DETAILED ACTION
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 statement (IDS) submitted on 02/27/2026. The submission is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
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.
Response to Arguments
Applicant’s arguments, see page 9-18, filed 05/06/2026, with respect to the rejection(s) of claim(s) 1-20 under USC 103 have been fully considered and are persuasive. Therefore, the rejection(s) of claim(s) 1-20 under USC 103 has been withdrawn. However, upon further consideration, a new ground(s) of rejection is made in view of Aghaee et al., “InAs-Al Hybrid devices passing the topological Gap protocol,” Physical review B, vol. 107, 245423, published June 21, 2023 (Aghaee) in view of Halimi et al., “Nonlinear Regression using smooth Bayesian Estimation,” Proceedings of IEEE ICASSP 2015, pp 2634-2638, 2015 (Halimi).
Response to Arguments, Claim 1, 35 U.S.C. §101
Applicant's arguments regarding claim 1 have been fully considered but are not persuasive.
Applicant first argues that claim 1 does not recite a mathematical concept because the claim does not expressly recite a mathematical formula, relying on Ex parte Hannun and USPTO
Subject Matter Eligibility Example 38. In particular, Applicant contends that the limitations
directed to normalizing measured nonlocal conductance values, extracting localization lengths,
and estimating localization lengths using a joint prior distribution do not constitute mathematical concepts because no mathematical formula itself appears in the claim. Applicant further argues that, consistent with Hannun, reliance on mathematical operations described in the Specification cannot render the claim abstract where the mathematical formula itself is not expressly recited.
Applicant's argument is not persuasive. The rejection does not rely merely on an unclaimed mathematical formula appearing in the Specification. Rather, claim 1 itself expressly requires "normalizing the measured nonlocal conductance values," "extracting localization
lengths based on the normalized nonlocal conductance values," and "estimating the
localization lengths for the HSSQ device by a joint prior distribution enforcing
smoothness over a function of gate voltages and the extracted localization lengths."
These limitations expressly recite operations and mathematical relationships between numerical quantities, including measured conductance values, normalized conductance values,
localization lengths, a joint prior distribution, and a function of gate voltages and localization
lengths.
Accordingly, the rejection is not premised on importing an undisclosed mathematical formula into the claim from the Specification. Rather, the mathematical relationships and operations are expressly reflected in the claim language itself. Applicant's reliance on Hannun and Example 38 therefore does not establish that claim 1 fails to recite a mathematical concept merely because the claim does not reproduce the mathematical operations in conventional equation notation.
Applicant additionally relies on Example 38 and argues that, just as "generating a normally distributed random value" and "simulating a digital representation" were not considered mathematical concepts in that example, the presently claimed normalization, extraction, and estimation using a joint prior distribution should likewise not be considered mathematical concepts. This argument is not persuasive because claim 1 is evaluated based on its own limitations. Here, claim 1 expressly defines relationships between measured numerical
conductance values, normalized values, extracted localization lengths, gate voltages, and a joint
prior distribution enforcing smoothness over a function thereof. Thus, the identified exception is based on the language actually recited by claim 1 and not merely on an implementation
disclosed outside the claim.
Applicant also relies on California Institute of Technology v. Broadcom Ltd. for the proposition that the use of a mathematical formula does not, by itself, establish patent ineligibility. The Examiner agrees that the mere presence or use of mathematics does not, standing alone, render a claim patent ineligible. However, the rejection does not conclude that claim 1 is ineligible merely because mathematics is involved. Rather, after identifying the mathematical concepts under Step 2A, Prong One, the claim is further evaluated as a whole under Step 2A, Prong Two and Step 2B. Accordingly, Applicant's reliance on Caltech does not overcome the rejection.
With respect to Step 2A, Prong Two, Applicant argues that claim 1 addresses a concrete
technological problem arising in HSSQ devices because junction-induced attenuation introduces
a random component into nonlocal conductance measurements and complicates the
relationship between the measured conductance and extracted localization lengths. Applicant
argues that normalization compensates for this device-specific physical artifact and thereby
permits more reliable localization-length estimation. Applicant further relies on paragraph 42 of
the Specification for the proposition that junction attenuation affects the nonlocal conductance
signal and has a random component.
These arguments have been considered but are not persuasive because they do not
demonstrate that the identified mathematical concepts are integrated into a practical application as actually required by claim 1. Although the measured conductance values originate from an HSSQ device and are affected by a physical junction, the claimed normalization operates on the measured nonlocal conductance values to mathematically remove the effect of attenuation.
Claim 1 does not require physically altering the junction, controlling the junction to reduce its attenuation, changing an operating condition of the HSSQ device, or otherwise physically compensating the device itself. Instead, the effect of the junction is accounted for in the data upon which the subsequent localization-length extraction and estimation are performed.
Likewise, the recited HSSQ device, including its plunger gates and top gates, establishes the particular technological environment associated with the measurement data. Claim 1 requires "obtaining measurements" associated with that device, but does not require selectively operating those gates as part of obtaining the measurements, nor does it require controlling or modifying the gates or other components of the HSSQ device based on the estimated localization lengths. Thus, the additional physical limitations provide the source and context of the data subjected to the claimed mathematical processing rather than imposing a meaningful technological application of the mathematical concepts beyond that processing.
Applicant additionally argues that the estimated localization lengths may be used to characterize the level of disorder in the HSSQ device and that improved localization-length estimation may lead to better composition or geometry of the stack of layers forming a superconducting wire.
Applicant specifically relies on paragraph 70 of the Specification concerning characterization of disorder.
This argument is not commensurate in scope with claim 1. Claim 1 terminates with "estimating the localization lengths for the HSSQ device." Claim 1 does not require using the estimated localization lengths to characterize a level of disorder, selecting a composition or geometry based on the estimated localization lengths, fabricating an improved HSSQ device, or otherwise modifying the HSSQ device. Although such uses may be described in the Specification or may constitute potential benefits of obtaining more reliable localization-length estimates, they are not limitations of claim 1 and therefore do not establish integration into a practical application for the claim as presently drafted.
Accordingly, considering claim 1 as a whole, the HSSQ device and conductance-measurement limitations provide the technological environment and data upon which the recited mathematical normalization, extraction, and joint-prior estimation are performed, while the processor is used as a tool for carrying out the estimation. The claim does not require a further technological operation or physical change resulting from the estimated localization lengths. The identified mathematical concepts therefore are not integrated into a practical application under Step 2A, Prong Two.
With respect to Step 2B, Applicant's arguments also do not establish that the additional
elements, individually or as an ordered combination, amount to significantly more than the
identified judicial exception. The processor performs its ordinary function of carrying out the
recited estimation, while the HSSQ device and measurement limitations provide the physical
environment and measurement data subjected to the mathematical analysis. As set forth in the
rejection, Martinez provides evidence regarding obtaining nonlocal conductance measurements
from semiconductor-superconductor hybrid devices using processing and measurement
circuitry. The Step 2B determination is therefore not based on Aghaee, Halimi, or the conclusion that the claimed mathematical concepts themselves are conventional.
For at least these reasons, Applicant's arguments have been considered but are not persuasive, and the rejection of claim 1 under 35 U.S.C. §101 is maintained.
Claim 1 is rejected under 35 U.S.C. §101 because the claimed invention is directed to a
judicial exception without reciting significantly more. Step 1: Claim 1 recites a method and therefore falls within the statutory category of a process.
Step 2A, Prong One: Claim 1 recites a judicial exception in the form of mathematical concepts.
In particular, the limitations of "normalizing the measured nonlocal conductance values to
remove an effect of the attenuation caused by the at least one junction and extracting
localization lengths based on the normalized nonlocal conductance values associated
with the HSSQ device" and "estimating the localization lengths for the HSSQ device by a
joint prior distribution enforcing smoothness over a function of gate voltages and the
extracted localization lengths for the HSSQ device" recite mathematical calculations and
relationships performed on measured numerical conductance values to derive localization
lengths and statistically estimate those localization lengths using a joint prior distribution and
smoothness function. The existing rejection similarly identifies the normalization, extraction, and joint prior distribution estimation as mathematical calculations and relationships.
Step 2A, Prong Two: The claim as a whole does not integrate the identified mathematical
concepts into a practical application. The additional elements include the HSSQ device
comprising a set of plunger gates formed in a first layer and a set of top gates formed above the
plunger gates in a second layer, obtaining measurements of nonlocal conductance values
associated with the HSSQ device wherein at least one junction attenuates one or more of the
measured values, and using a processor to perform the estimation.
Considered individually and in combination with the identified mathematical concepts, these
additional elements do not impose a meaningful limit on the mathematical analysis. Claim 1
merely requires obtaining measurements of nonlocal conductance values associated with the
HSSQ device. The claim does not require the processor performing the mathematical analysis
to control the plunger gates, top gates, junction, or other physical components of the HSSQ
device in response to the estimated localization lengths. Rather, the HSSQ device and its
recited gate and junction structure provide the technological environment from which the
numerical conductance data subjected to the mathematical analysis are obtained.
The recited normalization likewise operates on the measured nonlocal conductance values
to mathematically remove the effect of junction attenuation. Although the underlying attenuation results from a physical junction, the claim does not require physically altering, controlling, or compensating the junction itself to remove the attenuation. Instead, the measured numerical values are mathematically normalized after being obtained. The resulting localization lengths are then subjected to the recited joint prior distribution and smoothness estimation. Further, claim 1 ends with the estimated localization lengths. The claim does not require using those estimated localization lengths to subsequently control, modify, calibrate, manufacture, or otherwise cause a physical change in the HSSQ device. Thus, the physical HSSQ structure and measurement limitations provide the source and technological environment for the data upon which the recited mathematical operations are performed rather than applying the mathematical concepts to effect a further technological operation.
The use of a processor likewise does not integrate the exception into a practical application because the processor is recited as the tool that performs the mathematical estimation rather than as a component that effects a further technological result outside the mathematical analysis.
Accordingly, when claim 1 is considered as a whole, the additional elements amount to
obtaining physical measurement data from a particular technological environment and using a
processor to perform the recited mathematical normalization, extraction, and statistical
estimation. The additional elements therefore do not integrate the identified mathematical
concepts into a practical application. Step 2B: Claim 1 also does not recite additional elements, individually or as an ordered combination, that amount to significantly more than the identified judicial exception.
The use of a processor to perform the estimation merely uses a computer as a tool for carrying out the recited mathematical operations. The remaining additional elements concern the HSSQ device structure and obtaining nonlocal conductance measurements from that device.
As already established in the record, Martinez provides evidence that obtaining nonlocal conductance measurements from semiconductor superconductor hybrid devices using gate voltages, processing circuitry, and measurement circuitry was conventional in the relevant
technological field. Martinez teaches an apparatus for measuring nonlocal conductance of a
semiconductor component of a semiconductor superconductor hybrid device using a processing unit and connection circuitry, including applying gate voltages to gate electrodes, applying a bias voltage, and measuring current while the gate and bias voltages are applied.
Thus, considered separately from the identified mathematical concepts, the additional elements perform their conventional functions of providing the physical device from which measurement data are obtained, obtaining the measurement data, and using a processor to perform the calculations. Considered as an ordered combination, the elements likewise do not provide significantly more because the claim uses the measurement environment to supply data to the mathematical normalization and estimation process without requiring a further technological operation or physical modification resulting from the estimated localization lengths.
Accordingly, claim 1 is directed to mathematical concepts that are not integrated into a
practical application, and the additional elements, individually and as an ordered
combination, do not amount to significantly more than the judicial exception. Claim 1 is
therefore ineligible under 35 U.S.C. §101.
Claim Rejections - 35 USC § 103
5. 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 of this title, 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 1-6, 8-12, 14-19 are rejected under 35 U.S.C. 103 as being unpatentable over Aghaee et al., “InAs-Al Hybrid devices passing the topological Gap protocol,” Physical review B, vol. 107, 245423, published June 21, 2023 (Aghaee) in view of Halimi et al., “Nonlinear Regression using smooth Bayesian Estimation,” Proceedings of IEEE ICASSP 2015, pp 2634-2638, 2015 (Halimi).
Regarding claim 1, Aghaee teaches a method for estimating localization lengths in a
hybrid superconductor semiconductor quantum (HSSQ) device (Aghaee discloses lnAs Al
semiconductor superconductor hybrid devices and expressly teaches determining electron
localization length from experimentally measured nonlocal conductance. Specifically, Aghaee
explains that measurements of nonlocal conductance for different segment lengths enable
extraction of electron localization length in the semiconductor. See Aghaee, p. 245423 9, Sec.
I1.E, Fig. 6).
wherein the HSSQ device comprises a set of plunger gates formed in a first
layer of the HSSQ device and a set of top gates formed, above the set of plunger gates, in
a second layer of the HSSQ device, (Aghaee teaches a dual layer gate (DLG) device having
plunger gates and cutter gates arranged in respective gate layers. Aghaee expressly states that
the junctions have cutter gates in a second gate layer and that a second dielectric layer
separates the cutter gates from plunger gates in the first gate layer. See Aghaee, p. 245423
6, Fig. 3(a) through 3(c) and caption, p. 245423 5, Sec. I1.B. Aghaee additionally explains that
opening and closing the junctions is accomplished by cutter gates in the second gate layer,
separated from the first gate layer by a second dielectric layer. The recited "top gates" are
interpreted broadly as gates positioned in the second layer above the first layer plunger gates.
Aghaee's second layer cutter gates satisfy this structural relationship. The reference need not
use the same nomenclature where the disclosed structure satisfies the claimed relationship).
obtaining measurements of nonlocal conductance values associated with the
HSSQ device (Aghaee expressly teaches experimentally measuring nonlocal conductance.
Figure 6(a) shows measured nonlocal conductance as a function of plunger gate voltage and
bias voltage for different wire segment lengths. See Aghaee, p. 245423 9, Fig. 6(a) and
caption).
wherein at least one junction associated with the HSSQ device attenuates one
or more of the measured nonlocal conductance values associated with the HSSQ
device, (Aghaee teaches two tunnel junctions whose transparencies affect the conductance
measurements. The left and right cutter gate voltages control the respective tunnel junction
transparencies, and Aghaee teaches operating the junctions in a tunneling regime. See
Aghaee, p. 245423 5, Sec. I1.B. Further, in the localization length analysis, Aghaee expressly
explains that normalization is performed "to reduce the effect of the junctions" on the
measured conductance. See Aghaee, p. 245423 9, Sec. I1.E. Thus, although Aghaee does not
use the word "attenuates," Aghaee teaches that the junctions affect the magnitude of the
conductance used for localization length extraction and that this junction effect is reduced by
normalization, thereby teaching the claimed attenuation in substance).
normalizing the measured nonlocal conductance values to remove an effect
of the attenuation caused by the at least one junction, (Aghaee expressly teaches normalizing the measured nonlocal conductance by local conductances. Figure 6(b) explains
that the nonlocal conductance is normalized by the local conductances "to minimize the
contributions of the local effects." See Aghaee, p. 245423 9, Fig. 6(b) and caption. The
accompanying text further states that the measured conductances are normalized by the local
conductances "to reduce the effect of the junctions." See Aghaee, p. 245423 9, Sec. 11.E.
Thus, Aghaee teaches normalization for removing or reducing the junction induced contribution
to the measured nonlocal conductance).
and extracting localization lengths based on the normalized nonlocal
conductance values associated with the HSSQ device, (Aghaee teaches extracting
localization length by fitting the normalized nonlocal conductance to the expected conductance
decay relationship A exp(-2L/~)- Aghaee states that the localization length is obtained from a
linear fit, and Fig. 6(c) presents the extracted localization length as a function of plunger
gate voltage. See Aghaee, p. 245423 9, Fig. 6(b) and Fig. 6(c) and caption.
Thus, Aghaee teaches the claimed device structure, nonlocal conductance measurements,
junction dependent conductance effect, normalization to reduce that effect, and localization
length extraction).
Aghaee does not expressly teach "using a processor, estimating the localization lengths
for the HSSQ device by a joint prior distribution enforcing smoothness over a function of
gate voltages and the extracted localization lengths for the HSSQ device."
However, Halimi teaches the missing Bayesian smooth estimation technique. Halimi teaches a hierarchical Bayesian model for estimation of parameters associated with a sequence of measurements. Halimi explains that independently obtained parameter estimates may be noisy and that smoothing can be achieved by adding a correlation prior. See Halimi, p. 2634,
Introduction. Halimi further expressly teaches that the parameters of interest are assigned a
prior enforcing smooth evolution between consecutive signals, which improves the
resulting parameter estimation. See Halimi, p. 2634, Introduction. More particularly, Halimi, p.
2635, Sec. 2.3, Eq. (4) teaches a prior for each parameter that enforces a smoothness property
by constraining variation of the parameter, specifically assigning a Gaussian prior to its second
derivative and implementing the constraint using a discrete Laplacian operator D. Halimi
further defines the prior distributions for the parameters and hyperparameters and combines
them within the hierarchical Bayesian model. See Halimi, p. 2635, Secs. 2.3 through 2.6, Eqs.
(4) through (8). The model collectively defines the prior distributions of the unknown quantities
and derives the corresponding joint posterior distribution for Bayesian estimation.
Accordingly, Halimi teaches a joint Bayesian prior structure including a smoothness enforcing prior, even though Halimi refers expressly to the resulting distribution after incorporating observations as a "joint posterior distribution." The rejection does not rely on equating "joint prior" with "joint posterior." Rather, the combination of the several prior distributions in Halimi provides a joint prior structure over the parameters and hyperparameters, with the parameter prior expressly enforcing smoothness.
It would have been obvious to one of ordinary skill in the art before the effective filing
date of the claimed invention to modify the method of Aghaee by applying the Bayesian
estimation technique of Halimi, including the smoothness enforcing prior, to the
localization lengths extracted by Aghaee as a function of gate voltage, because Aghaee
already obtains extracted localization length values as a function of plunger gate voltage,
as shown in Fig. 6(c), while Halimi teaches a hierarchical Bayesian estimation technique
in which parameters associated with a sequence of measurements are assigned a prior
enforcing smooth evolution between consecutive signals to improve parameter
estimation. See Aghaee, p. 245423 9, Fig. 6(c). See Halimi, p. 2634, Introduction, and p.
2635, Sec. 2.3, Eq. (4). One of ordinary skill in the art would have been motivated to apply
Halimi's smooth Bayesian estimation technique to Aghaee's gate voltage dependent
localization length values because Halimi recognizes that independently estimated
parameters may be noisy and inconvenient for physical interpretation and expressly
teaches that imposing a prior enforcing smooth evolution improves estimation of such
parameters. Accordingly, applying Halimi's known smoothness enforcing Bayesian
estimation technique to Aghaee's known localization length values as a function of gate
voltage would have predictably provided smoother and less noise sensitive localization
length estimates, thereby improving the reliability and physical interpretation of the
localization length estimation. Such a modification would have involved the application
of a known parameter estimation technique to Aghaee's known gate voltage dependent
physical parameter data for Halimi's expressly taught purpose of improving parameter
estimation, with predictable results. The implementation of the resulting estimation using
a processor would likewise have been obvious because Halimi expressly employs
computational Bayesian estimation, including MCMC and Hamiltonian Monte Carlo
techniques, for obtaining the parameter estimates. See Halimi, p. 2634, Introduction, and
p. 2635, Sec. 2.6. Therefore, Aghaee in view of Halimi renders obvious the recited use of
a processor to estimate the localization lengths using a joint prior distribution enforcing
smoothness over a function of gate voltages and the extracted localization lengths.
Regarding claims 2, 9, 15, Aghaee as modified further teaches wherein the normalizing the measured nonlocal conductance values to remove an effect of the attenuation caused by the at least one junction comprises normalizing each of the measured nonlocal conductance values by a square root of a product of respective local conductance values (Specifically, Aghaee teaches in connection with the localization length extraction of Fig. 6 that the nonlocal conductance is normalized by the local conductances. Aghaee states in the Fig. 6 caption that the localization length is extracted by fitting the data to the expected value of the typical conductance, with the normalized nonlocal conductance expressed using the local conductances under a square root. Aghaee further states that "We normalize the nonlocal conductance ... by local conductances ... at zero bias to minimize the contributions of the local effects." See Aghaee, p. 245423 9, Fig. 6(b) and accompanying caption. Aghaee further explains in the accompanying discussion that the junctions are operated in the open junction regime, that the typical nonlocal conductance decays with length, and that, for fitting the measured conductances to this relationship, "we normalize it by the local conductances to reduce the effect of the junctions." See Aghaee, p. 245423 9, Sec. 11.E, Fig. 6).
Regarding claims 3, 16, Aghaee as modified further teaches wherein the measurements of the nonlocal conductance values associated with the HSSQ device are obtained by measuring nonlocal conductance values of sections of a superconducting wire associated with the HSSQ device by selectively supplying voltages to one or more of the set of plunger gates and the set of op gates, respectively (Aghaee teaches measuring nonlocal conductance for different length sections of the superconducting semiconductor wire. Aghaee explains that a variation of the device includes multiple junctions defining segments of different lengths and that this configuration enables measurement of the nonlocal conductance for the different segment lengths. See Aghaee, p. 245423 9, Sec. 11.E, Fig. 6. Figure 6(a) expressly shows measured nonlocal conductance versus plunger voltage and bias voltage for different length segments of the wire, Aghaee, p. 245423 9, Fig. 6(a) and accompanying caption. Aghaee further teaches selectively supplying voltages to the plunger gates to control respective sections of the wire. In particular, Aghaee teaches that the left and right plunger gates control the densities underneath corresponding sections of the Al and that the densities in the left, middle, and right sections can be controlled independently by the respective plunger gates. See Aghaee, p. 245423 4, Sec. 11.B, Fig. 2. Aghaee further teaches that the middle plunger gate voltage tunes the density in the wire. See Aghaee, p. 245423 5, Sec. 11.B. Aghaee also teaches selectively supplying voltages to the gates corresponding to the claimed top gates. Specifically, Aghaee teaches that the left and right cutter gate voltages are used to vary, respectively, the transparency of the left and right tunnel junctions, thereby providing independent tuning of density and junction transparency for each section of the gate defined nanowire. See Aghaee, p. 245423 5, Sec. 11.B, Fig. 2. As discussed with respect to claim 1, Aghaee's cutter gates correspond to the claimed top gates in the dual layer configuration. Aghaee further expressly explains that conductance measurements are performed as a function of the plunger gate voltage and the cutter gate voltages controlling the tunnel junction transparencies. Aghaee states that the cutter gates are used to open and close the junctions, with a more negative cutter gate voltage causing the corresponding junction to become more closed. See Aghaee, p. 245423 10, Sec. Ill, Fig. 8. Aghaee further selects sequences of cutter gate voltages corresponding to desired conductance values at the respective junctions.
Regarding claims 4, 10, Aghaee does not expressly teach the additional limitation further comprising constructing a statistical model based on an implicit description of the measurements of the nonlocal conductance values.
However, Halimi teaches constructing a statistical model based on an implicit description of measurements. Specifically, Halimi, in Sec. 2, Hierarchical Bayesian Model, and Sec. 2.1, Observation Model, constructs an observation model in which successive observed signals are represented as noisy nonlinear functions of unknown parameters. Halimi defines the observed signal according to an observation model in Eq. (1) and explains that the proposed nonlinear regression method estimates signal and noise parameters with smoothness constraints using that observation model. See Halimi, p. 2635, Sec. 2.1, Eq. (1).
Halimi further constructs a statistical likelihood from the observation model and the assumed
statistical properties of the measurement noise. Specifically, Sec. 2.2 states that the observation model defined in Eq. (1), together with the Gaussian properties of the noise sequence, yields the likelihood of the observed measurements, and Halimi further assumes independence between observations in constructing the statistical model. See Halimi, p. 2635, Sec. 2.2, Eq. (2). Halimi thereafter combines the observation model, likelihood, parameter priors, noise priors, and hyperparameter priors into a hierarchical Bayesian statistical model. See Halimi, p. 2635, Secs. 2.3 through 2.6, Eqs. (4) through (8).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to further modify the method of Aghaee by constructing the statistical observation model taught by Halimi based on Aghaee's measured nonlocal conductance values because Aghaee provides the experimentally measured nonlocal conductance data from which localization lengths are extracted, while Halimi teaches representing measured signals using a statistical observation model in which the measurements are described as noisy nonlinear functions of parameters and subsequently using that model for Bayesian parameter estimation. See Aghaee, p. 245423 9, Sec. 11.E, Fig. 6. See Halimi, p. 2635, Secs. 2.1 and 2.2, Eqs. (1) and (2). One of ordinary skill in the art would have been motivated to apply Halimi's statistical modeling technique to Aghaee's conductance measurements because Halimi expressly teaches using the observation model as the basis for estimating signal and noise parameters with smoothness constraints, thereby permitting the measured data to be incorporated into the Bayesian estimation framework relied upon with respect to claim 1. Such a modification would have predictably provided a statistical representation of Aghaee's measured nonlocal conductance data suitable for the smooth Bayesian parameter estimation taught by Halimi.
Regarding claims 5, 11, Aghaee does not expressly teach wherein the statistical model comprises estimates of likelihood that are used to extract localization lengths at each of the gate voltages independently.
However, Halimi teaches a statistical model comprising likelihood estimates and treating the observations independently. Specifically, Halimi defines successive observed signals as noisy
nonlinear functions of unknown parameters according to the observation model of Eq. (1). Halimi then derives a likelihood based on the observation model and the Gaussian properties of
the noise sequence. See Halimi, p. 2635, Sec. 2.1, Eq. (1), and Sec. 2.2, Eq. (2). Halimi further expressly states that assuming independence between the observations leads to the likelihood formulation used by the statistical model. See Halimi, p. 2635, Sec. 2.2. Thus, Halimi teaches forming likelihood estimates for respective observations under an independence assumption and using those likelihoods in estimating the corresponding unknown parameters.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to modify the statistical model applied to Aghaee's gate voltage dependent conductance measurements according to Halimi by determining likelihoods for the
measurements at the respective gate voltages under Halimi's disclosed independence
assumption and using those likelihoods to estimate the localization length corresponding to
each gate voltage, because Aghaee already extracts localization lengths from conductance
measurements obtained at respective plunger gate voltages, while Halimi teaches constructing
likelihoods from respective observations and expressly assuming independence between the
observations. See Aghaee, p. 245423 9, Fig. 6(a) through Fig. 6(c). See Halimi, p. 2635,
Secs. 2.1 and 2.2, Eqs. (1) and (2). One of ordinary skill in the art would have been motivated
to use Halimi's likelihood formulation with Aghaee's measurements because Halimi teaches that the likelihood provides the statistical relationship between the observed data and the
parameters being estimated, while treating the observations independently permits the
likelihood contribution associated with each respective measurement to be determined within
the statistical model. Applying this known likelihood based estimation technique to Aghaee's
measurements at respective gate voltages would therefore have predictably provided likelihood based estimates for extracting the corresponding localization lengths at the respective gate voltages.
Regarding claims 6, 12, 19, Aghaee does not expressly teach the additional limitation "wherein the joint prior distribution is constructed by starting with independent local priors, in which a distribution over the extracted localization lengths is assumed to be a product of the independent local priors, and adding one or more of a set of constraints onto the joint prior distribution such that a rate of change of the function is restricted to a specified maximum value.
However, Halimi teaches constructing a Bayesian prior distribution for parameters associated with respective observations and imposing a smoothness constraint on those parameters. Halimi explains that the prior used for each parameter enforces a smoothness property for the evolution of that parameter and expressly teaches that "This can be done by constraining the derivative of this parameter to be small." Halimi then assigns a Gaussian prior distribution to the second derivative of each parameter and employs a discrete Laplacian operator to impose the smoothness constraint. See Halimi, p. 2635, Sec. 2.3, Eq. (4). Halimi further teaches independence in constructing components of its probabilistic model. In
particular, Halimi assumes independence between observations in forming the likelihood and
additionally expressly assumes prior independence between noise variances in constructing
their joint prior. See Halimi, p. 2635, Secs. 2.2 and 2.4, Eqs. (2) and (5). Halimi's overall
Bayesian approach constructs a model in which parameters are assigned priors enforcing
smooth evolution between consecutive signals, with the prior defined using the discrete
Laplacian of the parameters.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to apply Halimi's prior construction and smoothness constraint to the localization lengths extracted from Aghaee's measurements by initially representing the
localization length estimates associated with the respective gate voltages using local prior
distributions and combining those priors into the joint probabilistic model, and then imposing
Halimi's disclosed derivative based smoothness constraint across the localization lengths,
because Aghaee obtains localization lengths as a function of gate voltage while Halimi teaches
Bayesian estimation of parameters associated with respective observations and expressly
teaches improving those estimates by imposing a prior that constrains the derivative of the
estimated parameter to be small. Halimi explains that the purpose of this prior is to enforce
smooth evolution between successive parameter estimates and thereby improve estimation.
One of ordinary skill in the art would have recognized that implementing Halimi's disclosed
requirement that the derivative remain small necessarily requires selecting or defining an
allowable degree of parameter variation, and specifying a maximum permitted rate of change
would have been a predictable implementation of that disclosed smoothness constraint,
because limiting the derivative to a selected maximum directly controls the amount by which
neighboring localization length estimates are permitted to vary. Such a modification would have predictably reduced noise and physically implausible variations between localization lengths extracted at neighboring gate voltages while preserving Aghaee's gate voltage dependent localization length estimation.
Regarding claim 8, the method recited is intrinsic to the apparatus recited in claim 1, as disclosed by Aghaee et al., “InAs-Al Hybrid devices passing the topological Gap protocol,” Physical review B, vol. 107, 245423, published June 21, 2023 (Aghaee) in view of Halimi et al., “Nonlinear Regression using smooth Bayesian Estimation,” Proceedings of IEEE ICASSP 2015, pp 2634-2638, 2015 (Halimi) as the recited method steps will be performed during the normal operation of the apparatus, as discussed above with regard to claim 1. Aghaee as modified further teaches measuring nonlocal conductance values of sections of a superconducting wire associated with the HSSQ device by selectively supplying voltages to one or more of the set of plunger gates and the set of top gates, respectively. (a device having multiple junctions defining wire segments of different lengths and explains that this arrangement enables measurement of nonlocal conductance for the different segment lengths and extraction of the electron localization length in the semiconductor. See Aghaee, p. 245423 9, Sec. I1.E, Fig. 6 and Fig. 27. Aghaee further teaches measuring conductances as a function of the plunger gate voltage and voltages controlling the tunnel junction transparencies. In particular, Aghaee identifies the plunger gate voltage as an actual control parameter of the device. See Aghaee, p. 245423 7, Fig. 4 and accompanying text. Aghaee additionally teaches measuring the differential conductances as a function of the plunger gate voltage and the voltages controlling the tunnel junction transparencies, and expressly teaches using the cutter gates to open and close the respective junctions. See Aghaee, p. 245423 10, Sec. Ill, Fig. 8. Aghaee further selects sequences of cutter gate voltages for the respective junctions based on desired junction conductances, thereby teaching selective application of voltages to the respective gates. As discussed above with respect to claim 1, Aghaee's cutter gates in the second gate layer correspond to the claimed top gates.
Regarding claim 14, Aghaee teaches a method for characterizing a level of disorder in a
hybrid superconductor semiconductor quantum (HSSQ) device (expressly identifies disorder as a principal consideration in HSSQ devices and analyzes different disorder strengths and disorder realizations. See Aghaee, Sec. I1.E, "Disorder and uniformity requirements," pp. 245423 7 through 245423 8, Figs. 5 and 23. Aghaee explains that disorder can be characterized by a random potential having a disorder strength and correlation length and discusses the relationship between disorder strength and relevant device length scales).
wherein the HSSQ device comprises a set of plunger gates formed in a first
layer of the HSSQ device and a set of top gates formed, above the set of plunger gates, in
a second layer of the HSSQ device (Aghaee teaches the dual layer gate device having
plunger gates in a first gate layer and cutter gates in a second gate layer separated from the
plunger gates by a second dielectric layer, as discussed above with respect to claim 1. See
Aghaee, p. 245423 6, Fig. 3(a) through Fig. 3(c) and caption, and p. 245423 5, Sec. 11.B.
Under the interpretation discussed with respect to claim 1, Aghaee's second layer cutter gates
correspond to the claimed top gates).
obtaining measurements of nonlocal conductance values associated with the
HSSQ device, wherein at least one junction associated with the HSSQ device attenuates
one or more of the measured nonlocal conductance values associated with the HSSQ
device (Aghaee teaches measuring nonlocal conductance through the HSSQ device and
controlling the tunnel junction transparencies using cutter gate voltages. Aghaee explains that
the conductances are measured as a function of gate voltages controlling the junction
transparencies and that the cutter gates open and close the respective junctions. See Aghaee,
Fig. 8 and accompanying discussion. As discussed with respect to claim 1, Aghaee further
expressly recognizes the effect of the junctions on the measured conductance).
normalizing the measured nonlocal conductance values to remove an effect
of the attenuation caused by the at least one junction and extracting localization lengths
based on the normalized nonlocal conductance values associated with the HSSQ
device (Aghaee expressly teaches a device having multiple junctions defining segments of
different lengths, measuring nonlocal conductance for the different segment lengths, and
thereby extracting electron localization length. Aghaee further teaches that the typical nonlocal
conductance decays with segment length and expressly states that the measured conductances
are normalized by the local conductances "to reduce the effect of the junctions." See
Aghaee, p. 245423 9, Sec. 11.E, Fig. 6 and Fig. 27).
using the processor, based on the estimated localization lengths,
characterizing the level of disorder in the HSSQ device (Aghaee teaches a direct physical
relationship between localization length and disorder in the HSSQ device. Aghaee explains that
disorder strength affects the relevant coherence and localization length scales and discusses
disorder averaged parameters including localization length. See Aghaee, Secs. 11.E and 11.F,
Fig. 7. More particularly, Aghaee uses experimentally extracted localization length to evaluate the disorder quality of the semiconductor superconductor device. After extracting localization length from the normalized nonlocal conductance, Aghaee finds a localization length of at least
approximately 1 μm and compares that localization length with the mean free path. Aghaee
explains that the longer localization length results from screening of charged imperfections by Al and states that this observation confirms the high quality of the Al 2DEG interface and
corroborates the disorder root cause analysis. See Aghaee, p. 245423 9, Sec. 11.E. Aghaee additionally teaches quantitatively relating a relevant length scale to disorder strength.
Specifically, Aghaee teaches using a transfer matrix calculation of the length scale to obtain
the disorder strength cV at which the minimum value of begins to exceed the device length. See Aghaee, p. 245423 8, Sec. I1.E, Fig. 23. Aghaee also analyzes simulated devices having different disorder strengths, including cV = 0.3 meV and cV = 0.9 meV, and explains the different device behavior resulting from weak and stronger disorder. See Aghaee, p. 245423 10, Sec. 11.F, Fig. 7.
Aghaee does not expressly teach the claimed step of "using a processor, based on the
extracted localization lengths, estimating the localization lengths for the HSSQ device" in
the same statistical estimation manner contemplated by the claim.
However, Halimi teaches processor implemented Bayesian estimation of parameters from initially determined or measured parameter information using a statistical model, including smooth estimation to improve the resulting parameter estimates, as discussed above with respect to claim 1. Halimi further reports that its Bayesian method produces smoother, more physically consistent estimates and improves the quality of the estimated parameters. See Halimi, p. 2637, Sec. 5 and Conclusion.
It would have been obvious to one of ordinary skill in the art before the effective filing
date of the claimed invention to modify Aghaee by applying Halim i's processor implemented parameter estimation technique to Aghaee's extracted localization lengths and to use the resulting estimated localization lengths to characterize the level of disorder in the HSSQ device, because Aghaee already extracts localization lengths from experimentally measured nonlocal conductance and expressly teaches that localization length is related to disorder and can be used to evaluate the quality and disorder characteristics of the semiconductor superconductor device, while Halimi teaches improving initially obtained parameter values through smooth Bayesian estimation to provide more physically consistent parameter estimates. See Aghaee, p. 245423 9, Sec. I1.E, Fig. 6. See Halimi, p. 2637, Sec. 5 and Conclusion. One of ordinary skill in the art would have been motivated to use Halimi's improved estimates when performing Aghaee's disorder analysis because Halimi teaches that its Bayesian estimation produces smoother, more physically consistent estimates and is more robust to noise and outliers, thereby providing more reliable parameter values for the subsequent physical characterization. Aghaee expressly establishes that changes in disorder affect relevant localization behavior and analyzes localization length in connection with disorder strength, charged imperfections, mean free path, and interface quality.
Regarding claim 17, Aghaee does not expressly teach the additional limitation "wherein estimating the localization lengths for the HSSQ device comprises estimating by a joint prior
distribution enforcing smoothness over a function of gate voltages and the normalized
localization lengths for the HSSQ device."
However, Halimi teaches the additional Bayesian smoothness estimation. Specifically, Halimi teaches a hierarchical Bayesian model for estimating parameters associated with successive measurements and explains that the parameters of interest are assigned a prior enforcing smooth evolution between consecutive signals. See Halimi, p. 2634, Introduction.
More particularly, Halimi teaches a prior for each parameter that enforces smoothness by
constraining variation of the parameter. Halimi explains that this is accomplished by constraining the derivative of the parameter to be small and assigning a Gaussian prior distribution to the second derivative, implemented using a discrete Laplacian operator D. See Halimi, p. 2635, Sec. 2.3, Eq. (4). Halimi further defines the prior distributions for the parameters and hyperparameters and combines them within the hierarchical Bayesian model to obtain the joint Bayesian distribution used for parameter estimation. See Halimi, p. 2635, Secs. 2.3 through 2.6, Eqs. (4) through (8).
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to apply Halimi's joint Bayesian estimation technique, including its smoothness enforcing prior, to Aghaee's localization length values associated with respective gate voltages because Aghaee already provides localization length values as a function of plunger gate voltage, while Halimi teaches improving parameter estimates associated with successive measurements by imposing a prior that enforces smooth evolution between the parameter values. See Aghaee, p. 245423 9, Fig. 6(c). See Halimi, p. 2634, Introduction, and p. 2635, Sec. 2.3, Eq. (4). One of ordinary skill in the art would have been motivated to apply Halimi's smoothness enforcing prior to Aghaee's gate voltage dependent localization length values because Halimi teaches that imposing smooth evolution between successive parameter estimates improves the resulting estimates and reduces undesirable variation. Such a modification would have predictably provided smoother and more physically consistent localization length estimates across the gate voltages.
Regarding claim 18, Aghaee does not expressly teach the additional limitation "further comprising constructing a statistical model based on an implicit description of the measurements of the nonlocal conductance values, and wherein the statistical model comprises estimates of likelihood that are used to extract localization lengths at each of the gate voltages independently."
However, Halimi teaches constructing a statistical model based on measured data and using likelihood estimates for respective observations. Specifically, Halimi teaches a hierarchical
Bayesian model having an observation model in which successive observed signals are
represented as noisy nonlinear functions of unknown parameters. Halimi defines the observed
signals according to the observation model of Eq. (1) and uses the observation model as the
basis for estimating the unknown parameters. See Halimi, p. 2635, Sec. 2.1, Eq. (1). Halimi further constructs a statistical likelihood from the observation model and the statistical
properties of the measurement noise. Specifically, Halimi teaches that the observation model of
Eq. (1), together with the Gaussian properties of the noise, yields the likelihood of the observed
measurements. Halimi further expressly assumes independence between the observations in
constructing the likelihood. See Halimi, p. 2635, Sec. 2.2, Eq. (2). Thus, Halimi teaches a
statistical model comprising likelihood estimates associated with respective observations and
treating those observations independently for parameter estimation.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to apply Halimi's statistical observation and likelihood model to Aghaee's nonlocal conductance measurements at the respective gate voltages and to use the resulting likelihood estimates to extract the localization length corresponding to each gate voltage independently because Aghaee already obtains conductance measurements and extracts localization lengths as a function of gate voltage, while Halimi teaches constructing a statistical observation model from measured signals, deriving likelihoods for the observed measurements, and expressly treating the observations independently in the likelihood formulation. See Aghaee, p. 245423 9, Fig. 6{a) through Fig. 6(c). See Halimi, p. 2635, Secs. 2.1 and 2.2, Eqs. (1) and (2). One of ordinary skill in the art would have been motivated to make such a modification because Halimi teaches that the likelihood provides the statistical relationship between the measured observations and the parameters being estimated, while the independence assumption permits the respective observations to contribute independently to the estimation.
Allowable Subject Matter
Claim 7, 13 and 20 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.
The following is a statement of reasons for the indication of allowable subject matter:
None of the prior art of record discloses or teaches the claimed combinations, or feature the following:
Claims 7, 13 and 29. The method of claim 6, wherein the independent local priors include a marginal prior with respect to values of the extracted localization lengths, a smoothness prior with respect to correlation among the values of the extracted localization lengths, and a mean free path prior with respect to values of neighboring extracted localization lengths.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Winkler (US. 20210126181) discloses SEMICONDUCTOR-SUPERCONDUCTOR HYBRID DEVICE, ITS MANUFACTURE AND USES.
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/TAQI R NASIR/ Examiner, Art Unit 2858
/LEE E RODAK/ Supervisory Patent Examiner, Art Unit 2858
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