DETAILED ACTION
This office action is in response to submission of application on 08/24/2022.
Claims 1-20 are presented for examination.
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 .
Information Disclosure Statement
The information disclosure statements (IDS) submitted on 11/24/2022 and 07/03/2024 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statements are being considered by the examiner.
Claim Rejections - 35 USC § 103
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 1-8, 10-18, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over
Zhao et al. (hereinafter Zhao), “Fermionic partial tomography via classical shadows” (published 09/09/2021), in view of
Hu et al. (hereinafter Hu), “Classical Shadow Tomography with Locally Scrambled Quantum Dynamics” (published 07/27/2021) and
Huggins et al. (hereinafter Huggins), U.S. Patent Application Publication US-20240296362-A1 (filed 06/28/2022).
Regarding Claim 1,
Zhao teaches generates a [Haar]-random unitary matrix; (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
;” A random unitary matrix
U
is generated from an ensemble
U
.)
computes a single-particle-basis fermion rotation based at least in part on the [Haar]-random unitary matrix; and (Pg. 3-4, section ‘Modification based on particle-number symmetry’: “Fermionic Gaussian unitaries that preserve particle number are naturally parametrized by
U
(
n
)
… Such unitaries are also called orbital-basis rotations…” An orbital-basis rotation
U
(
n
)
(i.e. single-particle-basis fermion rotation) is computed based on the random unitary matrix
U
.)
receives a specification of a fermion wavefunction over a plurality of fermions in a particle-number-conserving fermion system that occupy a plurality of modes; (Pg. 1, section ‘Fermionic RDMs’: “Consider a fixed-particle state
ρ
represented in second quantization on
n
fermion modes.” A fermion representation in second quantization (i.e. a specification of a fermion wavefunction) of a fixed-particle state (i.e. particle-number-conserving fermion system) occupying
n
modes is received.)
applies the single-particle-basis fermion rotation to the fermion wavefunction to obtain a rotated fermion wavefunction; and (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
;” The unitary map
U
(i.e. fermion rotation) is applied to the fixed-particle state
ρ
(i.e. fermion wavefunction) to obtain a rotated fermion wavefunction.)
measures the rotated fermion wavefunction to obtain a classical shadow measurement result that encodes an estimate of which of the modes are occupied by the fermions; and (Pg. 1, section ‘Introduction’: “In this Letter, we propose a randomized scheme… based on the theory of classical shadows [42]: a protocol of randomly distributed measurements from which one acquires a partial classical representation of an unknown quantum state (its ‘shadow’).” Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
; then perform a projective measurement in the computational basis,
{
|
z
⟩
|
z
∈
{
0,1
}
n
}
… which allows us to define the classical shadow
ρ
^
U
,
z
≔
M
U
-
1
(
U
†
|
z
⟩
⟨
z
|
U
)
associated with the particular copy of
ρ
for which
U
was applied and
|
z
⟩
was obtained.” A classical shadow
ρ
^
U
,
z
encoding the quantum state (i.e. an estimate of which of the modes are occupied by the fermions) is obtained by measuring the rotated fermion wavefunction.)
estimates a k-reduced density matrix (k-RDM) element of a k-RDM of the fermion wavefunction based at least in part on the classical shadow measurement result and the [Haar]-random unitary matrix; and (Pg. 3, Theorem 1: “…Thus the method of classical shadows estimates the fermionic k-RDM of any state
ρ
…” The elements of the fermionic k-RDM of the state
ρ
(i.e. the fermion wavefunction) are estimated based on the classical shadow, which is computed based on the random unitary matrix, as shown above.)
Zhao does not appear to explicitly disclose a Haar-random unitary matrix
However, Hu teaches a Haar-random unitary matrix (Pg. 1-2, section I: “Given a copy of an unknown quantum state
ρ
of
N
qubits, the classical shadow tomography protocol (see Fig. 1) first transforms the state
ρ
→
ρ
=
U
ρ
U
†
by a unitary
U
, which is randomly sampled (independently each time) from some probability distribution… if the observable is low-rank (such as many-body overlap fidelity), it is most efficient to adopt deep circuits, such that
U
effectively forms a global Haar random ensemble;”)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Zhao and Hu. Zhao teaches estimating the k-RDM of a fermionic quantum system using classical shadows which are computed using random unitary matrices. Hu teaches estimating a quantum state using classical shadows, where the unitary matrices are Haar-random. One of ordinary skill would have motivation to combine Zhao and Hu because “the variance of global Haar estimation is independent of system size, achieving the optimal sample complexity…” (Hu, pg. 8, section III.A).
Zhao and Hu do not appear to explicitly disclose A computing system comprising a classical computing device and a quantum computing device, and transmitting data between the devices.
However, Huggins teaches A computing system comprising: a classical computing device including a processor that: (0057: “The example system 100 includes a quantum processor 102 in data communication with a classical processor 104.” Computing system 100 includes a classical processor 104 (i.e. a classical computing device including a processor).)
outputs the single-particle-basis fermion rotation to a quantum computing device, wherein: (0059: “[T]he classical processor 104 can be configured to transmit data specifying trial wavefunctions to the quantum processor…” Data specifying trial wavefunctions (i.e. fermion rotations) are transmitted by the classical computing device to the quantum computing device.)
the quantum computing device:
receives the single-particle-basis fermion rotation; (0059: “[T]he classical processor 104 can be configured to transmit data specifying trial wavefunctions to the quantum processor…” Data specifying trial wavefunctions (i.e. fermion rotations) are received by the quantum computing device from the classical computing device.)
the processor of the classical computing device further:
receives the classical shadow measurement result; (0059: “[T]he classical processor 104 can be configured to… receive data representing results of measurement operations performed by the quantum processor…” The classical computing device receives measurement results (i.e. the classical shadow measurement result) from the quantum computing device.)
outputs the k-RDM element to an additional computing process. (0073: “the classical processor 104 outputs data representing the target quantum state. In some implementations the classical processor 104 can use the data representing the target quantum state to compute properties of the target quantum state…” The classical computing device outputs data representing the quantum state (i.e. the k-RDM element) for use in computing properties (i.e. an additional computing process).)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Zhao, Hu, and Huggins. Zhao teaches estimating the k-RDM of a fermionic quantum system using classical shadows which are computed using random unitary matrices. Hu teaches estimating a quantum state using classical shadows, where the unitary matrices are Haar-random. Huggins teaches a hybrid quantum-classical system for estimating the quantum state of a fermion system. One of ordinary skill would have motivation to combine Zhao, Hu, and Huggins because “[a] system implementing the presently described techniques can target quantum states and properties thereof with improved computational efficiency and improved accuracy… By separating the interaction between the quantum and classical computers in this manner, the need to minimize the latency is avoided—an especially appealing feature on NISQ platforms” (Huggins, 0022).
Regarding Claim 2, Zhao, Hu, and Huggins teach The computing system of claim 1, as shown above.
Zhao also teaches wherein:
the classical shadow measurement result is included among a plurality of classical shadow measurement results generated at the quantum computing device based at least in part on a respective plurality of Haar-random unitary matrices that includes the Haar-random unitary matrix; and (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
; then perform a projective measurement in the computational basis,
{
|
z
⟩
|
z
∈
{
0,1
}
n
}
… which allows us to define the classical shadow
ρ
^
U
,
z
≔
M
U
-
1
(
U
†
|
z
⟩
⟨
z
|
U
)
associated with the particular copy of
ρ
for which
U
was applied and
|
z
⟩
was obtained.” A plurality of classical shadow measurement results
ρ
^
U
,
z
are generated for a plurality of copies of quantum state
ρ
and their associated random unitary matrices
U
.)
the processor of the classical computing device estimates the k-RDM element based at least in part on the plurality of classical shadow measurement results and the corresponding Haar-random unitary matrices. (Pg. 3, Theorem 1: “…Thus the method of classical shadows estimates the fermionic k-RDM of any state
ρ
… given
M
=
O
[
n
k
k
3
/
2
log
n
ε
2
]
copies of
ρ
.” The elements of the fermionic k-RDM are estimated based on the plurality of classical shadow measurement results generated for the plurality of copies of
ρ
and their associated random unitary matrices
U
.)
Regarding Claim 3, Zhao, Hu, and Huggins teach The computing system of claim 1, as shown above.
Zhao also teaches wherein, at the additional computing process, the processor computes an estimated value of an observable based at least in part on the k-RDM element. (Pg. 1, section ‘Introduction’: “[C]alculating the k-RDM allows one to determine the expectation value of any k-body observable.”)
Regarding Claim 4, Zhao, Hu, and Huggins teach The computing system of claim 3, as shown above.
Zhao also teaches wherein:
the classical shadow measurement result is included among a plurality of classical shadow measurement results generated at the quantum computing device based at least in part on a respective plurality of Haar-random unitary matrices that includes the Haar-random unitary matrix; and (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
; then perform a projective measurement in the computational basis,
{
|
z
⟩
|
z
∈
{
0,1
}
n
}
… which allows us to define the classical shadow
ρ
^
U
,
z
≔
M
U
-
1
(
U
†
|
z
⟩
⟨
z
|
U
)
associated with the particular copy of
ρ
for which
U
was applied and
|
z
⟩
was obtained.” A plurality of classical shadow measurement results
ρ
^
U
,
z
are generated for a plurality of copies of quantum state
ρ
and their associated random unitary matrices
U
.)
the processor of the classical computing device further:
computes a plurality of k-RDM elements; and (Pg. 3, Theorem 1: “…Thus the method of classical shadows estimates the fermionic k-RDM of any state
ρ
… given
M
=
O
[
n
k
k
3
/
2
log
n
ε
2
]
copies of
ρ
.” The elements of the fermionic k-RDM are estimated based on the plurality of classical shadow measurement results generated for the plurality of copies of
ρ
and their associated random unitary matrices
U
.)
computes the estimated value of the observable as a linear combination of the plurality of k-RDM elements. (Pg. 27, Appendix E, section 3: “In the context of estimating a single observable, whose expectation value is a linear combination of RDM elements…”)
Regarding Claim 5, Zhao, Hu, and Huggins teach The computing system of claim 3, as shown above.
Zhao also teaches wherein:
the classical shadow measurement result is included among a plurality of classical shadow measurement results generated at the quantum computing device based at least in part on a respective plurality of Haar-random unitary matrices that includes the Haar-random unitary matrix; and (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
; then perform a projective measurement in the computational basis,
{
|
z
⟩
|
z
∈
{
0,1
}
n
}
… which allows us to define the classical shadow
ρ
^
U
,
z
≔
M
U
-
1
(
U
†
|
z
⟩
⟨
z
|
U
)
associated with the particular copy of
ρ
for which
U
was applied and
|
z
⟩
was obtained.” A plurality of classical shadow measurement results
ρ
^
U
,
z
are generated for a plurality of copies of quantum state
ρ
and their associated random unitary matrices
U
.)
the processor of the classical computing device further:
computes a plurality of k-RDM elements; and (Pg. 3, Theorem 1: “…Thus the method of classical shadows estimates the fermionic k-RDM of any state
ρ
… given
M
=
O
[
n
k
k
3
/
2
log
n
ε
2
]
copies of
ρ
.” The elements of the fermionic k-RDM are estimated based on the plurality of classical shadow measurement results generated for the plurality of copies of
ρ
and their associated random unitary matrices
U
.)
computes a plurality of estimated values of the observable, including the estimated value of the observable, in parallel based at least in part on the plurality of k- RDM elements. (Pg. 1, section ‘Introduction’: “[C]alculating the k-RDM allows one to determine the expectation value of any k-body observable.” Pg. 21, Appendix D: “These local qubit observables may then be measured in a parallel fashion via Pauli measurements.”)
Regarding Claim 6, Zhao, Hu, and Huggins teach The computing system of claim 5, as shown above.
Zhao also teaches wherein the processor computes the estimate of the
k
-RDM element with a sample complexity of [
N
=
O
(
1
ϵ
2
η
k
k
!
)
], where
ϵ
is a standard deviation of the estimate of the
k
-RDM element, [
η
is a number of fermions for which the fermion wavefunction is specified], and
k
is a number of ladder operator pairs with which the processor computes the
k
-RDM element. (Pg. 3, Theorem 1: “Thus the method of classical shadows estimates the fermionic
k
-RDM of any state
ρ
… to additive error
ε
, given
M
=
O
n
k
k
3
/
2
log
n
ε
2
copies of
ρ
.” The number of copies
M
of the state is the sample complexity, and it is derived based on error
ε
(i.e. standard deviation of the estimate) and
n
k
, which can be estimated by
n
k
k
!
, where
n
is the number of modes and
k
is the order of the interactions measured by the k-RDM (i.e. the number of ladder operator pairs).)
Hu teaches that the sample complexity scales with
η
rather than
n
, where
η
is a number of fermions for which the fermion wavefunction is specified. (Pg. 8, section III.B: “
M
is the sample complexity (the number of sample needed).
M
will be proportional to the single-shot variance Var
o
^
.” Pg. 8, section III.A: “[T]he variance of global Haar estimation is independent of system size, achieving the optimal sample complexity…” The sample complexity is proportional to the variance, which is independent of system size (i.e. number of modes
n
), and thus the sample complexity scales with the number of fermions
η
rather than the number of modes
n
.)
Regarding Claim 7, Zhao, Hu, and Huggins teach The computing system of claim 3, as shown above.
Zhao also teaches wherein the processor computes the estimated value of the observable with an operator dimension of
n
k
×
n
k
, where
n
is the number of modes and
k
is a number of ladder operator pairs with which the processor computes the
k
-RDM element. (Pg. 1, section ‘Introduction’: “[C]alculating the k-RDM allows one to determine the expectation value of any k-body observable.” Pg. 1, section ‘Fermionic RDMs’: “Consider a fixed-particle state
ρ
represented in second quantization on
n
fermion modes. The
k
-RDM of
ρ
, obtained by tracing out all but
k
particles, is typically represented as a 2
k
-index tensor,
D
q
1
…
q
k
p
1
…
p
k
k
∶
=
t
r
(
a
p
1
†
…
a
p
k
†
a
q
k
…
a
q
1
ρ
)
, where
a
p
†
,
a
p
are fermionic creation and annihilation operators,
p
∈
{
0
,
.
.
.
,
n
-
1
}
.” A k-RDM is a matrix indexed by pairs of
k
-mode subsets (i.e. ladder operator pairs). There are
n
k
ways to select a
k
-mode subset from the
n
modes, so the
k
-RDM has
n
k
rows and
n
k
columns, and the coefficient matrix (i.e. operator) used to compute the observable has the same
n
k
×
n
k
dimensions.)
Regarding Claim 8, Zhao, Hu, and Huggins teach The computing system of claim 1, as shown above.
Zhao also teaches wherein the Haar-random unitary matrix has a dimension
n
×
n
, where
n
is a number of modes for which the fermion wavefunction is specified. (Pg. 1, section ‘Fermionic RDMs’: “Consider a fixed-particle state
ρ
represented in second quantization on
n
fermion modes.” Pg. 4, section ‘Modification based on particle-number symmetry’: “Taking the intersection with the Clifford group requires that
u
be an
n
×
n
generalized permutation matrix…” The fermion state has
n
modes, and random unitary matrix
u
has dimension
n
×
n
.)
Regarding Claim 10, Zhao, Hu, and Huggins teach The computing system of claim 1, as shown above.
Huggins also teaches wherein the additional computing process includes storing the k-RDM element in memory. (0009: “In some implementations the method further comprises storing the computed classical shadow of the trial wavefunction in a classical memory of the classical computer.”)
Claims 11-18 are method claims containing substantially the same elements as system claims 1-8, respectively. Zhao, Hu, and Huggins teach the elements of claims 1-8, as shown above.
Claim 20 is a system claim containing substantially the same elements as system claim 1. Zhao, Hu, and Huggins teach the elements of claim 1, as shown above.
Zhao also teaches performing the disclosed steps a plurality of times. (Pg. 2, section. ‘Classical shadows and randomized measurements’: “Classical shadows require a simple measurement primitive: for each preparation of
ρ
, apply the unitary map
ρ
→
U
ρ
U
†
, where
U
is randomly drawn from some ensemble
U
; then perform a projective measurement in the computational basis,
{
|
z
⟩
|
z
∈
{
0,1
}
n
}
… which allows us to define the classical shadow
ρ
^
U
,
z
≔
M
U
-
1
(
U
†
|
z
⟩
⟨
z
|
U
)
associated with the particular copy of
ρ
for which
U
was applied and
|
z
⟩
was obtained.” Pg. 3, Theorem 1: “…Thus the method of classical shadows estimates the fermionic k-RDM of any state
ρ
… given
M
=
O
[
n
k
k
3
/
2
log
n
ε
2
]
copies of
ρ
.” A plurality of classical shadow measurement results
ρ
^
U
,
z
are generated for a plurality of copies of quantum state
ρ
and their associated random unitary matrices
U
. The fermionic k-RDM elements are estimated based on the plurality of classical shadow measurement results.)
Estimating k-RDMs in parallel. (Pg. 21, Appendix D: “These local qubit observables may then be measured in a parallel fashion via Pauli measurements.”)
computes an estimated value of an observable based at least in part on the plurality of k-RDMs; and (Pg. 1, section ‘Introduction’: “[C]alculating the k-RDM allows one to determine the expectation value of any k-body observable.”)
Huggins teaches outputs the estimated value of the observable. (0073: “the classical processor 104 outputs data representing the target quantum state. In some implementations the classical processor 104 can use the data representing the target quantum state to compute properties of the target quantum state…”)
Claims 9 and 19 are rejected under 35 U.S.C. 103 as being unpatentable over Zhao in view of Hu and Huggins, and further in view of
Lahtinen et al. (hereinafter Lahtinen), “A Short Introduction to Topological Quantum Computation” (published 09/12/2017).
Regarding Claim 9, Zhao, Hu, and Huggins teach The computing system of claim 1, as shown above.
Zhao, Hu, and Huggins do not appear to explicitly disclose wherein the quantum computing device is a topological quantum computing device.
However, Lahtinen teaches wherein the quantum computing device is a topological quantum computing device. (Pg. 19, section 4.1: “To illustrate the steps of operating a topological quantum computer, we focus on the simpler Ising anyons whose fusion space does exhibit natural tensor product structure.”)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the present application to combine Zhao, Hu, Huggins, and Lahtinen. Zhao teaches estimating the k-RDM of a fermionic quantum system using classical shadows which are computed using random unitary matrices. Hu teaches estimating a quantum state using classical shadows, where the unitary matrices are Haar-random. Huggins teaches a hybrid quantum-classical system for estimating the quantum state of a fermion system. Lahtinen teaches the implementation and benefits of a topological quantum computer. One of ordinary skill would have motivation to combine Zhao, Hu, Huggins, and Lahtinen because “the topological encoding and processing of quantum information provides in principle unparalleled protection over non-topological schemes” (Lahtinen, pg. 19, section 4). “Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers” (Lahtinen, pg. 1, Abstract).
Claim 19 is a method claim containing substantially the same elements as system claim 9. Zhao, Hu, Huggins, and Lahtinen teach the elements of claim 9, as shown above.
Conclusion
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/B.M.R./Examiner, Art Unit 2147
/VIKER A LAMARDO/Supervisory Patent Examiner, Art Unit 2147
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