The subject of the invention is a method and an apparatus for efficient data processing, using principles of Quantum Mechanics. A method of evolving a quantum register from an initial state ψ to a desired final state ψyes of said register characterized by comprising of backtracking to the state computationally equivalent to initial state ψ by mapping each and every unknown, undesirable final state ψnot of the quantum register to the superposition or ensemble of orthogonal states in the computations space, when the projection measurement of a quantum register or parts of said register rendered it in the undesirable state ψnot.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of evolving a quantum register from an initial state ψ to a desired final state ψyes of said register characterized in that comprising of backtracking to the state computationally equivalent to initial state ψ by mapping each and every unknown, undesirable final state ψnot of the quantum register to the superposition or ensemble of orthogonal states in the computations space, when the projection measurement of a quantum register or parts of said register rendered it in the undesirable state ψnot. 2. A method according to claim 1 characterized in that utilizing a degenerate state ψ in the calculation space, i.e. ψyes or ψnot being, respectively, superpositions or ensembles of states ψyesk or ψnotk. 3. A method according to claim 1, characterized in that backtracking is by an unitary operator acting on the quantum state of the register ψnot. 4. A method according to claim 1, characterized in that backtracking is a sequence of Hermitean projection measurements. 5. A method, according to claim 1 characterized in that any arbitrary sequence of methods claimed in claims 3 and 4 is used. 6. A method of reduction of a state ψ of a quantum register which is a superposition or an ensemble of desired states ψyes and undesired ψnot, where amplitude coefficients or the probabilities of the ensemble are not known, to the desired superposition state ψyes, characterized in that in the case of measurement projecting ψ to the undesired ψnot, any of the backtracking methods claimed by any of claims 1, 3, 4, 5 is applied to restore the state of the register to the state ψequiv, equivalent to ψ and repeating the sequence of measurement-backtracking, until the state ψyes is found or until probability that the solution exists given the number of unsuccessful retries falls below a preset threshold. 7. A method according to claim 6 characterized in that the state ψ is a degenerate state in the computation space, ψyes or ψnot being, respectively superpositions or ensembles of states ψyesk or ψnotk. 8. A method according to claim 6 or 7 characterized in that the transformations described in claim 3, 4 or 5 operate in orthogonal subspaces in the computational space, which includes but is not limited to the operation on a subset of qbits. 9. A method of reducing register characterized in that, in the case of exponentially large dimension of the search space N=2n where n is the length of the register, the dimensionality of the search space is recursively reduced at each step by using the method 6, 7 or 8 such that the resulting state ψyes of previous step is the initial state ψ the next step, and the measurements and backtracking transformations claimed in 1, 3, 4 or 5 do not increase the dimensionality of current space beyond the initial state ψ of a step, so the sequence of k steps allows for exponential speedup of the order of average dimension reduction dimψ/dim ψyes raised to the number of steps k. 10. A quantum computer characterized in that at least one of the qbits q in the register |x,q> is available for the projecting measurement H, in such a way that reduction of the said qubit to 0 or 1 does not destroy the state of the remaining part of the register, merely reducing x to the state compatible with the resulting value of q e.g. |x0, 0> or |x1, 1>.