Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
As per claims 11 and 18, the claims recite “lowering the number of qubits in the output quantum register to a closet number of the sum that is a power of two” and “lowering the number of qubits in the output quantum register to a power of two number which is closet to the sum” respectively. The language is unclear because the number of qubits is not the same thing as the register’s power of two capacity. Further, it’s not clear what it meant by “a closet number of the sum.” The term “closet” a relative term which renders the claim indefinite. The term “closet” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. Appropriate correction is required.
Claim 19 recites the limitation "using the same quantum registers" which depends on claim 1 but claim 1 recites only “a quantum register” in the singular. It does not introduce plural “quantum registers.” There is insufficient antecedent basis for this limitation in the claim.
Claim Rejections - 35 USC § 102
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
Claims 1-5, 19-20, 22-24 are rejected under 35 U.S.C. 102(a)(1) as being anticipated by Mazzola et al. US PG-Pub 2002/0188679 (hereinafter Mazzola).
As per claim 1, Mazzola teaches a method for providing a quantum variable (paragraphs 132-136 teaches re-parameterization and state-preparation method, including Algorithm 3.2, for loading stochastic processes and standard normal random variables into quantum states), comprising:
providing a quantum register comprising a set of qubits defining a quantum system (paragraph 136 expressly provides an n-qubit register and an operator G that loads a standard Gaussian distribution into that register);
representing states of the quantum system in a computational basis by an ordered set of consecutive nonnegative integer numbers, referred to as a set of indexes (paragraphs 136 and 145, the loaded quantum state is represented in the G distribution in paragraph 36 wherein i denotes a computational-basis state. Mazzola further specifies i=0,….,2^n – 1, which is an ordered set of consecutive nonnegative integer dices);
determining a random variable in accordance with a predefined classical- quantum format (Mazzola determines a standard Gaussian random variable represented by a classical probability mass function gi, discretized into 2^n bins, and encodes that distribution using amplitudes √gi. The predetermined association between classical probabilities, classical sample points, basis-state indices, and quantum amplitudes constitutes the claimed classical-quantum format),
wherein the random variable is valued in a finite domain of classical values (Mazzola prepares the Gaussian distribution on a finite discretized mesh containing 2^n classical values xi, with i=0,…,2^n – 1. The disclosed example fixes the finite truncation parameter at w = 5, see paragraph 145) such that each value of the domain is derived from a respective index of the set of indexes through an affine relationship (Mazzola expressly defines the classical mesh points as xi = -w +iAx, where Ax = 2w / 2^n. Thus, each classical value xi is obtained from its corresponding index I through an affine function, see paragraph 145), the affine relationship being defined by a scaling factor and an offset factor (In xi = - w + iAx, the scaling factor is Ax, and the offset factor is – w. Both are disclosed, see paragraph 145); and
encoding the set of qubits to represent the random variable (see paragraph 136, which shows encoding the n-qubit register as the G distribution, wherein gi is the classical probability mass associated with the corresponding Gaussian bin or mesh value), wherein the encoding is performed 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 (Because the amplitude of the basis state ii is square root of gi, its measurement probability is |square root gi|^2 = gi. Mazzola identifies gi as the probability mass of the discretized Gaussian distribution corresponding to index i. Thus, measuring i > occurs with the same probability as observing the associated classical value or bin when sampling the random variable. This limitation is expressly disclosed through the state definition and necessarily follows from the disclosed amplitude encoding).
As per 2, Mazzola further teaches the method of claim 1, wherein determining the random variable in accordance with the classical-quantum format (see paragraphs 136, and 145-148 and as mapped above in claim 1) further comprises:
determining a tolerance range (see paragraphs 94-98, Mazzola restricts each variable to an interview, divides that interval into cells, and expressly determines the cell side length. Further, Mazzola computes the discretization error resulting from replacing values in each cell with the cell midpoint. The half-cell interval, l/2, constitutes the claimed tolerance range because every value assigned to the cell is within l/2 of its midpoint representative);
performing the encoding such that an approximate of the domain value and the domain value are represented with the same quantum state (see paragraphs 49-51 and 94-95, Mazzola associates each register value with the midpoint of a corresponding grid cell. The actual classical values within that cell and the midpoint approximation are therefore represented by the same cell index and corresponding computational-basis state. Mazzola expressly state that the midpoint method is used and that values are restricted to discrete midpoints or equivalently integrated over their corresponding discrete cells) in case the difference between the domain value and the approximate is within the tolerance range (A cell has width l and is centered on the midpoint used as its representative. Accordingly, a domain value belongs to that cell – and is represented by the cell’s basis state – when its difference from the midpoint is no greater than l/2. This relationship is necessarily present in Mazzola’s midpoint-cell discretization).
As per claim 3, a method for providing quantum variables (see paragraphs 132-139), comprising:
providing a first quantum register comprising a first set of qubits defining a first quantum system and a second quantum register comprising a second set of qubits defining a second quantum system (see paragraphs 136-138);
representing states of the first quantum system in a computational basis by an ordered set of consecutive first indexes (see paragraphs 136 and 145);
representing states of the second quantum system in a computational basis by an ordered set of consecutive second indexes (see paragraphs 136-138); determining a first random variable and a second random variable of a classical-quantum format (see paragraphs 132-139), the first random variable being valued in a finite first domain of classical values (see paragraphs 145-146) such that each value of the first domain is derived from a respective first index of the set of first indexes through a first affine relationship, the first affine relationship (see paragraph 145) being defined by a first scaling factor and a first offset factor (see paragraphs 139 and 145), the second random variable being valued in a finite second domain of classical values (see paragraphs 136-139 and 145) such that each value of the second domain is derived from a respective second index of the set of second indexes through a second affine relationship (see paragraphs 139 and 145), the second affine relationship being defined by a second scaling factor and a second offset factor (see paragraphs 139 and 145); and encoding the first set of qubits and the second set of qubits for representing the first and second random variables (see paragraphs 136-138).
As per claim 4, Mazzola further teaches the method of claim 3, the first and second random variables being independent (see paragraphs 55, 132-139),
wherein the encoding comprises: encoding the first set of qubits (see paragraph 136) such that the probability of measuring a state of the first quantum system in the computational basis is the probability of observing the first domain value associated with the first index (see paragraphs 136, 145 and 148) representing said measured state when sampling the first random variable (see paragraph 136); and
encoding the second set of qubits (see paragraphs 133 and 137) such that the probability of measuring a state of the second quantum system in the computational basis is the probability of observing the second domain value associated with the second index (see paragraphs 136-138 and 145-148) representing said measured state when sampling the second random variable (see paragraphs 55, 136-138).
As per claim 5, Mazzola further teaches the method of claim 3, the first and second random variables being dependent (see paragraph 139), wherein the encoding of the first and second sets of qubits is performed (see paragraphs 137-139) such that the probability of measuring a state of a joint quantum system of the first and second quantum systems in the computational basis (see paragraphs 137-140) is the probability of jointly observing the first domain value associated with the first index representing said measured state (see paragraphs 138-140) when sampling the first random variable (see paragraph 138) and the second domain value associated with the second index representing said measured state (see paragraphs 138-140) when sampling the second random variable (see paragraphs 138-140).
As per claim 19, Mazzola further teaches the method of claim 1, further comprising performing a quantum algorithm (see paragraphs 61-69) using the method as a subroutine (see paragraphs 132-137) and using the same quantum registers (see paragraphs 65-69).
As per claim 20, Mazzola further teaches the method of claim 1, the scaling factor being a nonzero real number and/or the offset factor being a real number (see paragraph 145).
As per claims 22-33, they are rejected for substantially the same reasons provided for claim 1.
As per claim 24, Mazzola teaches a method for providing a quantum variable (see paragraphs 134-136), comprising:
providing a quantum register comprising a set of qubits defining a quantum system (paragraph 136);
representing states of the quantum system in a computational basis by an ordered set of consecutive nonnegative integer numbers, referred to as a set of indexes (paragraphs 136 and 145);
determining a set of ordered pairs (paragraphs 136, 145, and 148), where a first element of each ordered pair is a complex number (paragraphs 136, 145, 148), such that the sum of all the squared absolute values of the complex numbers across the set equals one (paragraphs 145-146), and a second element of each pair is a real number in a finite domain of classical values (paragraphs 145-146), the real number being derived from a respective index of the set of indexes through an affine relationship (paragraph 145), the affine relationship being defined by a scaling factor and an offset factor (paragraph 145); and
encoding the set of qubits to represent the set of ordered pairs (paragraphs 136, 145 and 148), wherein the encoding is performed such that the quantum state is the complex linear combination of states of the computational basis (paragraphs 136, 229-231), where the coefficients of the linear combination are the first elements in the ordered pairs (paragraphs 136 and 148), and the states of the computational basis are represented by the respective indexes (paragraphs 136 and 145), each index being the index in the set of indexes associated to the respective second element of the ordered pair (paragraphs 136 and 145).
Allowable Subject Matter
Claims 6-18 and 21 are objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims.
As per claim 6, the prior art of record failed to teach determining a sum of the first and second random variables, the determining of the sum comprising: providing an output quantum register comprising a third set of qubits, thereby defining a third quantum system, the first, second and third quantum systems forming a joint quantum system; determining a first set of weights for the first set of qubits respectively and a second set of weights for the second set of qubits respectively, the determining is performed such that the output quantum register after performing the sum represents a third random variable of the classical-quantum format; defining an unknown for each qubit of the first and second quantum registers; defining a monomial for each unknown, the monomial being the unknown multiplied by the weight associated to the respective qubit; defining a polynomial as the sum of the monomials; generating a unitary quantum transformation that is configured to act on the first quantum register and second quantum register, on the output quantum register, and on an auxiliary register, in order to evaluate the polynomial into the output quantum register; and applying the unitary quantum transformation on the first quantum register and second quantum register, thereby encoding the third set of qubits such that the states of the third quantum system in the computational basis represent values of a third random variable of the classical-quantum format.
As per claim 13, the prior art of record failed to teach performing a multiplication of the first and second random variables, the performing of the multiplication comprising: providing an output quantum register comprising a third set of qubits, thereby defining a third quantum system, the first, second and third quantum systems forming a joint quantum system; determining a first set of weights for the first set of qubits respectively and a second set of weights for the second set of qubits respectively and a third set of qubits for the pairs of qubits of the first set and second set of qubits respectively, the P202300674US01 Page 46of51 determining being performed such that the output quantum register after performing the multiplication represents a third random variable of the classical-quantum format; defining an unknown for each qubit of the first and second quantum registers; defining a polynomial as a sum of first degree monomials and second degree monomials, wherein each first degree monomial is associated with respective qubit of the first and second set of qubits, wherein each first degree monomial is defined as the product of the unknown and a weight associated with the respective qubit, wherein each second degree monomial is associated with respective pair of qubits of the first and second set of qubits, wherein each second degree monomial is defined as the product of the two unknowns associated to the two respective qubits and a weight associated with the respective pair of qubits; generating a unitary quantum transformation that is configured to act on the first quantum register and second quantum register, on the output quantum register, and on an auxiliary register, in order to evaluate the polynomials into the output quantum register; applying the unitary quantum transformation on the first and second quantum registers, thereby encoding the third set of qubits such that the states computational basis of the of the third quantum system represent values of a third random variable of the classical-quantum format.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Woerner et al., US PG-Pub 2021/0133613 teaches probability-distribution loading, random variables, affine discretization grids and quantum algorithms.
Allen US PG-Pub 2009/0083358 teaches fixed point scaling, aligning different operand scales, and determining result scales.
Lloyd et al. US PG-Pub 2009/0010090 teaches bucket brigade address decoding architecture for classical and quantum random access memories.
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/IDRISS N ALROBAYE/Supervisory Patent Examiner, Art Unit 2181
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