Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claim Rejections - 35 USC § 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 (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 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.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1-8, 10-20 are rejected under 35 U.S.C. 103 as being unpatentable over Freedman “Projective Plane and Planar Quantum Codes” in view of Wang “Threshold Error Rates for the Toric and Surface Codes”.
Regarding claim 1, Freedman teaches:
… wherein the logical qubit comprises a plurality of data qubits logically organized in a real projective plane topology… one or more stabilizers determined based on the real projective plane topology of the logical qubit;
(see pg. 328, para. 1 and fig. 2: Figure 2 shows a cellulation of RP2 [real projective plane] with nine edges, defining a distance 3 code for 1 [logical] qubit using 9 [data] qubits. And see pg. 327, para. 2-3: Consider a bit flip error in the qubit on some edge e, i.e., multiplication by σx on the corresponding tensor factor of H. This error will be detected by the eigenvalues of the stabilizer operators Bv for the two vertices in the boundary of e—unless there are bit flip errors on an even number of the edges (data qubits) incident at one or the other vertex. More generally, bit flip errors in the qubits on any collection of edges corresponding to a chain c1 ∈ C1(C;Z2) will be detected by the Bv for the vertices in the boundary of c1. Error correction by choosing any chain c2 ∈ C1(C;Z2), with the observed boundary vertices and acting by σx on the corresponding qubits, succeeds unless c1 + c2 contains an essential cycle. The length of the shortest essential cycle in C is thus the (bit flip error) distance of the code [6]. Similarly, phase errors are detected by the eigenvalues of the stabilizer operators Af. The observed faces correspond to vertices in the dual cellulation C∗ bounding a chain c∗ 1 ∈ C1(C∗;Z2) of edges at which phase errors have occurred (edges in C∗ are dual to edges in C). Error correction by choosing any c∗ 2 ∈ C1(C∗;Z2) with the observed boundary and acting by σz on the corresponding qubits succeeds unless c∗ 1 +c∗ 2 contains an essential cycle in C1(C∗;Z2). The length of the shortest essential cycle in the dual cellulation C∗ is thus the (phase error) distance of the code.) As you can see from fig. 2, the topology of the logical qubit defines multiple stabilizers, the pauli-x stabilizers represented as vertices, the pauli-z stabilizers represented as faces, and data qubits are represented as edges.
However, Freedman does not teach how the error information is physically extracted from the stabilizers or the surrounding physical system used to implement the logical qubit.
In the analogous art of topological quantum computing, Wang provides further context, teaching:
A method performed by a quantum computing system comprising a classical computing entity, a controller, and a quantum processor, the controller configured to (a) control operation of the quantum processor and (b) communicate with the classical computing entity, (see pg. 2, para. 4: Note that classical computation is required to diagnose the errors from the quantum circuits in a real life quantum computer. And see pg. 5, section 3 Syndrome Extraction: Syndrome extraction on the toric code is done simultaneously for both X and Z syndromes. In our simulations, this is achieved using the circuits in figure 5. First, the ancilla qubits are prepared in their designated states. Then each ancilla interacts with the data qubits to its north, west, east and south (in that order). Finally, the ancilla are measured in the designated bases. And see pg. 7, para. 1: Thus a minimum-weight perfect matching reproduces the observed syndrome using the fewest errors. Since each edge in the matching represents one error chain, in order to error correct one applies corrections on the qubits along the error chains given by the matching.) Wang states that classical computation is required to diagnose the errors, it is then inherently disclosed that a controller of some kind in part of this system to control the quantum computer (processor) to perform the error correction based off of the error diagnosis. This is a very well-known system in the art, and the inherent disclosure of a controller, classical computer, and quantum processor would be readily apparent to one of ordinary skill in the art.
the method comprising: causing, by the controller, performance of at least one syndrome circuit segment to generate a syndrome of a logical qubit, the at least one syndrome circuit segment performed at least in part by causing performance of a sequence of at-least-two-physical-qubits interactions… and the sequence of at-least-two-physical-qubits interactions is determined based at least in part on one or more stabilizers…; (see pg. 5, section 3 and fig. 5: Syndrome extraction… is done simultaneously for both X and Z syndromes. In our simulations, this is achieved using the circuits in figure 5. First, the ancilla qubits are prepared in their designated states. Then each ancilla interacts with the data qubits to its north, west, east and south (in that order). Finally, the ancilla are measured in the designated bases. And see fig. 3b, an ancilla qubit is provided for each stabilizer so that the syndrome may be extracted. The syndrome extraction circuit of fig. 5, and which data qubits the ancilla qubit interacts with corresponds to the stabilizer the ancilla qubit is located on.) based at least in part on the syndrome of the logical qubit, determining, by the classical computing entity, at least one quantum error correction; (see pg. 7, para. 1: Thus a minimum-weight perfect matching reproduces the observed syndrome using the fewest errors. Since each edge in the matching represents one error chain, in order to error correct one applies corrections on the qubits along the error chains given by the matching.)
and causing, by the controller or the classical computing entity, a classical memory of at least one of the controller or the classical computing entity to be updated based on at least one of the syndrome or the at least one quantum error correction. (see pg. 5, last para.- pg. 6, para. 1 and fig. 6: Since syndrome extraction is itself a physical process, it too is prone to errors. Under faulty syndrome extraction, error correction works in these schemes by collating the eigenvalue measurements over the duration of the computation, forming a 3d syndrome structure (figure 6).) This collation of syndrome data over time would require syndrome data being stored at a classical memory of the controller or the classical computing entity, as would be readily apparent to one of ordinary skill in the art.
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 2, the combination of Wang and Freedman teaches the method of claim 1. Freedman further teaches:
wherein each stabilizer of the one or more stabilizers comprises four instances of a same operator, with each instance of the four instances of the same operator acting on a different data qubit of the plurality of data qubits. (see fig. 2, the two face z-stabilizers depicted in the center square shape are each connected to four edges (data qubits). Each of these two z-stabilizers then comprise four instances of z operators, each of the operators acting on a different data qubit (edge).)
Regarding claim 3, the combination of Wang and Freedman teaches the method of claim 1. Freedman further teaches:
wherein at least one stabilizer of the one or more stabilizers comprises two instances of a first operator and two instances of a second operator, with each instance of the first operator and each instance of the second operator acting on a different data qubit of the plurality of data qubits. (see fig. 2, the two face z-stabilizers depicted in the center square shape are each connected to four edges (data qubits). Each of these two z-stabilizers then comprise two instances of a first operator (a z operator) and two instances of a second operator (a z operator), each of the operators acting on a different data qubit (edge).)
Regarding claim 4, the combination of Wang and Freedman teaches the method of claim 1. Freedman further teaches:
wherein each stabilizer of the one or more stabilizers is a weight four stabilizer. (see fig. 2, the two face z-stabilizers depicted in the center square shape are each connected to four edges (data qubits), therefore these z-stabilizers are weight four stabilizers.)
Regarding claim 5, the combination of Wang and Freedman teaches the method of claim 1. Freedman further teaches:
Further comprising causing, by the controller, the at least one quantum error correction to be applied to the logical qubit. (see pg. 327, para. 2: Consider a bit flip error in the qubit on some edge e, i.e., multiplication by σx on the corresponding tensor factor of H. This error will be detected by the eigenvalues of the stabilizer operators Bv for the two vertices in the boundary of e—unless there are bit flip errors on an even number of the edges incident at one or the other vertex. More generally, bit flip errors in the qubits on any collection of edges corresponding to a chain c1 ∈ C1(C;Z2) will be detected by the Bv for the vertices in the boundary of c1. Error correction by choosing any chain c2 ∈ C1(C;Z2), with the observed boundary vertices and acting by σx on the corresponding qubits, succeeds unless c1 + c2 contains an essential cycle.)
Freedman’s description of error correction corresponds to the description of error correction described by Wang (pg. 5, last para. – pg. 6, para. 1: The observed eigenvalue changes form the nodes on a graph. Each pair of nodes is connected by a weighted edge, which is associated with a chain of errors producing those two observed terminals. A perfect matching of the graph is then a set of errors reproducing the syndrome. As there are many possible error chains linking any two nodes, we choose any of the possible chains of maximum probability. In our simulations, since all sites have equal probability of error, this equates to the shortest length error chains. An edge linking two nodes is assigned a weight equal to this shortest length. Thus a minimum-weight perfect matching reproduces the observed syndrome using the fewest errors. Since each edge in the matching represents one error chain, in order to error correct one applies corrections on the qubits along the error chains given by the matching.) This correction is considered to be caused by the controller, as described in the rejection of claim 1.
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 6, the combination of Wang and Freedman teaches the method of claim 5. Wang further teaches:
wherein causing the at least one quantum error correction to be applied to the logical qubit comprises at least one of
(a) updating a classical qubit registry corresponding to logical qubit based on the at least one quantum error correction,
(b) causing performance of a physical correction to one or more data qubits of the logical qubit, or (pg. 5, last para. – pg. 6, para. 1: The observed eigenvalue changes form the nodes on a graph. Each pair of nodes is connected by a weighted edge, which is associated with a chain of errors producing those two observed terminals. A perfect matching of the graph is then a set of errors reproducing the syndrome. As there are many possible error chains linking any two nodes, we choose any of the possible chains of maximum probability. In our simulations, since all sites have equal probability of error, this equates to the shortest length error chains. An edge linking two nodes is assigned a weight equal to this shortest length. Thus a minimum-weight perfect matching reproduces the observed syndrome using the fewest errors. Since each edge in the matching represents one error chain, in order to error correct one applies corrections on the qubits along the error chains given by the matching.)
(c) causing a logical operation to be performed at least in part on one or more data qubits of the logical qubit to be modified based at least in part on the at least one quantum error correction. (pg. 5, last para. – pg. 6, para. 1: The observed eigenvalue changes form the nodes on a graph. Each pair of nodes is connected by a weighted edge, which is associated with a chain of errors producing those two observed terminals. A perfect matching of the graph is then a set of errors reproducing the syndrome. As there are many possible error chains linking any two nodes, we choose any of the possible chains of maximum probability. In our simulations, since all sites have equal probability of error, this equates to the shortest length error chains. An edge linking two nodes is assigned a weight equal to this shortest length. Thus a minimum-weight perfect matching reproduces the observed syndrome using the fewest errors. Since each edge in the matching represents one error chain, in order to error correct one applies corrections on the qubits along the error chains given by the matching.)
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 7, the combination of Wang and Freedman teaches the method of claim 1. Wang further teaches:
performance of the at least one syndrome circuit segment comprises performance of a plurality of syndrome circuit segments. (see page. 5, section 3 and fig. 5: Syndrome extraction… is done simultaneously for both X and Z syndromes. In our simulations, this is achieved using the circuits in figure 5. First, the ancilla qubits are prepared in their designated states. Then each ancilla interacts with the data qubits to its north, west, east and south (in that order). Finally, the ancilla are measured in the designated bases. This particular interaction order leads to ancilla qubits being in a simple product state at the end of the cycle, as each syndrome circuit can be shown to occur strictly before or after its neighboring syndrome circuits.) Each interaction between the ancilla qubit and a neighboring (north, west, east, or south) data qubit is considered to be a syndrome circuit segment. Additionally, the full syndrome circuit depicted in fig. 5 would be repeated for each ancilla qubit (one for each of the stabilizers of the logical qubit).
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 8, the combination of Wang and Freedman teaches the method of claim 1. Wang further teaches:
at least one of at-least-two-physical-qubits interactions of the sequence of at-least-two-physical-qubits interactions includes interaction of at least one ancilla qubit with at least one data qubit of the plurality of data qubits of the logical qubit. (see page. 5, section 3 and fig. 5: Syndrome extraction… is done simultaneously for both X and Z syndromes. In our simulations, this is achieved using the circuits in figure 5. First, the ancilla qubits are prepared in their designated states. Then each ancilla interacts with the data qubits to its north, west, east and south (in that order). Finally, the ancilla are measured in the designated bases. This particular interaction order leads to ancilla qubits being in a simple product state at the end of the cycle, as each syndrome circuit can be shown to occur strictly before or after its neighboring syndrome circuits.)
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 10, the combination of Wang and Freedman teaches the method of claim 1. Wang further teaches:
wherein updating the classical memory based on at least one of the syndrome or the at least one quantum error correction comprises tracking the syndrome of the logical qubit in the classical memory. (see pg. 5, last para.- pg. 6, para. 1 and fig. 6: Since syndrome extraction is itself a physical process, it too is prone to errors. Under faulty syndrome extraction, error correction works in these schemes by collating the eigenvalue measurements over the duration of the computation, forming a 3d syndrome structure (figure 6).) This collation of syndrome data over time (tracking the syndrome of the logical qubit) would require syndrome data being stored at a classical memory of the controller or the classical computing entity, as would be readily apparent to one of ordinary skill in the art.
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Regarding claim 11, the combination of Wang and Freedman teaches the method of claim 1. Wang further teaches:
wherein coherence of the plurality of data qubits of the logical qubit is maintained during performance of the at least one syndrome circuit segment. (see pg. 3, para. 2: Using the ancilla qubits, the eigenvalues of these stabilizers may be measured whilst still preserving a quantum state.). If the quantum state is preserved, the coherence of the data qubits entangled in that quantum state is maintained.
Regarding claim 12, the combination of Wang and Freedman teaches the method of claim 1. Wang further teaches:
Further comprising, prior to causing performance of the at least one syndrome circuit segment, causing performance of a state preparation circuit segment for preparing a state of a respective ancilla qubit; using the respective ancilla qubit to perform the sequence of at-least-two-physical-qubits interactions, and causing the respective ancilla qubit to be read after the performance of the sequence of at-least-two-physical-qubits interactions, wherein the syndrome of the logical qubit is generated based at least in part on a result of the reading of the respective ancilla qubit. (see page. 5, section 3 and fig. 5: Syndrome extraction… is done simultaneously for both X and Z syndromes. In our simulations, this is achieved using the circuits in figure 5. First, the ancilla qubits are prepared in their designated states. Then each ancilla interacts with the data qubits to its north, west, east and south (in that order). Finally, the ancilla are measured in the designated bases. This particular interaction order leads to ancilla qubits being in a simple product state at the end of the cycle, as each syndrome circuit can be shown to occur strictly before or after its neighboring syndrome circuits.)
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman and Wang before them, before the effective filing date of the claimed invention to incorporate the method/system for topological error correction (Wang) into the logical qubit in RP2 (Freedman). One of ordinary skill in the art, attempting to implement Freedman’s RP2 logical qubit would turn to use Freedman as a roadmap for specific implementation details for how topological quantum syndrome extraction and error correction are performed. Further, Wang provides the additional benefit of temporal error correction/detection (Wang, fig. 7) which allows for the detection of syndrome measurement errors, for example due to a preparation or measurement error in the ancilla qubit (Wang, pg. 7, last para.).
Claims 13-18 and 19-20 correspond to claims 1-6 and 10-11 (respectively), and are rejected accordingly.
Claim 9 is rejected under 35 U.S.C. 103 as being unpatentable over Freedman in view of Wang and Monroe (US Patent No. 9858531).
Regarding claim 9, the combination of Freedman and Wang teaches the method of claim 8.
However, the combination of Freedman and Wang fails to teach:
wherein the logical qubit is one of a plurality of logical qubits and the at least one ancilla qubit is used to perform syndrome circuit segments for two or more logical qubits of the plurality of logical qubits.
In the analogous art of quantum computing, Monroe teaches:
wherein the logical qubit is one of a plurality of logical qubits and the at least one ancilla qubit is used to perform syndrome circuit segments for two or more logical qubits of the plurality of logical qubits. (see col. 23, line 65 – col. 24, line 1: re-using the four ancilla qubits for each logical memory qubit reduces the number of physical qubits and parallel operations necessary for state preparation. And see col. 24, lines 19-26: In order to construct effective arithmetic circuits, Toffoli gate… is needed…. Toffoli gate is a 3-qubit gate… fault tolerant implementation requires preparation of a special three (logical) qubit state.)
It would have been obvious to one of ordinary skill in the art, having the teachings of Freedman, Wang, and Monroe before them, before the effective filing date of the claimed invention to incorporate reusing ancilla qubits for multiple logical qubits (Monroe) into the system for performing error correction on a logical qubit in RP2 (Freedman and Wang), to allow for benefits such as: reduced number of physical qubits and parallel operations needed for state preparation (Monroe, col. 23, line 65- col. 24-line 1) and the ability to implement effective arithmetic circuits (Monroe, col. 24, lines 19-26).
Conclusion
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/JACK KENSINGTON BARNETT/Examiner, Art Unit 2111
/MARK D FEATHERSTONE/Supervisory Patent Examiner, Art Unit 2111
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