qcs.bib

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# COPYRIGHT 2020 RIGETTI COMPUTING
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########################################################
# INTRODUCTORY REFERENCES - HISTORY OF QUANTUM COMPUTING
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# first experimental demonstration of algo using NMR (1998)
@article{IkeNMRProcessor,
  title = {Experimental Implementation of Fast Quantum Searching},
  author = {Chuang, Isaac L. and Gershenfeld, Neil and Kubinec, Mark},
  journal = {Phys. Rev. Lett.},
  volume = {80},
  issue = {15},
  pages = {3408--3411},
  numpages = {0},
  year = {1998},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.80.3408},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.3408}
}

# first experimental demonstration using optics (2000)
@article{KwiatOpticsProcessor,
  title={Grover’s search algorithm: An optical approach},
  volume={47},
  ISSN={1362-3044},
  url={http://dx.doi.org/10.1080/09500340008244040},
  DOI={10.1080/09500340008244040},
  number={2-3},
  journal={Journal of Modern Optics},
  publisher={Informa UK Limited},
  author={Kwiat, P. G. and Mitchell, J. R. and Schwindt, P. D. D. and White, A. G.},
  year={2000},
  month={Feb},
  pages={257–266}
}

# first experimental demonstration of an algo using ions (2003)
@article{GuideIonProcessor,
  title={Implementation of the {D}eutsch--{J}ozsa algorithm on an ion-trap quantum computer},
  author={Gulde, Stephan and Riebe, Mark and Lancaster, Gavin PT and Becher, Christoph and Eschner, J{\"u}rgen and H{\"a}ffner, Hartmut and Schmidt-Kaler, Ferdinand and Chuang, Isaac L and Blatt, Rainer},
  journal={Nature},
  volume={421},
  number={6918},
  pages={48},
  year={2003},
  month={Jan},
  publisher={Nature Publishing Group},
  doi={10.1038/nature01336}
}

# first experimental demonstration of algo using SC (2009)
@article{DiCarloSCProcessor,
  title={Demonstration of two-qubit algorithms with a superconducting quantum processor},
  volume={460},
  ISSN={1476-4687},
  url={http://dx.doi.org/10.1038/nature08121},
  DOI={10.1038/nature08121},
  number={7252},
  journal={Nature},
  publisher={Springer Science and Business Media LLC},
  author={DiCarlo, L. and Chow, J. M. and Gambetta, J. M. and Bishop, Lev S. and Johnson, B. R. and Schuster, D. I. and Majer, J. and Blais, A. and Frunzio, L. and Girvin, S. M. and et al.},
  year={2009},
  month={Jun},
  pages={240–244}
}

# quantum supremacy demonstration (2019)
@article{GoogleSupremacy,
  title={Quantum supremacy using a programmable superconducting processor},
  author={Arute, Frank and Arya, Kunal and Babbush, Ryan and Bacon, Dave and Bardin, Joseph C and Barends, Rami and Biswas, Rupak and Boixo, Sergio and Brandao, Fernando GSL and Buell, David A and others},
  journal={Nature},
  volume={574},
  number={7779},
  pages={505--510},
  year={2019},
  month={Oct},
  publisher={Nature Publishing Group},
  doi={10.1038/s41586-019-1666-5}
}

# high fidelity 99.9 2Q and 99.99 1Q ion trap gates (2016)
@article{Ballance2016,
  archivePrefix = {arXiv},
  arxivId = {1512.04600},
  author = {Ballance, C. J. and Harty, T. P. and Linke, N. M. and Sepiol, M. A. and Lucas, D. M.},
  doi = {10.1103/PhysRevLett.117.060504},
  eprint = {1512.04600},
  issn = {0031-9007},
  journal = {Physical Review Letters},
  month = {Aug},
  number = {6},
  pages = {060504},
  primaryClass = {quant-ph},
  title = {{High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits}},
  volume = {117},
  year = {2016}
}

# Rigetti 99% 2Q gate (2019)
@article{HongEntanglingGate,
  title = {Demonstration of a parametrically activated entangling gate protected from flux noise},
  author = {Hong, Sabrina S. and Papageorge, Alexander T. and Sivarajah, Prasahnt and Crossman, Genya and Didier, Nicolas and Polloreno, Anthony M. and Sete, Eyob A. and Turkowski, Stefan W. and da Silva, Marcus P. and Johnson, Blake R.},
  journal = {Physical Review A},
  volume = {101},
  number = {1},
  pages = {012302},
  numpages = {8},
  year = {2020},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.101.012302},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.101.012302}
}

# quantum supremacy term (2012)
@misc{PreskillSupremacy,
  title={Quantum computing and the entanglement frontier},
  author={John Preskill},
  year={2012},
  eprint={1203.5813},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# the NISQ paper (2018)
@article{PreskillNISQ,
  title={Quantum Computing in the {NISQ} era and beyond},
  volume={2},
  ISSN={2521-327X},
  url={http://dx.doi.org/10.22331/q-2018-08-06-79},
  DOI={10.22331/q-2018-08-06-79},
  journal={Quantum},
  publisher={Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
  author={Preskill, John},
  year={2018},
  month={Aug},
  pages={79}
}

######################################################
# INTRODUCTORY REFERENCES - BUILDING THE QUANTUM CLOUD
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# NIST definition of cloud computing (2011)
@techreport{NISTCloudComputing,
  author = {Mell, Peter M. and Grance, Timothy},
  title = {{SP} 800-145. {T}he {NIST} Definition of Cloud Computing},
  year = {2011},
  publisher = {National Institute of Standards \& Technology},
  address = {Gaithersburg, MD, United States},
}

##################################################
# INTRODUCTORY REFERENCES - VARIATIONAL ALGORITHMS
##################################################

# theoretical backing of VQE (2016)
@article{McCleanTheoryVQE,
  doi = {10.1088/1367-2630/18/2/023023},
  url = {https://doi.org/10.1088%2F1367-2630%2F18%2F2%2F023023},
  year = 2016,
  month = {Feb},
  publisher = {{IOP} Publishing},
  volume = {18},
  number = {2},
  pages = {023023},
  author = {Jarrod R McClean and Jonathan Romero and Ryan Babbush and Al{\'{a}}n Aspuru-Guzik},
  title = {The theory of variational hybrid quantum-classical algorithms},
  journal = {New Journal of Physics},
  abstract = {Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the quantum variational eigensolver’ was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.}
}

# proposal for QAOA (2014)
@misc{FarhiQAOA,
  title={A Quantum Approximate Optimization Algorithm},
  author={Edward Farhi and Jeffrey Goldstone and Sam Gutmann},
  year={2014},
  eprint={1411.4028},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# experimental demonstration of QAOA for clustering on superconducting qubits (2017)
@misc{RigettiClustering,
  title={Unsupervised Machine Learning on a Hybrid Quantum Computer},
  author={J. S. Otterbach and R. Manenti and N. Alidoust and A. Bestwick and M. Block and B. Bloom and S. Caldwell and N. Didier and E. Schuyler Fried and S. Hong and P. Karalekas and C. B. Osborn and A. Papageorge and E. C. Peterson and G. Prawiroatmodjo and N. Rubin and Colm A. Ryan and D. Scarabelli and M. Scheer and E. A. Sete and P. Sivarajah and Robert S. Smith and A. Staley and N. Tezak and W. J. Zeng and A. Hudson and Blake R. Johnson and M. Reagor and M. P. da Silva and C. Rigetti},
  year={2017},
  eprint={1712.05771},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# proposal of VQE as an algorithm + experimental demonstration on photonic processor (2014)
@article{PeruzzoPhotonicVQE,
  title={A variational eigenvalue solver on a photonic quantum processor},
  volume={5},
  ISSN={2041-1723},
  url={http://dx.doi.org/10.1038/ncomms5213},
  DOI={10.1038/ncomms5213},
  number={4213},
  journal={Nature Communications},
  publisher={Springer Science and Business Media LLC},
  author={Peruzzo, Alberto and McClean, Jarrod and Shadbolt, Peter and Yung, Man-Hong and Zhou, Xiao-Qi and Love, Peter J. and Aspuru-Guzik, Alán and O’Brien, Jeremy L.},
  year={2014},
  month={Jul}
}

# experimental demonstration of H2 VQE on Xmon qubits (2016)
@article{GoogleXmonVQE,
  title = {Scalable Quantum Simulation of Molecular Energies},
  author = {O'Malley, P. J. J. and Babbush, R. and Kivlichan, I. D. and Romero, J. and McClean, J. R. and Barends, R. and Kelly, J. and Roushan, P. and Tranter, A. and Ding, N. and Campbell, B. and Chen, Y. and Chen, Z. and Chiaro, B. and Dunsworth, A. and Fowler, A. G. and Jeffrey, E. and Lucero, E. and Megrant, A. and Mutus, J. Y. and Neeley, M. and Neill, C. and Quintana, C. and Sank, D. and Vainsencher, A. and Wenner, J. and White, T. C. and Coveney, P. V. and Love, P. J. and Neven, H. and Aspuru-Guzik, A. and Martinis, J. M.},
  journal = {Phys. Rev. X},
  volume = {6},
  issue = {3},
  pages = {031007},
  numpages = {13},
  year = {2016},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.6.031007},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.6.031007}
}

# Rigetti quantum kitchen sinks (2018)
@misc{RigettiQKS,
  title={Quantum Kitchen Sinks: An algorithm for machine learning on near-term quantum computers},
  author={C. M. Wilson and J. S. Otterbach and N. Tezak and R. S. Smith and A. M. Polloreno and Peter J. Karalekas and S. Heidel and M. Sohaib Alam and G. E. Crooks and M. P. da Silva},
  year={2018},
  eprint={1806.08321},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# variational quantum linear solver (2019)
@misc{Bravo-PietroVQLS,
  title={Variational Quantum Linear Solver: A Hybrid Algorithm for Linear Systems},
  author={Carlos Bravo-Prieto and Ryan LaRose and M. Cerezo and Yigit Subasi and Lukasz Cincio and Patrick J. Coles},
  year={2019},
  eprint={1909.05820},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# variational quantum thermalizer (2019)
@misc{GuillaumeVQT,
  title={Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm},
  author={Guillaume Verdon and Jacob Marks and Sasha Nanda and Stefan Leichenauer and Jack Hidary},
  year={2019},
  eprint={1910.02071},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# Oliver group SC qubits overview (2019)
@misc{OliverSCStateOfPlay,
  title={Superconducting Qubits: Current State of Play},
  author={Morten Kjaergaard and Mollie E. Schwartz and Jochen Braumüller and Philip Krantz and Joel I-Jan Wang and Simon Gustavsson and William D. Oliver},
  year={2019},
  eprint={1905.13641},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

#################################################
# QUANTUM-CLASSICAL CLOUD ARCHITECTURE REFERENCES
#################################################

# quantum programming languages - openQASM spec (2017)
@misc{CrossQASM,
  title={Open Quantum Assembly Language},
  author={Andrew W. Cross and Lev S. Bishop and John A. Smolin and Jay M. Gambetta},
  year={2017},
  eprint={1707.03429},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# quantum programming languages - the Quil paper (2016)
@misc{SmithQuil,
  title={A Practical Quantum Instruction Set Architecture},
  author={Robert S. Smith and Michael J. Curtis and William J. Zeng},
  year={2016},
  eprint={1608.03355},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# barren plateaus (2018)
@article{McCleanBarrenPlateaus,
  title={Barren plateaus in quantum neural network training landscapes},
  volume={9},
  ISSN={2041-1723},
  url={http://dx.doi.org/10.1038/s41467-018-07090-4},
  DOI={10.1038/s41467-018-07090-4},
  number={4812},
  journal={Nature Communications},
  publisher={Springer Science and Business Media LLC},
  author={McClean, Jarrod R. and Boixo, Sergio and Smelyanskiy, Vadim N. and Babbush, Ryan and Neven, Hartmut},
  year={2018},
  month={Nov}
}

###########################
# LATENCY BUDGET REFERENCES
###########################

# Rigetti fab paper with high T1 (2019)
@misc{RigettiFabT1,
  title={Manufacturing low dissipation superconducting quantum processors},
  author={Ani Nersisyan and Stefano Poletto and Nasser Alidoust and Riccardo Manenti and Russ Renzas and Cat-Vu Bui and Kim Vu and Tyler Whyland and Yuvraj Mohan and Eyob A. Sete and Sam Stanwyck and Andrew Bestwick and Matthew Reagor},
  year={2019},
  eprint={1901.08042},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# recent SC qubit with 1.6 ms T1 (2019)
@misc{GyensisZeroPi,
  title={Experimental realization of an intrinsically error-protected superconducting qubit},
  author={Andras Gyenis and Pranav S. Mundada and Agustin Di Paolo and Thomas M. Hazard and Xinyuan You and David I. Schuster and Jens Koch and Alexandre Blais and Andrew A. Houck},
  year={2019},
  eprint={1910.07542},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# the Quilc compiler repository
@software{PetersonQuil,
  author       = {Robert S Smith and
                  Eric C Peterson and
                  Erik J Davis and
                  Mark G Skilbeck},
  title        = {\textit{quilc: {A}n Optimizing {Q}uil Compiler}, 2020, 
  \href{https://doi.org/10.5281/zenodo.3677536}{\ttfamily zenodo:3677536}},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3677536},
  url          = {https://doi.org/10.5281/zenodo.3677536}
}

###################################
# PARAMETRIC COMPILATION REFERENCES
###################################

# executable and linkable format (ELF) standard for understanding binaries (1995)
@article{ELFStandard,
  title={{T}ool {I}nterface {S}tandard ({TIS}) {E}xecutable and {L}inking Format ({ELF}) Specification Version 1.2},
  author={TIS Committee and others},
  journal={TIS Committee},
  year={1995}
}

# POSIX standard for understanding shared memory
@ARTICLE{POSIXStandard,
  author={},
  journal={IEEE Std 1003.1, 2016 Edition}, 
  title={Standard for {I}nformation {T}echnology--{P}ortable {O}perating {S}ystem {I}nterface ({POSIX(R)}) {B}ase {S}pecifications, {I}ssue 7}, 
  year={2016},
  volume={},
  number={},
  pages={1-3957},}

# repository with Quil specification
@misc{QuilRepo,
  author       = {Robert S Smith},
  title        = {\textit{Quil: A {P}ortable {Q}uantum {I}nstruction {L}anguage}, 2020, 
  \href{https://doi.org/10.5281/zenodo.3677540}{\ttfamily zenodo:3677540}},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3677540},
  url          = {https://doi.org/10.5281/zenodo.3677540}
}

###############################
# ACTIVE QUBIT RESET REFERENCES
###############################

# IBM reset by pumping to the readout resonator (2018)
@article{EggerActiveReset,
  archivePrefix = {arXiv},
  arxivId = {1802.08980},
  author = {Egger, D.J. and Werninghaus, Max and Ganzhorn, Marc and Salis, Gian and Fuhrer, Andreas and M{\"{u}}ller, P. and Filipp, Stefan},
  doi = {10.1103/PhysRevApplied.10.044030},
  eprint = {1802.08980},
  issn = {2331-7019},
  journal = {Physical Review Applied},
  month = {Oct},
  number = {4},
  pages = {044030},
  primaryClass={quant-ph},
  title = {{Pulsed Reset Protocol for Fixed-Frequency Superconducting Qubits}},
  volume = {10},
  year = {2018}
}

# Walraff reset by pumping to readout resonator (2018)
@article{MagnardActiveReset,
  archivePrefix = {arXiv},
  arxivId = {1801.07689},
  author = {Magnard, Paul and Kurpiers, Philipp and Royer, Baptiste and Walter, Theo and Besse, J.-C. and Gasparinetti, Simone and Pechal, Marek and Heinsoo, Johannes and Storz, Simon and Blais, Alexandre and Wallraff, Andreas},
  doi = {10.1103/PhysRevLett.121.060502},
  eprint = {1801.07689},
  issn = {0031-9007},
  journal = {Physical Review Letters},
  month = {Aug},
  number = {6},
  pages = {060502},
  primaryClass = {quant-ph},
  title = {{Fast and Unconditional All-Microwave Reset of a Superconducting Qubit}},
  volume = {121},
  year = {2018}
}

# riste active qubit reset (2012)
@article{RisteActiveReset,
  title={Feedback Control of a Solid-State Qubit Using High-Fidelity Projective Measurement},
  volume={109},
  ISSN={1079-7114},
  url={http://dx.doi.org/10.1103/PhysRevLett.109.240502},
  DOI={10.1103/physrevlett.109.240502},
  number={24},
  journal={Physical Review Letters},
  publisher={American Physical Society (APS)},
  author={Ristè, D. and Bultink, C. C. and Lehnert, K. W. and DiCarlo, L.},
  year={2012},
  month={Dec}
}

# fast gateware & demonstration of active reset on SC qubits at BBN (2017)
@article{RyanBBNHardware,
  title={Hardware for dynamic quantum computing},
  volume={88},
  ISSN={1089-7623},
  url={http://dx.doi.org/10.1063/1.5006525},
  DOI={10.1063/1.5006525},
  number={10},
  journal={Review of Scientific Instruments},
  publisher={AIP Publishing},
  author={Ryan, Colm A. and Johnson, Blake R. and Ristè, Diego and Donovan, Brian and Ohki, Thomas A.},
  year={2017},
  month={Oct},
  pages={104703}
}

# control flow graphs (1986)
@book{DragonBook,
 author = {Aho, Alfred V. and Sethi, Ravi and Ullman, Jeffrey D.},
 title = {Compilers: Principles, Techniques, and Tools},
 year = {1986},
 isbn = {0-201-10088-6},
 publisher = {Addison-Wesley Longman Publishing Co., Inc.},
 address = {Boston, MA, USA},
}

###################################
# BENCHMARKING FRAMEWORK REFERENCES
###################################

# the GHZ state (2007)
@misc{GHZState,
  title={Going Beyond Bell's Theorem},
  author={Daniel M. Greenberger and Michael A. Horne and Anton Zeilinger},
  year={2007},
  eprint={0712.0921},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# gavin max-cut QAOA performance (2018)
@misc{CrooksQAOA,
  title={Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem},
  author={Gavin E. Crooks},
  year={2018},
  eprint={1811.08419},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# IBM quantum volume paper (2019)
@article{CrossQuantumVolume,
  title={Validating quantum computers using randomized model circuits},
  volume={100},
  ISSN={2469-9934},
  url={http://dx.doi.org/10.1103/PhysRevA.100.032328},
  DOI={10.1103/physreva.100.032328},
  number={3},
  pages = {012302},
  journal={Physical Review A},
  publisher={American Physical Society (APS)},
  author={Cross, Andrew W. and Bishop, Lev S. and Sheldon, Sarah and Nation, Paul D. and Gambetta, Jay M.},
  year={2019},
  month={Sep}
}

# quantum volume and variational algos (2018)
@article{MollVariational,
  title={Quantum optimization using variational algorithms on near-term quantum devices},
  volume={3},
  ISSN={2058-9565},
  url={http://dx.doi.org/10.1088/2058-9565/aab822},
  DOI={10.1088/2058-9565/aab822},
  number={3},
  journal={Quantum Science and Technology},
  publisher={IOP Publishing},
  author={Moll, Nikolaj and Barkoutsos, Panagiotis and Bishop, Lev S and Chow, Jerry M and Cross, Andrew and Egger, Daniel J and Filipp, Stefan and Fuhrer, Andreas and Gambetta, Jay M and Ganzhorn, Marc and et al.},
  year={2018},
  month={Jun},
  pages={030503}
}

# CQC work on phase gadget compilation (2019)
@misc{CowtanPhaseGadgets,
  title={Phase Gadget Synthesis for Shallow Circuits},
  author={Alexander Cowtan and Silas Dilkes and Ross Duncan and Will Simmons and Seyon Sivarajah},
  year={2019},
  eprint={1906.01734},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# sandia generalized volumetric benchmarks (2019)
@misc{RobinVolumetrics,
  title={A volumetric framework for quantum computer benchmarks},
  author={Robin Blume-Kohout and Kevin C. Young},
  year={2019},
  eprint={1904.05546},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

# eric's paper on compiling 2Q gates (2019)
@misc{PetersonPolytopes,
  title={Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope},
  author={Eric C. Peterson and Gavin E. Crooks and Robert S. Smith},
  year={2019},
  eprint={1904.10541},
  archivePrefix={arXiv},
  primaryClass={quant-ph}
}

#############################
# ACKNOWLEDGEMENTS REFERENCES
#############################

@software{QCSPaperSupplement,
  author       = {Peter J. Karalekas},
  title        = {\textit{Supplementary notebooks and datasets for: A 
                   quantum-classical cloud platform optimized for
                   variational hybrid algorithms}, 2020, \href{https://doi.org/10.5281/zenodo.3606734}{\ttfamily zenodo:3606734}},
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.3606734},
  url          = {https://doi.org/10.5281/zenodo.3606734}
}

#####################
# APPENDIX REFERENCES
#####################

# using VQE as a benchmark (2019)
@article{McCaskeyBenchmarkVQE,
  title={Quantum chemistry as a benchmark for near-term quantum computers},
  author={McCaskey, Alexander J and Parks, Zachary P and Jakowski, Jacek and Moore, Shirley V and Morris, Titus D and Humble, Travis S and Pooser, Raphael C},
  journal={npj Quantum Information},
  volume={5},
  number={1},
  pages={1--8},
  year={2019},
  publisher={Nature Publishing Group},
  doi={s41534-019-0209-0}
}

# the pyQuil library, used to run all appendix examples
@software{PyQuilZenodo,
  author       = {Peter J. Karalekas and
                  Matthew P. Harrigan and
                  Steven Heidel and
                  William J. Zeng and
                  M. Sohaib Alam and
                  Mike I. Appleby and
                  Lauren E. Capelluto and
                  Gavin E. Crooks and
                  Michael J. Curtis and
                  Erik J. Davis and
                  Kyle V. Gulshen and
                  Christopher B. Osborn and
                  Johannes S. Otterbach and
                  Eric C. Peterson and
                  Anthony M. Polloreno and
                  Guen Prawiroatmodjo and
                  Nicholas C. Rubin and
                  Mark G. Skilbeck and
                  Nikolas A. Tezak and
                  Robert S. Smith},
  title        = {\textit{Py{Q}uil: {Q}uantum {P}rogramming in {P}ython}, 2020, \href{https://doi.org/10.5281/zenodo.3553165}{\ttfamily zenodo:3553165}},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3553165},
  url          = {https://doi.org/10.5281/zenodo.3553165}
}

# twirling reference 1 (2007)
@article{Bartlett2007,
  title={Reference frames, superselection rules, and quantum information},
  volume={79},
  ISSN={1539-0756},
  url={http://dx.doi.org/10.1103/RevModPhys.79.555},
  DOI={10.1103/revmodphys.79.555},
  number={2},
  journal={Rev. Mod. Phys.},
  publisher={American Physical Society (APS)},
  author={Bartlett, Stephen D. and Rudolph, Terry and Spekkens, Robert W.},
  year={2007},
  month={Apr},
  pages={555–609}
}

# twirling reference 2 (1996)
@article{Bennet1996,
  title = {Mixed-state entanglement and quantum error correction},
  author = {Bennett, Charles H. and DiVincenzo, David P. and Smolin, John A. and Wootters, William K.},
  journal = {Physical Review A},
  volume = {54},
  number = {5},
  pages = {3824--3851},
  numpages = {0},
  year = {1996},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.54.3824},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.54.3824}
}

# forest benchmarking library, used in tomography and RO symmetrization
@misc{ForestBenchmarking,
  author       = {Kyle V. Gulshen and
                  Joshua Combes and
                  Matthew P. Harrigan and
                  Peter J. Karalekas and
                  Marcus P. da Silva and
                  M. Sohaib Alam and
                  Amy Brown and
                  Shane Caldwell and
                  Lauren Capelluto and
                  Gavin Crooks and
                  Daniel Girshovich and
                  Blake R. Johnson and
                  Eric C. Peterson and
                  Anthony Polloreno and
                  Nicholas C. Rubin and
                  Colm A. Ryan and
                  Alexa Staley and
                  Nikolas A. Tezak and
                  Joseph Valery},
  author+an    = {1=jointfirst; 2=jointfirst},
  title        = {\textit{{F}orest {B}enchmarking: {QCVV} using {PyQuil}}, 2019, \href{https://doi.org/10.5281/zenodo.3455847}{\ttfamily zenodo:3455847}},
  doi          = {10.5281/zenodo.3455847},
  url          = {https://doi.org/10.5281/zenodo.3455847}
}

# exponential scaling of readout correction (2015)
@article{Ryan2015,
  archivePrefix = {arXiv},
  author = {Ryan, Colm A. and Johnson, Blake R. and Gambetta, Jay M. and Chow, Jerry M. and da Silva, Marcus P. and Dial, Oliver E. and Ohki, Thomas A.},
  doi = {10.1103/PhysRevA.91.022118},
  eprint = {1310.6448},
  isbn = {1050-2947},
  issn = {1050-2947},
  journal = {Physical Review A},
  month = {Feb},
  number = {2},
  pages = {022118},
  primaryClass = {quant-ph},
  title = {{Tomography via correlation of noisy measurement records}},
  volume = {91},
  year = {2015}
}

# mike and ike for euler decomposition
@book{MikeAndIke,
  author = {Nielsen, Michael A. and Chuang, Isaac L.},
  title = {Quantum Computation and Quantum Information: 10th Anniversary Edition},
  year = {2011},
  isbn = {1107002176, 9781107002173},
  edition = {10th},
  publisher = {Cambridge University Press},
  address = {New York, NY, USA},
} 

# matplotlib library (Hinton plotting)
@Article{Matplotlib,
  Author    = {Hunter, J. D.},
  Title     = {Matplotlib: A 2D graphics environment},
  Journal   = {Computing in Science \& Engineering},
  Volume    = {9},
  Number    = {3},
  Pages     = {90--95},
  abstract  = {Matplotlib is a 2D graphics package used for Python for
  application development, interactive scripting, and publication-quality
  image generation across user interfaces and operating systems.},
  publisher = {IEEE COMPUTER SOC},
  doi       = {10.1109/MCSE.2007.55},
  year      = 2007
}

# scipy library (original source of Hinton)
@article{SciPy,
   title={Sci{P}y 1.0: fundamental algorithms for scientific computing in {P}ython},
   volume={17},
   ISSN={1548-7105},
   url={http://dx.doi.org/10.1038/s41592-019-0686-2},
   DOI={10.1038/s41592-019-0686-2},
   number={3},
   journal={Nature Methods},
   publisher={Springer Science and Business Media LLC},
   author={Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and et al.},
   year={2020},
   month={Feb},
   pages={261–272}
}


# linear inversion for state tomography, in wood thesis (2015)
@Misc{WoodThesis,
  author={{Wood, Christopher James}},
  title={Initialization and characterization of open quantum systems (\url{http://hdl.handle.net/10012/9557})},
  year={2015},
  publisher="UWSpace",
  url={http://hdl.handle.net/10012/9557}
}

# the quantum virtual machine (QVM) repository, used in VQE plot
@software{RigettiQVM,
  author       = {Robert S Smith},
  title        = {\textit{qvm: {T}he {R}igetti Quantum Virtual Machine}, 2020, \href{https://doi.org/10.5281/zenodo.3677538}{\ttfamily zenodo:3677538}},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3677538},
  url          = {https://doi.org/10.5281/zenodo.3677538}
}