantum cryptosystem of the quantum search, computation, and retrieval system as recited in claim 8, wherein quantum cryptographic algorithms, keys, and references thereto, are steganographically encoded and referenced within classical fields protected by n-bit keys, and references thereto, based on steganographically embedding 1-to-n quantum cryptographic algorithms, keys, and references thereto, within 1-to-n classical fields, and references thereto, comprising the following steps:

(1) Initializing the sequence by encoded reference to quantum computational results, resulting in generation of non-orthogonal qubits;

(2) Generating a non-orthogonal qubit result reference field comprising 1-to-n classical bits;

(3) Generating a pseudo-random key sequence using a classical (non-quantum) XOR operation;

(4) Encrypting the XOR pseudo-random result employing a commutative one-way accumulator;

(5) Pseudo-randomly interspersing check bits among (classical) data bits;

(6) Embedding reference (classical) check bits to calculated non-orthogonal qubits and references thereto; and

(7) embedding classical data referenced by classical check bits into variable-length message data and overhead fields.

19. A quantum cryptosystem as recited in claim 18 that employs a reversible computational method to the method for retrieving 1-to-n embedded quantum cryptographic algorithms, keys, and references thereto, from 1-to-n classically encrypted fields, and references thereto.

20. A quantum cryptosystem as recited in claim 18 wherein classical (non-quantum) data fields protected by n-bit keys, and references thereto, are steganographically encoded and referenced within quantum cryptographic algorithms, keys, and references thereto.

21. An integrated classical (non-quantum)-quantum cryptosystem of the quantum search, computation, and retrieval system recited in claim 18 that steganographically embeds 1-to-n classical (non-quantum) cryptographic algorithms, keys, and references thereto, within 1-to-n quantum cryptographic algorithms, keys, and references thereto, comprising the following steps:

(1) Initializing the sequence by encoded reference to classical (non-quantum) encryption algorithms and keys;

(2) Generating a random quantum key sequence resulting in non-orthogonal qubits;

(3) Calculating a spin-polarized phase angle pointer to 1-to-w classical (non-quantum) cryptographic algorithms and keys;

(4) Calculating the associated inner product φ

|Ψ

between the vectors |φ

and |Ψ

(5) Calculating the associated tensor product |φ

|Ψ

of |φ

and |Ψ

(6) Embedding reference quantum check qubits to calculated classical (non-quantum) cryptographic algorithms, keys, and references thereto; and

(7) Embedding the quantum computational result into the transmitted quantum message.

22. An integrated classical (non-quantum)-quantum cryptosystem as recited in claim 21 that employs a reversible computational method to the method for retrieving 1-to-n embedded classical (non-quantum) cryptographic algorithms, keys, and references thereto, from 1-to-n quantum encrypted fields, and references thereto.