DETAILED ACTION
Notice of Pre-AIA or AIA Status
1. The present application 18/614,546, filed on 06/13/2026, is being examined under the first inventor to file provisions of the AIA .
Drawings
2. The drawings received on 03/22/2024 are accepted by the Examiner.
Information Disclosure Statement
3. The information disclosure statement (IDS) submitted on 03/06/2026 and 04/08/2024 are being considered by the examiner.
Priority
4. Acknowledgment is made of applicant's claim for priority based on provisional application filed on 09/12/2023.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
5. Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to non-statutory subject matter.
Claims 1-20 are rejected under 35 U.S.C 101 because the claimed invention is directed to a judicial exception (i.e., an abstract idea) without significantly more. Claim 1 is directed to an abstract idea for a quantum computer, as explained in detail below. The claim does not include elements that are sufficient to amount to significantly more than the judicial exception because the elements can be concepts performed in the human mind which do not add meaningful limits to practicing the abstract idea.
Claim 1 recites a method for a quantum computer comprising at least in part:
receiving a target matrix comprising only real eigenvalues (e.g., observing a matrix can be performed in the human mind);
presenting the target matrix as block encoding (e.g., observing and evaluating encoding with respect to the matrix can be performed in the human mind using pen and paper);
precomputing a polynomial approximation for a function to be applied to the target matrix (e.g., evaluating and computing a polynomial approximation for a function to be applied on the matrix can be performed in the human mind using pen and paper);
selecting coefficients for a generating function that match the precomputed polynomial approximation (e.g., inputting parameters or configuration for a generating function that match the computed polynomial approximation can be performed in the human mind using pen and paper);
generating a polynomial history state comprising a superposition of polynomials on the block encoded target matrix by at least mapping the generating function to a quantum algorithm (e.g., outputting a polynomial value based on the encoded matrix by mapping the generation function to a quantum algorithm can be performed in human mind including an observation, evaluation, judgement and opinion);
Claim 1, as it is recited, falls within one of the groupings of abstract ideas [e.g., mental process] enumerated in the 2019 PEG. The recited concept can be performed in the human mind, including observation, evaluation, judgement, and opinion, using a quantum computer as a tool. That is, other than reciting a computer, nothing in the claim precludes the step from practically being performed in the mind. The formulating and the encoding features in the claim are recited at a high level of generality and add no more to the claimed invention than the use of a computer to perform an abstract idea. The additional feature merely uses a computer as a tool to generate a result after a series of data gathering/manipulating steps, which constitutes insignificant extra-solution activity. Thus, the judicial exception is not integrated into a practical application. The additional feature in the claim does not appear to be improve the functioning of a computer or any other technology or technical field. The additional feature does not amount to significantly more than the above-identified judicial exception (the abstract idea). Looking at the limitation as an ordered combination adds nothing that is not already present when the elements are considered individually. There is no indication that the combination of elements improves the functioning of a computer or any other technology. Therefore, claim 1 is not patent eligible.
Claims 2 and 5-9 recite features similar to those of claim 1 and fall within one of the groupings of abstract ideas [e.g., a mental process] enumerated in the 2019 PEG. The recited concept can be performed in human mind including observation, evaluation, judgement, opinion. Claims 2 and 5-9 further recite that the polynomial approximation is a Chebyshev polynomial, generating an eigenvalue estimation function based on a polynomial history state and applying an inverse quantum transformation to the generating function to compute an eigenvalue. Claims 2 and 5-9 do not have include additional features that integrate the judicial exception into a practical application. Claims 2 and 5-9 merely use a computer as a tool to generate a result after a series of data gathering/manipulating step, which constitutes insignificant extra-solution activity. The claimed features recited in claims 2 and 5-9 do not appear to be improve the functioning of a computer or to any other technology or technical field. Therefore, claims 2 and 5-9 are not patent eligible.
Claims 3 and 4 recite features similar to those of claim 1 and fall within one of the groupings of abstract ideas [e.g., a mental process] enumerated in the 2019 PEG. The recited concept can be performed in human mind including observation, evaluation, judgement, opinion. Claims 3 and 4 further recite the target matrix is a diagonalizable matrix or a non-Hermitian matrix. Claims 3 and 4 do not have include additional features that integrate the judicial exception into a practical application. Claims 3 and 4 merely use a computer as a tool to generate a result after a series of data gathering/manipulating step, which constitutes insignificant extra-solution activity. The claimed features recited in claims 3 and 4 do not appear to be improve the functioning of a computer or to any other technology or technical field. Therefore, claims 3 and 4 are not patent eligible.
Claim 10 recites a quantum computing system comprising at least in part:
receive a target matrix comprising only real eigenvalues (e.g., observing a matrix can be performed in the human mind);
present the target matrix as block encoding (e.g., observing and evaluating encoding with respect to the matrix can be performed in the human mind using pen and paper);
precompute a polynomial approximation for a function to be applied to the target matrix (e.g., evaluating and computing a polynomial approximation for a function to be applied on the matrix can be performed in the human mind using pen and paper);
select coefficients for a generating function that match the precomputed polynomial approximation (e.g., inputting parameters or configuration for a generating function that match the computed polynomial approximation can be performed in the human mind using pen and paper);
generate a polynomial history state comprising a superposition of polynomials on the block encoded target matrix by at least mapping the generating function to a quantum algorithm (e.g., outputting a polynomial value based on the encoded matrix by mapping the generation function to a quantum algorithm can be performed in human mind including an observation, evaluation, judgement and opinion);
Claim 10, as it is recited, falls within one of the groupings of abstract ideas [e.g., mental process] enumerated in the 2019 PEG. The recited concept can be performed in the human mind, including observation, evaluation, judgement, and opinion, using a quantum computer as a tool. That is, other than reciting a computer comprising processing hardware, nothing in the claim precludes the step from practically being performed in the mind. The formulating and the encoding features in the claim are recited at a high level of generality and add no more to the claimed invention than the use of a computer to perform an abstract idea. The additional feature merely uses a computer as a tool to generate a result after a series of data gathering/manipulating steps, which constitutes insignificant extra-solution activity. Thus, the judicial exception is not integrated into a practical application. The additional feature in the claim does not appear to be improve the functioning of a computer or any other technology or technical field. The additional feature does not amount to significantly more than the above-identified judicial exception (the abstract idea). Looking at the limitation as an ordered combination adds nothing that is not already present when the elements are considered individually. There is no indication that the combination of elements improves the functioning of a computer or any other technology. Therefore, claim 10 is not patent eligible.
Claims 12 and 15-18 recite features similar to those of claim 10 and fall within one of the groupings of abstract ideas [e.g., a mental process] enumerated in the 2019 PEG. The recited concept can be performed in human mind including observation, evaluation, judgement, opinion. Claims 12 and 15-18 further recite that the polynomial approximation is a Chebyshev polynomial, generating an eigenvalue estimation function based on a polynomial history state and applying an inverse quantum transformation to the generating function to compute an eigenvalue. Claims 12 and 15-18 do not have include additional features that integrate the judicial exception into a practical application. Claims 12 and 15-18 merely use a computer as a tool to generate a result after a series of data gathering/manipulating step, which constitutes insignificant extra-solution activity. The claimed features recited in claims 12 and 15-18 do not appear to be improve the functioning of a computer or to any other technology or technical field. Therefore, claims 12 and 15-18 are not patent eligible.
Claims 13 and 14 recite features similar to those of claim 1 and fall within one of the groupings of abstract ideas [e.g., a mental process] enumerated in the 2019 PEG. The recited concept can be performed in human mind including observation, evaluation, judgement, opinion. Claims 13 and 14 further recite the target matrix is a diagonalizable matrix or a non-Hermitian matrix. Claims 13 and 14 do not have include additional features that integrate the judicial exception into a practical application. Claims 13 and 14 merely use a computer as a tool to generate a result after a series of data gathering/manipulating step, which constitutes insignificant extra-solution activity. The claimed features recited in claims 13 and 14 do not appear to be improve the functioning of a computer or to any other technology or technical field. Therefore, claims 13 and 14 are not patent eligible.
Claim 19 recites a method for a quantum computer comprising at least in part:
receiving a diagonalizable matrix A comprising only real eigenvalues (e.g., observing a matrix can be performed in the human mind);
block encoding I.Math.I+L2.Math.I-2L.Math.AαA to generate a first component, where L is an-by-n lower shift matrix and α.sub.A is a normalization factor ≥2∥A∥ (e.g., observing and evaluating encoding with respect to the matrix using mathematical equation can be performed in the human mind using pen and paper);
receiving a set of coefficients β; reversing the set of coefficients and applying I.Math.I −L.sup.2.Math.I to generate a second component; receiving, as a third component, an initial state ψ (e.g., inputting and manipulating parameters using the mathematical equation can be performed in the human mind using pen and paper);
applying a quantum linear system algorithm to the first, second, and third components to generate the Chebyshev history state (e.g., outputting a polynomial value by mapping the encoded matrix to a quantum algorithm can be performed in human mind including an observation, evaluation, judgement and opinion);
Claim 19, as it is recited, falls within one of the groupings of abstract ideas [e.g., mental process] enumerated in the 2019 PEG. The recited concept can be performed in the human mind, including observation, evaluation, judgement, and opinion, using a quantum computer as a tool. That is, other than reciting a computer, nothing in the claim precludes the step from practically being performed in the mind. The formulating and the encoding features in the claim are recited at a high level of generality and add no more to the claimed invention than the use of a computer to perform an abstract idea. The additional feature merely uses a computer as a tool to generate a result after a series of data gathering/manipulating steps, which constitutes insignificant extra-solution activity. Thus, the judicial exception is not integrated into a practical application. The additional feature in the claim does not appear to be improve the functioning of a computer or any other technology or technical field. The additional feature does not amount to significantly more than the above-identified judicial exception (the abstract idea). Looking at the limitation as an ordered combination adds nothing that is not already present when the elements are considered individually. There is no indication that the combination of elements improves the functioning of a computer or any other technology. Therefore, claim 19 is not patent eligible.
Claim 20 recites features similar to those of claim 19 and fall within one of the groupings of abstract ideas [e.g., a mental process] enumerated in the 2019 PEG. The recited concept can be performed in human mind including observation, evaluation, judgement, opinion. Claim 20 recites the target matrix is a diagonalizable matrix. Claim 20 does not have additional features that integrate the judicial exception into a practical application. Claim 20 merely uses a computer as a tool to generate a result after a series of data gathering/manipulating step, which constitutes insignificant extra-solution activity. The claimed feature recited in claim 20 does not appear to be improve the functioning of a computer or to any other technology or technical field. Therefore, claim 20 is not patent eligible.
Claim Rejections - 35 USC § 103
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 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 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1-5, 8, 10-14, 17, 19 and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Low et al. (“Hamiltonian Simulation by Qubitization”, 2019), hereinafter Low and in view of Williams et al. (EP 4485293 A1), hereinafter Williams.
Referring to claims 1 and 10, Low discloses a method for a quantum computer (See page 1, Abstract, page 2, 1. Introduction, a quantum computer is configured to estimate time-evolution operator e−iˆHt to error ϵ, where the Hamiltonian ˆ H =(⟨G|⊗ˆ I)ˆU(|G⟩⊗ˆ I)) comprising:
receiving a target matrix comprising only real eigenvalues (See page 5, Section 2: Overview of the Quantum Signal Processor, receiving a Hermitian matrix ˆH with bounded spectral norm ∥ ˆH∥ ≤ 1, note the Hermitian matrix ˆH has eigenbasis of eigenbasis of ˆ H|λ⟩ = λ|λ⟩, for each eigenstate of ˆH, ˆ U|G⟩|λ⟩ = ˆU|Gλ⟩ = λ|Gλ⟩+ 1 −|λ|2|G⊥ λ⟩;
presenting the target matrix as block encoding (See page 5, Section 2: Overview of the Quantum Signal Processor, an encoding of ˆH = ⟨G|ˆU|G⟩ by the oracles, also note page 4, defintion 1, a signal operator ˆH with spectral norm ∥ ˆ H∥ ≤ 1 is encoded in the standard-form if we may query a unitary oracle ˆU : Ha⊗Hs → Ha⊗Hs and a unitary state preparation oracle ˆG|0⟩a = |G⟩a ∈ Ha with the property (⟨G|a ⊗ ˆ Is)ˆU(|G⟩a ⊗ ˆ Is) = ˆH);
precomputing a polynomial approximation for a function to be applied to the target matrix (See pages 6-7, Section 2: Overview of the Quantum Signal Processor; Given a Hermitian matrix ˆH=⟨G|a ˆU|G⟩ a encoded in standard-form as described in Definition1, the iterate ˆW of Eq. (6) can be constructed using at most one query each to ˆG,controlled-U, their universe , at most one additional qubit, Observe that ˆWN efficiently produces Chebyshev polynomials TN[ˆH] [9].We call any function [·] of the signal ˆH target operators when they occur in the top-left block and are thus automatically in standard-form. The fact that Chebyshev polynomials are the best polynomial basis for L∞function approximation on a finite interval [33] suggests that the any target operator [ˆH]=A[ˆH]+iB[ˆH] could be approximated with a judicious choice of controls on the ancilla register);
selecting coefficients for a generating function that match the precomputed polynomial approximation (See page 12 and Lemma 12, selecting coefficients A, B, C, D for real functions that match the polynomial); generating a polynomial history state comprises […] the block encoded target matrix by at least mapping the generating function to a quantum algorithm (See page 12 and Lemma 12, selecting coefficients A, B, C, D for real functions that match the polynomial prepare and measure in the basis of the state |G⟩a, consider the component ⟨G|a ˆ iB(θλ))|λ⟩⟨λ| ≡ A[ ˆ W⃗ φ|G⟩a = λ(A(θλ) + H]+iB[ ˆH]. Any choice of phases ⃗ φ ∈ RQ generates sophisticated interference effects between elements of the sequence, leading to (A,B,C,D) with some non-trivial functional dependence on ˆH. Though the dependence of the output on ⃗ φ seems hard to intuit, they nevertheless specify a program for computing functions of ˆ H, similar to how a list of numbers might specify a polynomial).
Low does not explicitly disclose a superposition of polynomials onto the block encoded target.
Williams discloses generating a polynomial history state comprising a superposition of polynomials onto the block encoded target matrix by at least mapping the generating function to a quantum algorithm (See para. [0159]-para. [0172], Figures 4A-4C and Figure 5A, the system uses a Fourier feature map and/or a Chebyshev feature map to create a superposition of all basis states, also note in para. [0184] and Figure 6B, the quantum Chebyshev transform on the Chebyshev extreme grid maps computational basis state).
Therefore, it would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention was made to modify the polynomial history state of Low to include a superposition of polynomials, as taught by Williams. Skilled artisan would have been motivated to build quantum models that efficiently solve complex machine learning problems (See Williams, para. [0003], para. [0004]). In addition, both references (Williams and Low) teach features that are directed to analogous art and they are directed to the same field of endeavor, such as data encoding in quantum computing systems. This close relation between both references highly suggests an expectation of success.
As to claims 2 and 11, Low discloses wherein the polynomial approximation is a Chebyshev polynomial (See pages 6-7, Section 2: Overview of the Quantum Signal Processor; Given a Hermitian matrix ˆH=⟨G|a ˆU|G⟩ a encoded in standard-form as described in Definition1, the iterate ˆW of Eq. (6) can be constructed using at most one query each to ˆG,controlled-U, their universe , at most one additional qubit, Observe that ˆWN efficiently produces Chebyshev polynomials TN[ˆH] [9].We call any function [·] of the signal ˆH target operators when they occur in the top-left block and are thus automatically in standard-form. The fact that Chebyshev polynomials are the best polynomial basis for L∞function approximation on a finite interval [33] suggests that the any target operator [ˆH]=A[ˆH]+iB[ˆH] could be approximated with a judicious choice of controls on the ancilla register).
As to claims 3 and 12, Low discloses wherein the target matrix is a diagonalizable matrix (See page 14, eiΦˆW can be diagonalized to obtain its eigenvalues θλ± and eigenvectors |Gλ±).
As to claims 4 and 13, Low discloses wherein the target matrix is a non-Hermitian matrix (See page 17, Section 7.1: Developments after preprint release, the matrix can be normal matrices).
As to claims 5 and 14, Low discloses generating an eigenvalue estimation for the function based on the polynomial history state (See page 6, computing each ejgenstate for the function square root (1−|λ|2 ) based on states spanned by the subspace {|G⟩|λ⟩, ˆWπ/2,±|G⟩|λ⟩} and to a state in the span of{|G⟩|λ⟩, ˆWπ/2,∓|G⟩|λ⟩})
As to claims 8 and 17, Low in view of Williams discloses wherein the polynomial history state is utilized to apply polynomial functions to the eigenvalues of non-normal matrices via a quantum eigenvalue transformation (See Williams, para. [0159]-para. [0172], Figures 4A-4C and Figure 5A, the system uses a Fourier feature map and/or a Chebyshev feature map to create a superposition of all basis states, also note in para. [0184] and Figure 6B, the quantum Chebyshev transform on the Chebyshev extreme grid maps computational basis state).
Therefore, it would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention was made to modify the polynomial history of Low to apply polynomial functions via a quantum eigenvalue transformation, as taught by Williams. Skilled artisan would have been motivated to build quantum models that efficiently solve complex machine learning problems (See Williams, para. [0003], para. [0004]). In addition, both references (Williams and Low) teach features that are directed to analogous art and they are directed to the same field of endeavor, such as data encoding in quantum computing systems. This close relation between both references highly suggests an expectation of success.
Referring to claim 19, Low discloses a method for preparing a Chebyshev history state (See pages 6-7, Section 2: Overview of the Quantum Signal Processor; Given a Hermitian matrix ˆH=⟨G|a ˆU|G⟩ a encoded in standard-form as described in Definition1, the iterate ˆW of Eq. (6) can be constructed using at most one query each to ˆG,controlled-U, their universe , at most one additional qubit, Observe that ˆWN efficiently produces Chebyshev polynomials TN[ˆH] [9].We call any function [·] of the signal ˆH target operators when they occur in the top-left block and are thus automatically in standard-form. The fact that Chebyshev polynomials are the best polynomial basis for L∞function approximation on a finite interval [33] suggests that the any target operator [ˆH]=A[ˆH]+iB[ˆH] could be approximated with a judicious choice of controls on the ancilla register), comprising: receiving a diagonalizable matrix A comprising only real eigenvalues (See page 5, Section 2: Overview of the Quantum Signal Processor, receiving a Hermitian matrix ˆH with bounded spectral norm ∥ ˆH∥ ≤ 1, note the Hermitian matrix ˆH has eigenbasis of eigenbasis of ˆ H|λ⟩ = λ|λ⟩, for each eigenstate of ˆH, ˆ U|G⟩|λ⟩ = ˆU|Gλ⟩ = λ|Gλ⟩+ 1 −|λ|2|G⊥ λ⟩;
block encoding I ⊗ I+L2. ⊗.I-2L⊗.(A/αA) to generate a first component, where L is a n-by-n lower shift matrix and α.A is a normalization factor ≥2∥A∥ (See page 5, Section 2: Overview of the Quantum Signal Processor, an encoding of ˆH = ⟨G|ˆU|G⟩ by the oracles, also note page 4, defintion 1, a signal operator ˆH with spectral norm ∥ ˆ H∥ ≤ 1 is encoded in the standard-form if we may query a unitary oracle ˆU : Ha⊗Hs → Ha⊗Hs and a unitary state preparation oracle ˆG|0⟩a = |G⟩a ∈ Ha with the property (⟨G|a ⊗ ˆ Is)ˆU(|G⟩a ⊗ ˆ Is) = ˆH); receiving a set of coefficients β […] the set of coefficients and applying I⊗ I −L2⊗ I to generate a second component (See page 12 and Lemma 12, selecting coefficients A, B, C, D for real functions that match the polynomial); […].
Low does not explicitly disclose reversing a set of coefficients.
Williams discloses reversing the set of coefficients to generate a second component (See para. [0178], the quantum Chebyshev transform circuit runs in reverse direction to perform the inverse quantum Chebyshev transform, which equivalently maps Chebyshev basis states to computation states); receiving, as a third component, an initial state ψ; and applying a quantum linear system algorithm to the first, second, and third components to generate the Chebyshev history state (See para. [0178], claim 7, receiving or determining a differentiated quantum circuit, the differentiated quantum circuit comprising gate operations for encoding, for each of the one or more input features, a value amplitudes the set of basis states of the quantum register, wherein in the represents a derivative of the Chebyshev polynomial of order k with respect to the one or more input features, wherein the differentiated quantum circuit is obtainable by one of:-applying the parameter shift rule to the encoding quantum circuit;- performing (mid-)circuit measurements on the encoding quantum circuit with symmetrically shifted data points; or determining analytical derivatives for the Chebyshev polynomial of order k, k = 0, ..., N- 1, expressing the analytical derivatives in terms of lower-order Chebyshev polynomials, and determining a series of quantum circuits configured to encode the lower-order Chebyshev polynomials as an effective unitary transformation).
Therefore, it would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention was made to modify the system of Low to reverse the set of coefficients, as taught by Williams. Skilled artisan would have been motivated to build quantum models that efficiently solve complex machine learning problems (See Williams, para. [0003], para. [0004]). In addition, both references (Williams and Low) teach features that are directed to analogous art and they are directed to the same field of endeavor, such as data encoding in quantum computing systems. This close relation between both references highly suggests an expectation of success.
As to claim 20, Low discloses wherein the diagonalizable matrix A is a non-Hermitian matrix (See page 17, Section 7.1: Developments after preprint release, the matrix can be normal matrices).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Haah et al. (US 2019/0392343 A1) discloses one or more unitary-valued functions are generated by a classical computer generating using projectors with a predetermined number of significant bits. A quantum computing device is then configured to implement the one or more unitary-valued functions. In further embodiments, a quantum circuit description for implementing quantum signal processing that decomposes complex-valued periodic functions is generated by a classical computer, wherein the generating further includes representing approximate polynomials in a Fourier series with rational coefficients. A quantum computing device is then configured to implement a quantum circuit defined by the quantum circuit description.
Reilly et al. (WO 2023169680 A1) disclose quantum computing methods and devices, wherein a computation corresponding to a certain desired unitary transformation of the Hilbert space of a quantum system, such as a set of qubits, is implemented by selective application of control pulses in order realize a continuous time quantum computation rather than by decomposing the unitary transformation into operations taken from a fixed set of gates.
In this approach, an input matrix A is encoded in the overall Hamiltonian acting on the quantum system as an off-diagonal block connecting a first subspace with a second subspace. This achieved by means of "Hamiltonian Engineering" which efficiently uses time varying semi-classical control fields, the values of the K control field settings at a set of n time instances provide a number of N = n K control parameters that, with the aid of an optimization algorithm executed in a precomputation step, are chosen such that an effective Hamiltonian with the desired of diagonal block A is obtained.
The effective Hamiltonian thus obtained is then either applied alternatingly with a standard Hamiltonian to obtain a time evolution corresponding to a given function f applied to the input matrix A, or its time evolution is executed and the canonical ensemble average is sampled in order to compute arbitrary matrix elements of the given function applied to the effective Hamiltonian H.
In either case, the required control pulses are optimized by means of classical compression techniques, such as a deep learning neural network, to maximize, during the information-loading phase of the computation, the amount of classical information loaded into the system, and, during the computational phase, the number of elementary continuous time quantum transformations, respectively.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to YUK TING CHOI whose telephone number is (571)270-1637. The examiner can normally be reached Monday-Friday 9am-6pm.
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/YUK TING CHOI/ Primary Examiner, Art Unit 2164
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