IP Library › Granted Patent US 12,505,331
Granted Patent B2
US 12,505,331 · App. 17/282,449 · Granted Dec 23, 2025

Quantum convolutional neural networks

Inventors: Iris Cong (Cambridge, MA); Soonwon Choi (El Cerrito, CA); Mikhail D. Lukin (Cambridge, MA)
Assignee: President and Fellows of Harvard College
G06N3/04G06F11/0706G06N3/063G06N10/60
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Quick Facts
Patent No.
US 12,505,331
App. No.
17/282,449
Granted
Dec 23, 2025
Kind
B2
Abstract

Systems and methods for quantum convolutional neural networks are described. Systems and methods can apply convolving and pooling layers to input qudits. The qudits can be measured to identify information about the input qudits. Systems and methods can also apply quantum convolutional neural network encoding and decoding techniques for quantum error correction.

Claims (53)

1 . A method comprising:

convolving a plurality of input qudits in a classical or quantum state by applying at least one convolving layer of quantum channels to convolving subgroups of the plurality of input qudits, wherein a size of each convolving subgroup of the plurality of input qudits is independent of a number of the plurality of input qudits;

pooling the plurality of input qudits by applying at least one pooling layer comprising:

dividing the plurality of input qudits into pooling subgroups of the plurality of input qudits, wherein a size of each pooling subgroup of the plurality of input qudits is independent of the number of the plurality of input qudits, and input qudits in each pooling subgroup are in proximity to each other, and

within each pooling subgroup of the plurality of input qudits, performing a pooling layer generalized measurement of a state of a subset of one or more input qudits, and applying at least one quantum channel to at least some of the input qudits in the pooling subgroup on which the pooling layer generalized measurement has not been performed based on an outcome of the pooling layer generalized measurement of the state of the subset of the one or more input qudits in the pooling subgroup;

repeating said convolving and said pooling at least once to the plurality of input qudits on which a pooling layer generalized measurement has not been performed;

applying a fully connected quantum channel to a selected subgroup of input qudits on which a pooling layer generalized measurement has not been performed, wherein a size of the selected subgroup is independent of the number of the plurality of input qudits; and

performing a final generalized measurement of a state of at least some of the input qudits on which a pooling layer generalized measurement has not been performed, wherein an outcome of the final generalized measurement is indicative of the classical or quantum state of the plurality of input qudits.

2 . The method of claim 1 , wherein one or more of the pooling layer generalized measurements and the final generalized measurement comprises projecting the input qudits into a subspace in a complete set of orthogonal subspaces.

3 . The method of claim 2 , wherein the outcome of one or more of the pooling layer generalized measurements and the final generalized measurement comprises the subspace in which the input qudits were projected.

4 . The method of claim 3 , wherein, for the one or more of the pooling layer generalized measurements and the final generalized measurement, each subspace in a corresponding complete set of orthogonal subspaces has dimension equal to one.

5 . The method of claim 4 , wherein each subspace of dimension equal to one is spanned by a basis state which is a product state of single-qudit states in a computational basis of the input qudits.

6 . The method of claim 1 , wherein the plurality of input qudits are qubits.

7 . The method of claim 1 , wherein the quantum channels are unitaries.

8 . The method of claim 1 , wherein the input qudits in each convolving subgroup are in proximity to each other.

9 . The method of claim 8 , wherein the at least one convolving layer is translationally invariant.

10 . The method of claim 1 , wherein the at least one pooling layer is translationally invariant.

11 . The method of claim 1 , wherein one or more of the quantum channels in the at least one convolving layer, the quantum channels in the at least one pooling layer, the fully connected quantum channel, the pooling layer generalized measurements, and the final generalized measurement is parametrized using at least one variational parameter.

12 . The method of claim 11 , wherein the at least one variational parameter is optimized to minimize a cost function having a cost value that depends on the at least one variational parameter and on at least one training set.

13 . The method of claim 1 , wherein each convolving subgroup comprises at most four input qudits, and each pooling subgroup comprises at most four input qudits.

14 . The method of claim 1 , wherein the plurality of input qudits comprises neutral atoms interacting via Rydberg states.

15 . The method of claim 1 , further comprising determining, based on the outcome of the final generalized measurement, a phase of matter to which the plurality of input qudits belongs.

16 . The method of claim 1 , further comprising determining, based on the outcome of the final generalized measurement, a class of classical or quantum states to which the plurality of input qudits belongs.

17 . A system comprising:

an energy source configured to selectively apply quantum channels to qudits;

a measurement device configured to selectively perform generalized measurements of a state of the qudits; and

a controller comprising:

a processor operatively coupled to the energy source and the measurement device, and

a computer readable storage medium having instructions stored thereon that cause the processor to control the energy source and the measurement device to:

convolve a plurality of input qudits in a classical or quantum state by applying, with the energy source, at least one convolving layer of quantum channels to convolving subgroups of the plurality of input qudits, wherein a size of each convolving subgroup of the plurality of input qudits is independent of a number of the plurality of input qudits,

pool the plurality of input qudits by applying at least one pooling layer comprising:

dividing the plurality of input qudits into pooling subgroups of the plurality of input qudits, wherein a size of each pooling subgroup of the plurality of input qudits is independent of a number of the plurality of input qudits, and the input qudits in each pooling subgroup are in proximity to each other, and

within each pooling subgroup of the plurality of input qudits, performing, with the measurement device, a pooling layer generalized measurement of a state of a subset of one or more qudits, and applying, with the energy source, at least one quantum channel to at least some of the qudits in the pooling subgroup on which the pooling layer generalized measurement has not been performed based on an outcome of the pooling layer generalized measurement;

repeat said convolving and said pooling at least once to the plurality of input qudits on which a pooling layer generalized measurement has not been performed,

apply, with the energy source, a fully connected quantum channel to a selected subgroup of input qudits on which a pooling layer generalized measurement has not been performed, wherein a size of the selected subgroup is independent of the number of the plurality of input qudits, and

perform, with the measurement device, a final generalized measurement of a state of at least some of the qudits on which a pooling layer generalized measurement has not been performed, wherein an outcome of the final generalized measurement is indicative of the classical or quantum state of the plurality of input qudits.

18 . The system of claim 17 wherein one or more of the pooling layer generalized measurements and the final generalized measurement comprises projecting input qudits into a subspace in a complete set of orthogonal subspaces.

19 . The system of claim 18 , wherein the outcome of one or more of the pooling layer generalized measurements and the final generalized measurement comprises the subspace in which the input qudits were projected.

20 . The system of claim 19 , wherein for the one or more of the pooling layer generalized measurements and the final generalized measurement, each subspace in a corresponding complete set of orthogonal subspaces has dimension equal to one.

21 . The system of claim 20 , wherein each subspace of dimension equal to one is spanned by a basis state which is a product state of single-qudit states in a computational basis of the input qudits.

22 . The system of claim 17 wherein the energy source comprises one or more of at least one laser light source, at least one microwave generator, and at least one magnetic field generator.

23 . The system of claim 17 wherein the measurement device comprises one of more of at least one photodetector, at least one microwave resonator, and at least one cavity resonator.

24 . The system of claim 17 wherein the plurality of input qudits are qubits.

25 . The system of claim 17 wherein the quantum channels in one or more of the quantum channels are unitaries.

26 . The system of claim 17 wherein the input qudits in each convolving subgroup are in proximity to each other.

27 . The system of claim 26 , wherein the at least one convolving layer is translationally invariant.

28 . The system of claim 17 wherein the at least one pooling layer is translationally invariant.

29 . The system of claim 17 wherein one or more of the quantum channels in the at least one convolving layer, the quantum channels in the at least one pooling layer, the fully connected quantum channel, the pooling layer generalized measurements, and the final generalized measurement is parametrized using at least one variational parameter.

30 . The system of claim 29 , wherein the at least one variational parameter is optimized to minimize a cost function having a cost value that depends on the at least one variational parameter and on at least one training set.

31 . The system of claim 17 wherein each convolving subgroup comprises at most four qudits, and each pooling subgroup comprises at most four input qudits.

32 . The system of claim 17 wherein the plurality of input qudits comprises neutral atoms interacting via Rydberg states.

33 . The system of claim 17 wherein the instructions further cause the processor to determine, based on the outcome of the final generalized measurement, a phase of matter to which the plurality of input qudits belongs.

34 . The system of claim 17 wherein the instructions further cause the processor to determine, based on the outcome of the final generalized measurement, a class of classical or quantum states to which the plurality of input qudits belongs.

Assignments (2)
CONFIRMATORY LICENSE Recorded Apr 15, 2025
From: HARVARD UNIVERSITY
To: NATIONAL SCIENCE FOUNDATION
Reel/Frame 070851/0967 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Dec 2, 2022
From: CHOI, SOONWON; CONG, IRIS; LUKIN, MIKHAIL D.
To: PRESIDENT AND FELLOWS OF HARVARD COLLEGE
Reel/Frame 061951/0954 →
Continuity (2)
Provisional Application 62742100 · Oct 5, 2018
Related Publication 20210383189A1 · Dec 9, 2021
References Cited (204)
US 3872470A · Hoerz et al. · 1975 [cited by applicant]
US 4479199A · Friedlander et al. · 1984 [cited by applicant]
US 5684621A · Downing · 1997 [cited by applicant]
US 6988058B1 · Sherwin et al. · 2006 [cited by applicant]
US 11380455B2 · Keesling Contreras et al. · 2022 [cited by applicant]
US 11710579B2 · Keesling Contreras et al. · 2023 [cited by applicant]
US 11985451B2 · Kim et al. · 2024 [cited by applicant]
US 12051520B2 · Keesling Contreras et al. · 2024 [cited by applicant]
US 20020089718A1 · Penninckx et al. · 2002 [cited by applicant]
US 20040000666A1 · Lidar et al. · 2004 [cited by applicant]
US 20040017833A1 · Cundiff et al. · 2004 [cited by applicant]
US 20040126114A1 · Liu et al. · 2004 [cited by applicant]
US 20060225165A1 · Maassen van den Brink et al. · 2006 [cited by applicant]
US 20070113012A1 · Cable et al. · 2007 [cited by applicant]
US 20080116449A1 · Macready et al. · 2008 [cited by applicant]
US 20080185576A1 · Hollenberg et al. · 2008 [cited by applicant]
US 20080237579A1 · Barker et al. · 2008 [cited by applicant]
US 20080313430A1 · Bunyk · 2008 [cited by applicant]
US 20090204877A1 · Betts · 2009 [cited by applicant]
US 20090299947A1 · Amin et al. · 2009 [cited by applicant]
US 20110238607A1 · Coury et al. · 2011 [cited by applicant]
US 20140025926A1 · Yao et al. · 2014 [cited by applicant]
US 20140200689A1 · Utsunomiya et al. · 2014 [cited by applicant]
US 20140253987A1 · Christmas · 2014 [cited by applicant]
US 20150317558A1 · Adachi et al. · 2015 [cited by applicant]
US 20160064108A1 · Saffman et al. · 2016 [cited by applicant]
US 20160125311A1 · Fuechsle et al. · 2016 [cited by applicant]
US 20160328253A1 · Majumdar · 2016 [cited by applicant]
US 20170300817A1 · King et al. · 2017 [cited by applicant]
US 20180217629A1 · MacFaden · 2018 [cited by applicant]
US 20180218279A1 · Lechner et al. · 2018 [cited by applicant]
US 20180260731A1 · Zeng et al. · 2018 [cited by applicant]
US 20190266508A1 · Bunyk et al. · 2019 [cited by applicant]
US 20200185120A1 · Keesling Contreras et al. · 2020 [cited by applicant]
US 20210279631A1 · Pichler et al. · 2021 [cited by applicant]
US 20210365827A1 · Monroe et al. · 2021 [cited by applicant]
US 20210383189A1 · Cong et al. · 2021 [cited by applicant]
US 20220060668A1 · Kim et al. · 2022 [cited by applicant]
US 20220138608A1 · Ramette et al. · 2022 [cited by applicant]
US 20220197102A1 · Christen et al. · 2022 [cited by applicant]
US 20220293293A1 · Contreras et al. · 2022 [cited by applicant]
US 20220391743A1 · Wild et al. · 2022 [cited by applicant]
US 20230326623A1 · Keesling Contreras et al. · 2023 [cited by applicant]
US 20230400492A1 · Xu et al. · 2023 [cited by applicant]
US 20240029911A1 · Lukin et al. · 2024 [cited by applicant]
US 20240185113A1 · Cong et al. · 2024 [cited by applicant]
US 20240289665A1 · Pichler et al. · 2024 [cited by applicant]
US 20240346352A1 · Bluvstein et al. · 2024 [cited by applicant]
US 20240347995A1 · Levine et al. · 2024 [cited by applicant]
CN 106980178A · 2017 [cited by applicant]
EP 1171968B1 · 2002 [cited by applicant]
EP 3113084A1 · 2017 [cited by applicant]
EP 3438726A1 · 2019 [cited by applicant]
GB 0205011A · 1923 [cited by applicant]
JP 2004045453A · 2004 [cited by applicant]
JP 2007233041A · 2007 [cited by applicant]
JP 2008134450A · 2008 [cited by applicant]
JP 2008158325A · 2008 [cited by applicant]
JP 2014197733A · 2014 [cited by applicant]
JP 2017078832A · 2017 [cited by applicant]
WO WO2014051886A1 · 2014 [cited by applicant]
WO WO2019014589A1 · 2019 [cited by applicant]
WO WO2020072981A1 · 2020 [cited by applicant]
WO WO2020172588A1 · 2020 [cited by applicant]
WO WO2020236574A1 · 2020 [cited by applicant]
WO WO2021007560A1 · 2021 [cited by applicant]
WO WO2021141918A1 · 2021 [cited by applicant]
WO WO2022132388A2 · 2022 [cited by applicant]
WO WO2022132389A2 · 2022 [cited by applicant]
WO WO2022174072A1 · 2022 [cited by applicant]
WO WO2022132388A3 · 2022 [cited by applicant]
WO WO2022132389A3 · 2022 [cited by applicant]
WO WO2023287503A2 · 2023 [cited by applicant]
WO WO2023287503A3 · 2023 [cited by applicant]
WO WO2023287503A9 · 2023 [cited by applicant]
WO WO2023080936A2 · 2023 [cited by applicant]
WO WO2023080936A3 · 2023 [cited by applicant]
WO WO2023132865 · 2023 [cited by applicant]
WO WO2024155291A2 · 2024 [cited by applicant]
Wikipedia. Convolutional neural network. Version from Jul. 24, 2018. https://en.wikipedia.org/w/index.php?title=Convolutional_neural_network&oldid=851809760. (Year: 2018). [cited by examiner]
Auger et al., “Blueprint for fault-tolerant quantum computation with Rydberg atoms.” Physical Review A 96(5): 052320 (2017). [cited by applicant]
Beugnon et al., “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers” Nature Physics, vol. 3, p. 1-4 (2007). [cited by applicant]
Chao et al., “Fault-tolerant quantum computation with few qubits.” npj Quantum Information 4.1 (2018): 42. [cited by applicant]
Cong et al., “Hardware-efficient, fault-tolerant quantum computation with Rydberg atoms”, Physical Review X 12(2): 021049 (2022). [cited by applicant]
Couvert et al., “Optimal transport of ultracold atoms in the non-adiabatic regime” Europhysics Letters, 83: 5 pages (2008). [cited by applicant]
Dordevic et al., “Entanglement transport and a nanophotonic interface for atoms in optical tweezers” arXiv: 16 pages (2021). [cited by applicant]
Fowler et al., “Surface code quantum communication” arXiv, pp. 1-4 (2010). [cited by applicant]
Fowler et al., “Surface Codes: Towards practical large-scale quantum computation” Physical Review, vol. 86 (3), p. 1-54 (2012). [cited by applicant]
Graham et al., “Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer” arXiv, p. 1-25 (2022). [cited by applicant]
Hashizume et al., “Deterministic Fast Scrambling with Neutral Atom Arrays” Physical Review Letters, vol. 126: 14 pages (2021). [cited by applicant]
International Search Report and Written Opinion for Application No. PCT/US2021/060136 dated Aug. 11, 2022. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2022/031297 dated Feb. 21, 2023. [cited by applicant]
International Search Report and Written Opinion of Application No. PCT/US2021/060138 dated Aug. 19, 2022. [cited by applicant]
Kaufman et al., “Quantum thermalization through entanglement in an isolated many-body system” arXiv: 19 pages (2016). [cited by applicant]
Labuhn et al., “Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms” arXiv: 1-12 (2016). [cited by applicant]
Lengwenus et al., “Coherent Transport of Atomic Quantum in a Scalable Shift Register” Physical Review Letters, 105: 4 pages (2010). [cited by applicant]
Low et al., “Practical trapped-ion protocols for universal qudit-based quantum computing”, Physical Review Research 2(3): 033128 (2020). [cited by applicant]
Rehn et al., “A fractionalised “Z2” classical Heisenberg spin liquid” arXiv: 5 pages (2016). [cited by applicant]
Reichle et al., “Transport Dynamics of single ions in segmented microstructed Paul trap arrays” Forschritte der Physik Progress of Physics, 54 (8-10): 666-685 (2006). [cited by applicant]
Satzinger et al. “Realizing topologically ordered states on a quantum processor,” 27 pages, (2021). [cited by applicant]
Savary et al., “Quantum Spin Liquids” arXiv: 60 pages (2016). [cited by applicant]
Yang et al., “Coherence Preservation of a Single Neutral Atom Qubit Transferred between Magic-Intensity Optical Traps” Physical Review Letter, 117: 6 pages (2016). [cited by applicant]
Yoder et al., “Universal fault-tolerant gates on concatenated stabilizer codes”, Physical Review X 6(3): 031039 (2016). [cited by applicant]
Du et al., “Superconducting circuit probe for analog quantum simulators”, [cited by applicant]
International Search Report and Written Opinion for Application No. PCT/US2022/039189 dated Aug. 4, 2023. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US22/37325 dated Jun. 16, 2023. [cited by applicant]
Keating et al., “Adiabatic quantum computation with Rydberg-dressed atoms”, Physical Review A 87, 052314, May 2013. [cited by applicant]
Levine, “Quantum Information Processing and Quantum Simulation with Programmable Rydberg Atom Arrays” The Department of Physics at Harvard University, PHD Thesis (2021). [cited by applicant]
Meschede, “Quantum engineering with neutral atoms one by one”, [cited by applicant]
Wang et al., “Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap”, [cited by applicant]
Willner et al., “Optics and photonics: Key enabling technologies”, [cited by applicant]
Aliferis et al., “Computation by measurements: A unifying picture,” Arxiv: 13 pages (2004). [cited by applicant]
Anonymous., “Magneto-optical trap,” Wikipedia, retrieved online <https://web.archive.org/web/20210125084412/https://en.wikipedia.org/wiki/Magneto-optical_trap>: 7 pages (2022). [cited by applicant]
Cong et al., “Quantum convolutional neural networks” Nature Physics, vol. 15, p. 1273-78 (2019). [cited by applicant]
Extended European Search Report for EP Application No. 19854402.5 dated May 9, 2022. [cited by applicant]
Extended European Search Report for EP Application No. 19868908.5 dated Jun. 13, 2022. [cited by applicant]
Grant et al., “Hierarchical quantum classifiers” ARXIV, p. 1-16 (2018). [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2022/016173 dated May 24, 2022. [cited by applicant]
Killoran et al., “Continuous-variable quantum neural networks” ARXIV, p. 1-21 (2018). [cited by applicant]
Kim and Swingle., “Robust entanglement renormalization on a noisy quantum computer” ARXIV, p. 1-17 (2017). [cited by applicant]
Morgado et al., “Quantum simulation and computing with Rydberg-interacting qubits,” Arxiv, Cornell University Library: 36 pages (2020). [cited by applicant]
Tanasittikosol et al., “Microwave dressing of Rydberg dark states,” Arxiv, Cornell University Library: 12 pages (2011). [cited by applicant]
Verdon et al., “A Universal Training Algorithm for Quantum Deep Learning” ARXIV, p. 1-83, (2018). [cited by applicant]
Wu et al., “Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays,” arXiv.org: 16 pages (2022). [cited by applicant]
Adachi et al., “Application of Quantum Annealing to Training of Deep Neural Networks,” arXiv.org: 18 pages (2015). [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2019/054831 dated Feb. 6, 2020. [cited by applicant]
Barredo et al., “An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays,” arXiv:1607.03042, Jul. 11, 2016, pp. 1-7. [cited by applicant]
Barredo et al., “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science, 354(6315): 1021-1023 (2016). [cited by applicant]
Barredo et al., “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature, 561: 79-82 (2018). [cited by applicant]
Baur et al., “Single-Photon Switch Based on Rydberg Blockade,” Phys. Rev. Lett., 112: 073901 (2014). [cited by applicant]
Brion et al., “Quantum Computing with Collective Ensembles of Multilevel Systems,” Phys. Rev. Lett., 99: 260501 (2007). [cited by applicant]
Browaeys et al., “Many-body physics with individually controlled Rydberg atoms,” Nature Physics, 16: 132-142 (2020). [cited by applicant]
Bruzewicz et al., “Trapped-Ion Quantum Computing: Progress and Challenges,” Applied Physics Reviews, 6(2): 021314 (2019). [cited by applicant]
Debnath et al., “Demonstration of a small programmable quantum computer with atomic qubits,” Nature, 536(7614): 63-66 (2016). [cited by applicant]
Ebert et al., “Coherence and Rydberg Blockade of Atomic Ensemble Qubits,” Phys. Rev. Lett., 115: 093601 (2015). [cited by applicant]
Endres et al., “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science, 354 (6315): 1024-1027 (2016). [cited by applicant]
Endres et al., “Cold Matter Assembled Atom-by-Atom,” arXiv:1607.03044, Jul. 11, 2016, pp. 1-12. [cited by applicant]
Engstrom et al., “Calibration of spatial light modulators suffering from spatially varying phase response,” Optics Express, 21(13): 16086-16103 (2013). [cited by applicant]
Extended European Search Report for EP Application No. EP 18831504 mailed Mar. 30, 2021. [cited by applicant]
Farhi et al., “Classification with Quantum Neural Networks on Near Term Processors,” arXiv:1802.06002, 1-21 (2018). [cited by applicant]
Fienup., “Phase retrieval algorithms: a comparison,” Applied Optics 21(15): 2758-2769 (1982). [cited by applicant]
Fowler et al., “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A, 86: 032324 (2012). [cited by applicant]
Gerchberg et al., “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik, 35(2): 237-246 (1972). [cited by applicant]
Gorniaczyk et al., “Single-Photon Transistor Mediated by Interstate Rydberg Interactions,” Phys. Rev. Lett., 113: 053601 (2014). [cited by applicant]
Gunter et al., “Interaction Enhanced Imaging of Individual Rydberg Atoms in Dense Gases,” Phys. Rev. Lett., 108: 013002 (2012). [cited by applicant]
Gunter et al., “Observing the Dynamics of Dipole-Mediated Energy Transport by Interaction-Enhanced Imaging,” Science, 342(6161): 954-956 (2013). [cited by applicant]
Haegeman et al., “Order Parameter for Symmetry-Protected Phases in One Dimension,” Phys. Rev. Lett., 109(5): 050402-1-5 (2012). [cited by applicant]
Haldane, “Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Neel State,” Phys. Rev. Lett., 50(15): 1153-1156 (1983). [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US18/42080 dated Oct. 22, 2018. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2019/049115 dated Jan. 7, 2020. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2020/019309 dated Jul. 14, 2020. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2020/033100 dated Sep. 2, 2020. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2020/041709 dated Oct. 28, 2020. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US2021/012209 mailed May 3, 2021. [cited by applicant]
Isenhower et al., “Demonstration of a neutral atom controlled-NOT quantum gate,” arXiv:0907.5552, Nov. 24, 2009, pp. 1-5. [cited by applicant]
Jahromi et al., “Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions,” Physical Review B, 94(12): (10 pages) (2016). [cited by applicant]
Jahromi et al., “Topological Z [cited by applicant]
Jaksch et al., “The cold atom Hubbard toolbox,” Arxiv, (30 pages) (2004). [cited by applicant]
Johnson et al., “Rabi Oscillations between Ground and Rydberg States with Dipole-Dipole Atomic Interactions,” Physical Review Letters, 110(11): 113003-1-4 (2008). [cited by applicant]
Kaufman et al., “Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers,” arXiv:1312.7182, Jun. 17, 2014, pp. 1-17. [cited by applicant]
Labuhn et al., “Tunable two-demensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature, 534(7609): 667-670 (2016). [cited by applicant]
Leonardo et al., “Computer generation of optimal holograms for optical trap arrays,” Optics Express, 15(4): 1913-1922 (2007). [cited by applicant]
Lester et al., “Rapid production of uniformly-filled arrays of neutral atoms,” arXiv:1506.04419, Jun. 14, 2015, pp. 1-5. [cited by applicant]
Lu et al., “Aluminum nitride integrated photonics platform for the ultraviolet to visible spectrum,” Optics Express, 26(9): 11147 (2018). [cited by applicant]
Ma et al., “Generation of three-dimensional optical structures by dynamic holograms displayed on a twisted nematic liquid crystal display,” Applied Physics B Lasers and Optics, 110(4): 531-537 (2013). [cited by applicant]
Matsumoto et al., “High-quality generation of a multispot pattern using a spatial light modulator with adaptive feedback,” Optics Letters, 37(15): 3135-3137 (2012). [cited by applicant]
Mazurenko, “Optical Imaging of Rydberg Atoms,” Thesis (S.B.)—Massachusetts Institute of Technology, Dept. of Physics (2012). [cited by applicant]
Mehta et al., “Towards fast and scalable trapped-ion quantum logic with integrated photonics,” Proc. SPIE 10933, Advances in Photonics of Quantum Computing, Memory, and Communication XII, 109330B (2019). [cited by applicant]
Murmann et al., “Two Fermions in a Double Well: Exploring a Fundamental Building Block of the Hubbard Model,” arXiv:1410.8784, Feb. 17, 2015, pp. 1-12. [cited by applicant]
Negretti et al., “Quantum computing implementation with neutral particles,” Arxiv, (19 pages) (2011). [cited by applicant]
Nogrette et al., “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Physical Review X, 4: Article 021034 pp. 1-9 (2014). [cited by applicant]
Perez-Garcia et al., “PEPS as unique ground states of local Hamiltonians,” Quant. Inf. Comp., 8: 0650 (2008). [cited by applicant]
Persson et al., “An algorithm for improved control of trap intensities in holographic optical tweezers,” Proceedings of SPIE, 8458: 8 pages (2012). [cited by applicant]
Persson et al., “Minimizing intensity fluctuations in dynamic holographic optical tweezers by restricted phase change,” Optics Express, 18(11): 11250-11263 (2010). [cited by applicant]
Persson et al., “Real-time generation of fully optimized holograms for optical trapping applications,” Proceedings of SPIE, 8097: 10 pages (2011). [cited by applicant]
Persson et al., “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Optics Express, 20(20): 22334-22343 (2012). [cited by applicant]
Persson., “Thesis for the Degree of Doctor of Philosophy: Advances in Holographic Optical Trapping,” Department of Physics University o Gothenburg: 82 pages (2013). [cited by applicant]
Pichler et al., “Computational complexity of the Rydberg blockade in two dimensions,” arXiv: 1809.04954 (2018). [cited by applicant]
Poland et al., “Development of a doubly weighted Gerchberg-Saxton algorithm for use in multibeam imaging applications,” Optics Letters, 39(8): 2431-2434 (2014). [cited by applicant]
Pollmann et al., “Detection of symmetry-protected topological phases in one dimension,” Phys. Rev. B, 86(12): 125441-1-13 (2012). [cited by applicant]
Prongue et al., “Optimized kinoform structures for highly efficient fan-out elements,” Applied Optics, 31(26): 5706-5711 (1992). [cited by applicant]
Saffman et al., “Quantum information with Rydberg atoms,” Rev. Mod. Phys., 82(3): 2313-2363 (2010). [cited by applicant]
Saffman et al., “Scaling the neutral-atom Rydberg gate quantum computer by collective encoding in holmium atoms,” Phys. Rev. A, 78: 012336 (2008). [cited by applicant]
Shi, “Deutsch, Toffoli, and CNOT Gates via Rydberg Blockade of Neutral Atoms,” Arxiv.org, Cornell University Library, 201 Olin Library Cornell University Ithaca, NY (2018). [cited by applicant]
Shi, “Fast, Accurate, and Realizable Two-Qubit Entangling Gates by Quantum Interference in Detuned Rabi Cycles of Rydberg Atoms,” Arxiv.org, Cornell University Library, 201 Olin Library Cornell University Ithaca, NY (20… [cited by applicant]
Sorace-Agaskar et al., “Multi-layer integrated photonics from the ultraviolet to the infrared,” Proc. SPIE 10510, Frontiers in Biological Detection: From Nanosensors to Systems X, 105100D (2018). [cited by applicant]
Tamura et al., “Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements,” Optics Express, 24(8): 8132-8141 (2016). [cited by applicant]
Thimons et al., “Investigating the Gerchberg-Saxton Phase Retrieval Algorithm,” SIAM: 11 pages (2018). [cited by applicant]
Torlai et al., “Integrating Neural Networks with a Quantum Simulator for State Reconstruction,” Cornell University Library, (15 pages) (2019). [cited by applicant]
Urban et al., “Observation of Rydberg blockade between two atoms,” Nature Physics, 5: 110-114 (2009). [cited by applicant]
Verresen et al., “One-dimensional symmetry protected topological phases and their transitions,” Phys. Rev. B, 96(16): 165124-1-23 (2017). [cited by applicant]
Verstraete et al., “Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States,” Phys. Rev. Lett., 96: 220601 (2006). [cited by applicant]
Vidal, “Class of Quantum Many-Body States That Can Be Efficiently Simulated,” Phys. Rev. Lett., 101(11): 110501-1-4 (2008). [cited by applicant]
Wang et al., “Coherent Addressing of Individual Neutral Atoms in a 3D Optical Lattice,” Physical Review Letters, 115(4): 043003-1-5 (2015). [cited by applicant]
Yavuz et al., “Fast Ground State Manipulation of Neutral Atoms in Microscopic Optical Traps,” Physical Review Letters, 96(6): 063001-1-4 (2006). [cited by applicant]
Ying, “Entangled Many-Body States as Resources of Quantum Information Processing,” Center for Quantum Technologies National University of Singapore (2013). [cited by applicant]
Zimmermann et al., “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” arXiv:1011.1004, Apr. 8, 2011, pp. 1-15. [cited by applicant]
International Search Report and Written Opinion for International Application No. PCT/US23/26737 dated Sep. 30, 2024. [cited by applicant]
Jaksch et al., “Fast quantum gates for neutral atoms.” arXiv (2000): 2208. [cited by applicant]
Keating et al., “Robust quantum logic in neutral atoms via adiabatic Rydberg dressing.” Physical Review A 91 (2015): 012337. [cited by applicant]
Monroe et al., “Remapping the quantum frontier.” Physics World 21.08 (2008): 32. [cited by applicant]
Nickerson et al., “Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links.” Physical Review X 4.4 (2014): 041041. [cited by applicant]
Ramette et al., “Fault-tolerant connection of error-corrected qubits with noisy links.” npj Quantum Information 10.1 (2024): 58. [cited by applicant]
Weimer et al. “A Rydberg quantum simulator.” Nature Physics 6.5 (2010): 382-388. [cited by applicant]