Towards quantum-enabled cell-centric therapeutics

In recent years, there has been tremendous progress in the development of quantum computing hardware, algorithms and services leading to the expectation that in the near future quantum computers will be capable of performing simulations for natural science applications, operations research, and machine learning at scales mostly inaccessible to classical computers. Whereas the impact of quantum computing has already started to be recognized in fields such as cryptanalysis, natural science simulations, and optimization among others, very little is known about the full potential of quantum computing simulations and machine learning in the realm of healthcare and life science (HCLS). Herein, we discuss the transformational changes we expect from the use of quantum computation for HCLS research, more specifically in the field of cell-centric therapeutics. Moreover, we identify and elaborate open problems in cell engineering, tissue modeling, perturbation modeling, and bio-topology while discussing candidate quantum algorithms for research on these topics and their potential advantages over classical computational approaches.

[1]  Jad C. Halimeh,et al.  Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group , 2023, 2307.03236.

[2]  Hassaan Maan,et al.  scGPT: Towards Building a Foundation Model for Single-Cell Multi-omics Using Generative AI , 2023, bioRxiv.

[3]  Xuegong Zhang,et al.  Large Scale Foundation Model on Single-cell Transcriptomics , 2023, bioRxiv.

[4]  Ewout van den Berg,et al.  Evidence for the utility of quantum computing before fault tolerance , 2023, Nature.

[5]  P. Ellinor,et al.  Transfer learning enables predictions in network biology , 2023, Nature.

[6]  Michal Stkechly,et al.  Connecting the Hamiltonian structure to the QAOA energy and Fourier landscape structure , 2023, 2305.13594.

[7]  Kaitlin N. Smith,et al.  Empirical overhead of the adapted surface code on defective qubit arrays , 2023, 2305.00138.

[8]  J. Leskovec,et al.  Foundation models for generalist medical artificial intelligence , 2023, Nature.

[9]  Kaitlin N. Smith,et al.  Clifford-based Circuit Cutting for Quantum Simulation , 2023, ISCA.

[10]  Ansuman T. Satpathy,et al.  Co-opting signalling molecules enables logic-gated control of CAR T cells , 2023, Nature.

[11]  Frederik F. Flöther,et al.  How can quantum technologies be applied in healthcare, medicine, and the life sciences? , 2023, Research Directions: Quantum Technologies.

[12]  I. Tavernelli,et al.  Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers , 2023, The journal of physical chemistry letters.

[13]  Louai Labanieh,et al.  CAR immune cells: design principles, resistance and the next generation , 2023, Nature.

[14]  Frederik F. Flöther The state of quantum computing applications in health and medicine , 2023, Research Directions: Quantum Technologies.

[15]  Zhaoxiong Chen,et al.  Transformer for one stop interpretable cell type annotation , 2023, Nature Communications.

[16]  N. W. Talarico,et al.  Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive. , 2022, The journal of physical chemistry. A.

[17]  W. Lim,et al.  Decoding CAR T cell phenotype using combinatorial signaling motif libraries and machine learning , 2022, Science.

[18]  W. Lim The emerging era of cell engineering: Harnessing the modularity of cells to program complex biological function , 2022, Science.

[19]  Miki Ebisuya,et al.  Scaling up complexity in synthetic developmental biology , 2022, Science.

[20]  Alexandro E. Trevino,et al.  Graph deep learning for the characterization of tumour microenvironments from spatial protein profiles in tissue specimens , 2022, Nature Biomedical Engineering.

[21]  L. Parida,et al.  Topology and redescriptions detect multiple alternative biological pathways from clinical phenotypes , 2022, Experimental biology and medicine.

[22]  Michelle M. Li,et al.  Graph representation learning in biomedicine and healthcare , 2022, Nature Biomedical Engineering.

[23]  D. Gottesman Opportunities and Challenges in Fault-Tolerant Quantum Computation , 2022, 2210.15844.

[24]  Fabian J Theis,et al.  Modeling intercellular communication in tissues using spatial graphs of cells , 2022, Nature Biotechnology.

[25]  J. McClean,et al.  Quantum error mitigation , 2022, Reviews of Modern Physics.

[26]  S. Lloyd,et al.  Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis , 2022, PRX Quantum.

[27]  K. Clarkson,et al.  Towards Quantum Advantage on Noisy Quantum Computers , 2022, ArXiv.

[28]  L. Carter,et al.  Hallucinating symmetric protein assemblies , 2022, Science.

[29]  A. Ekici,et al.  Anti-CD19 CAR T cell therapy for refractory systemic lupus erythematosus , 2022, Nature Medicine.

[30]  J. Gambetta,et al.  The future of quantum computing with superconducting qubits , 2022, Journal of Applied Physics.

[31]  Patrick J. Coles,et al.  Challenges and opportunities in quantum machine learning , 2022, Nature Computational Science.

[32]  S. Maniscalco,et al.  Link Prediction with Continuous-Time Classical and Quantum Walks , 2022, Entropy.

[33]  Tanvi P. Gujarati,et al.  Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor , 2022, Chemical science.

[34]  William M. Kirby,et al.  Exact and efficient Lanczos method on a quantum computer , 2022, Quantum.

[35]  S. Ovchinnikov,et al.  Scaffolding protein functional sites using deep learning , 2022, Science.

[36]  A. Elofsson,et al.  Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search , 2022, bioRxiv.

[37]  Michael J. Hoffmann,et al.  Suppressing quantum errors by scaling a surface code logical qubit , 2022, Nature.

[38]  P. Zoller,et al.  Practical quantum advantage in quantum simulation , 2022, Nature.

[39]  Marco Cuturi,et al.  Supervised Training of Conditional Monge Maps , 2022, NeurIPS.

[40]  N. W. Talarico,et al.  Quantum network medicine: rethinking medicine with network science and quantum algorithms , 2022, 2206.12405.

[41]  Brian A. Joughin,et al.  Screening for CD19-specific chimaeric antigen receptors with enhanced signalling via a barcoded library of intracellular domains , 2022, Nature Biomedical Engineering.

[42]  B. Sankaran,et al.  Robust deep learning based protein sequence design using ProteinMPNN , 2022, bioRxiv.

[43]  David Sutter,et al.  Circuit knitting with classical communication , 2022, IEEE Transactions on Information Theory.

[44]  I. Tavernelli,et al.  Quantum machine learning framework for virtual screening in drug discovery: a prospective quantum advantage , 2022, Mach. Learn. Sci. Technol..

[45]  L. Parida,et al.  Epidemiological topology data analysis links severe COVID-19 to RAAS and hyperlipidemia associated metabolic syndrome conditions , 2022, medRxiv.

[46]  S. Vallecorsa,et al.  Quantum neural networks force fields generation , 2022, Mach. Learn. Sci. Technol..

[47]  M. Samwald,et al.  Mapping global dynamics of benchmark creation and saturation in artificial intelligence , 2022, Nature Communications.

[48]  E. Berg,et al.  Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors , 2022, Nature Physics.

[49]  D. Weissman,et al.  CAR T cells produced in vivo to treat cardiac injury , 2022, Science.

[50]  Po-Hsuan Cameron Chen,et al.  Artificial intelligence for diagnosis and Gleason grading of prostate cancer: the PANDA challenge , 2022, Nature Medicine.

[51]  S. Tavaré,et al.  Three-dimensional imaging mass cytometry for highly multiplexed molecular and cellular mapping of tissues and the tumor microenvironment , 2021, Nature Cancer.

[52]  G. Burkard,et al.  Semiconductor spin qubits , 2021, Reviews of Modern Physics.

[53]  Frederik F. Flöther,et al.  Quantum Kernels for Real-World Predictions Based on Electronic Health Records , 2021, IEEE Transactions on Quantum Engineering.

[54]  S. Yelin,et al.  Markov chain Monte Carlo enhanced variational quantum algorithms , 2021, Quantum Science and Technology.

[55]  Nicolas P. D. Sawaya,et al.  Biology and medicine in the landscape of quantum advantages , 2021, Journal of the Royal Society Interface.

[56]  G. Nolan,et al.  Annotation of Spatially Resolved Single-cell Data with STELLAR , 2021, bioRxiv.

[57]  S. Keeney,et al.  Computed structures of core eukaryotic protein complexes , 2021, Science.

[58]  Giuseppe De Pietro,et al.  BRACS: A Dataset for BReAst Carcinoma Subtyping in H&E Histology Images , 2021, Database J. Biol. Databases Curation.

[59]  A. Abbott Quantum computers to explore precision oncology , 2021, Nature Biotechnology.

[60]  Ryuuichirou Hayakawa,et al.  Quantum algorithm for persistent Betti numbers and topological data analysis , 2021, Quantum.

[61]  Blake R. Johnson,et al.  Quality, Speed, and Scale: three key attributes to measure the performance of near-term quantum computers , 2021, 2110.14108.

[62]  N. Kaulgud,et al.  Quantum K-means clustering method for detecting heart disease using quantum circuit approach , 2021, Soft Computing.

[63]  K. Brown,et al.  Fault-tolerant control of an error-corrected qubit , 2021, Nature.

[64]  M. Motta,et al.  Emerging quantum computing algorithms for quantum chemistry , 2021, WIREs Computational Molecular Science.

[65]  A. Hierlemann,et al.  speedingCARs: accelerating the engineering of CAR T cells by signaling domain shuffling and single-cell sequencing , 2021, bioRxiv.

[66]  Theodore J. Yoder,et al.  Scalable error mitigation for noisy quantum circuits produces competitive expectation values , 2021, Nature Physics.

[67]  Michael S. Bernstein,et al.  On the Opportunities and Risks of Foundation Models , 2021, ArXiv.

[68]  Kenneth L. Clarkson,et al.  Quantum Topological Data Analysis with Linear Depth and Exponential Speedup , 2021, ArXiv.

[69]  L. Parida,et al.  CuNA: Cumulant-based Network Analysis of genotype-phenotype associations in Parkinson's Disease , 2021, medRxiv.

[70]  K. Rogers,et al.  Spatial omics and multiplexed imaging to explore cancer biology , 2021, Nature Methods.

[71]  Nick Orr,et al.  The topology of data: opportunities for cancer research , 2021, Bioinform..

[72]  P. Wocjan,et al.  Szegedy Walk Unitaries for Quantum Maps , 2021, Communications in Mathematical Physics.

[73]  Oriol Vinyals,et al.  Highly accurate protein structure prediction with AlphaFold , 2021, Nature.

[74]  Andrea Simonetto,et al.  Best Approximate Quantum Compiling Problems , 2021, ACM Transactions on Quantum Computing.

[75]  Fabian J Theis,et al.  Graph representation learning for single-cell biology , 2021 .

[76]  T. Dey,et al.  Gene expression data classification using topology and machine learning models , 2021, BMC Bioinformatics.

[77]  Andrew W. Cross,et al.  OpenQASM 3: A Broader and Deeper Quantum Assembly Language , 2021, ACM Transactions on Quantum Computing.

[78]  J. Martinis Optimal design of a superconducting transmon qubit with tapered wiring , 2021, 2104.01544.

[79]  Yi Yan Yang,et al.  Accelerated antimicrobial discovery via deep generative models and molecular dynamics simulations , 2021, Nature Biomedical Engineering.

[80]  C. Gonzalez Cloud based QC with Amazon Braket , 2021, Digitale Welt.

[81]  Tyler T. Risom,et al.  Whole-cell segmentation of tissue images with human-level performance using large-scale data annotation and deep learning , 2021, Nature Biotechnology.

[82]  G. Jafari,et al.  Topological analysis of interaction patterns in cancer-specific gene regulatory network: persistent homology approach , 2021, Scientific Reports.

[83]  Z. Bar-Joseph,et al.  GCNG: graph convolutional networks for inferring gene interaction from spatial transcriptomics data , 2020, Genome biology.

[84]  Connor T. Hann,et al.  Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes , 2020, PRX Quantum.

[85]  Jean-Philippe Thiran,et al.  Quantifying Explainers of Graph Neural Networks in Computational Pathology , 2020, 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[86]  Arthur Pesah,et al.  Absence of Barren Plateaus in Quantum Convolutional Neural Networks , 2020, Physical Review X.

[87]  Stefan Woerner,et al.  The power of quantum neural networks , 2020, Nature Computational Science.

[88]  K. Temme,et al.  A rigorous and robust quantum speed-up in supervised machine learning , 2020, Nature Physics.

[89]  Frederic T. Chong,et al.  Optimization of Simultaneous Measurement for Variational Quantum Eigensolver Applications , 2020, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).

[90]  P. Barkoutsos,et al.  Quantum HF/DFT-embedding algorithms for electronic structure calculations: Scaling up to complex molecular systems. , 2020, The Journal of chemical physics.

[91]  H. Nayfeh,et al.  Demonstration of quantum volume 64 on a superconducting quantum computing system , 2020, Quantum Science and Technology.

[92]  P. Barkoutsos,et al.  Quantum algorithm for alchemical optimization in material design† , 2020, Chemical science.

[93]  Y. Chen,et al.  Engineering CAR-T Cells for Next-Generation Cancer Therapy. , 2020, Cancer cell.

[94]  David Baker,et al.  De novo protein design by deep network hallucination , 2020, Nature.

[95]  Amanda R. Kulick,et al.  Senolytic CAR T cells reverse senescence-associated pathologies , 2020, Nature.

[96]  V. Dunjko,et al.  Towards quantum advantage via topological data analysis , 2020, Quantum.

[97]  C. Mackall,et al.  The Emerging Landscape of Immune Cell Therapies , 2020, Cell.

[98]  D. Weissman,et al.  Recent advances in mRNA vaccine technology. , 2020, Current opinion in immunology.

[99]  Howard Y. Chang,et al.  Single-cell RNA sequencing in cardiovascular development, disease and medicine , 2020, Nature Reviews Cardiology.

[100]  Gary D Bader,et al.  A reference map of the human binary protein interactome , 2020, Nature.

[101]  Aviv Madar,et al.  Single residue in CD28-costimulated CAR T cells limits long-term persistence and antitumor durability. , 2020, The Journal of clinical investigation.

[102]  B. Zybailov,et al.  Integration of Flow Cytometry and Single Cell Sequencing. , 2020, Trends in biotechnology.

[103]  Pablo G. Cámara,et al.  Identification of relevant genetic alterations in cancer using topological data analysis , 2020, Nature Communications.

[104]  Jiří Damborský,et al.  Machine Learning in Enzyme Engineering , 2020 .

[105]  Andrea Simonetto,et al.  Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers , 2020, IEEE Transactions on Quantum Engineering.

[106]  Oliver J. Klein,et al.  An RNA vaccine drives expansion and efficacy of claudin-CAR-T cells against solid tumors , 2020, Science.

[107]  Lior Pachter,et al.  Highly multiplexed single-cell RNA-seq by DNA oligonucleotide tagging of cellular proteins , 2019, Nature Biotechnology.

[108]  Alicia J. Kollár,et al.  Quantum Simulators: Architectures and Opportunities , 2019, 1912.06938.

[109]  J. Bluestone,et al.  Treg cell-based therapies: challenges and perspectives , 2019, Nature Reviews Immunology.

[110]  Jonathan S. Packer,et al.  Massively multiplex chemical transcriptomics at single-cell resolution , 2019, Science.

[111]  Mustafa Suleyman,et al.  Key challenges for delivering clinical impact with artificial intelligence , 2019, BMC Medicine.

[112]  J. Gambetta,et al.  Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor , 2019, Physical Review Research.

[113]  A. Lin,et al.  Off-target toxicity is a common mechanism of action of cancer drugs undergoing clinical trials , 2019, Science Translational Medicine.

[114]  Adam J. Riesselman,et al.  Protein design and variant prediction using autoregressive generative models , 2019, Nature Communications.

[115]  Hannes Bernien,et al.  Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms. , 2019, Physical review letters.

[116]  Thomas M. Norman,et al.  Exploring genetic interaction manifolds constructed from rich single-cell phenotypes , 2019, Science.

[117]  Mohammad Lotfollahi,et al.  scGen predicts single-cell perturbation responses , 2019, Nature Methods.

[118]  Alessandro Chiesa,et al.  Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives , 2019, Advanced Quantum Technologies.

[119]  Niels Kornerup,et al.  Review of a Quantum Algorithm for Betti Numbers , 2019, ArXiv.

[120]  Yuhei Umeda,et al.  Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks , 2019, Canadian Conference on AI.

[121]  Omar Shehab,et al.  Noise reduction using past causal cones in variational quantum algorithms , 2019, ArXiv.

[122]  Craig Gidney,et al.  How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits , 2019, Quantum.

[123]  G. Corrado,et al.  End-to-end lung cancer screening with three-dimensional deep learning on low-dose chest computed tomography , 2019, Nature Medicine.

[124]  G. Corrado,et al.  End-to-end lung cancer screening with three-dimensional deep learning on low-dose chest computed tomography , 2019, Nature Medicine.

[125]  G. Kells,et al.  Error generation and propagation in Majorana-based topological qubits , 2019, Physical Review B.

[126]  R. Barzilay,et al.  A Deep Learning Mammography-based Model for Improved Breast Cancer Risk Prediction. , 2019, Radiology.

[127]  Maria Anna Rapsomaniki,et al.  A Single-Cell Atlas of the Tumor and Immune Ecosystem of Human Breast Cancer , 2019, Cell.

[128]  Yun Seong Nam,et al.  Toward convergence of effective field theory simulations on digital quantum computers , 2019, Physical Review A.

[129]  Dmitri Maslov,et al.  Ground-state energy estimation of the water molecule on a trapped ion quantum computer , 2019, ArXiv.

[130]  M. Sauer,et al.  Super-resolution microscopy demystified , 2019, Nature Cell Biology.

[131]  Karsten M. Borgwardt,et al.  Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology , 2018, ICLR.

[132]  Andrew W. Cross,et al.  Validating quantum computers using randomized model circuits , 2018, Physical Review A.

[133]  Kevin K. Yang,et al.  Machine-learning-guided directed evolution for protein engineering , 2018, Nature Methods.

[134]  Nathan Killoran,et al.  PennyLane: Automatic differentiation of hybrid quantum-classical computations , 2018, ArXiv.

[135]  Alán Aspuru-Guzik,et al.  Potential of quantum computing for drug discovery , 2018, IBM J. Res. Dev..

[136]  Soonwon Choi,et al.  Quantum convolutional neural networks , 2018, Nature Physics.

[137]  Alán Aspuru-Guzik,et al.  Quantum computational chemistry , 2018, Reviews of Modern Physics.

[138]  Magdalena Zernicka-Goetz,et al.  Deconstructing and reconstructing the mouse and human early embryo , 2018, Nature Cell Biology.

[139]  Michel Sadelain,et al.  Chimeric Antigen Receptor Therapy. , 2018, The New England journal of medicine.

[140]  S. Brierley,et al.  Variational Quantum Computation of Excited States , 2018, Quantum.

[141]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

[142]  Andrew W. Cross,et al.  The IBM Q experience and QISKit open-source quantum computing software , 2018 .

[143]  D. Weissman,et al.  mRNA vaccines — a new era in vaccinology , 2018, Nature Reviews Drug Discovery.

[144]  R. Pooser,et al.  Cloud Quantum Computing of an Atomic Nucleus. , 2018, Physical Review Letters.

[145]  Michael J. T. Stubbington,et al.  The Human Cell Atlas: from vision to reality , 2017, Nature.

[146]  Yoram Reich,et al.  What is a reference? , 2017 .

[147]  M. Prunotto,et al.  Opportunities and challenges in phenotypic drug discovery: an industry perspective , 2017, Nature Reviews Drug Discovery.

[148]  Yuhei Umeda,et al.  Time Series Classification via Topological Data Analysis , 2017 .

[149]  Christos Kyprianou,et al.  Assembly of embryonic and extraembryonic stem cells to mimic embryogenesis in vitro , 2017, Science.

[150]  J. Wargo,et al.  Primary, Adaptive, and Acquired Resistance to Cancer Immunotherapy , 2017, Cell.

[151]  Pablo G. Cámara,et al.  Topological methods for genomics: present and future directions. , 2017, Current opinion in systems biology.

[152]  Sebastian Thrun,et al.  Dermatologist-level classification of skin cancer with deep neural networks , 2017, Nature.

[153]  Cristian Romero García,et al.  Quantum Machine Learning , 2017, Encyclopedia of Machine Learning and Data Mining.

[154]  D. M. Smith,et al.  Single-Cell Transcriptome Profiling of Human Pancreatic Islets in Health and Type 2 Diabetes , 2016, Cell metabolism.

[155]  Kole T. Roybal,et al.  Engineering T Cells with Customized Therapeutic Response Programs Using Synthetic Notch Receptors , 2016, Cell.

[156]  Hans Clevers,et al.  Modeling Development and Disease with Organoids , 2016, Cell.

[157]  C. Figdor,et al.  Cancer vaccine triggers antiviral-type defences , 2016, Nature.

[158]  Özlem Türeci,et al.  Systemic RNA delivery to dendritic cells exploits antiviral defence for cancer immunotherapy , 2016, Nature.

[159]  Charles H. Yoon,et al.  Dissecting the multicellular ecosystem of metastatic melanoma by single-cell RNA-seq , 2016, Science.

[160]  J. Carter,et al.  Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States , 2016, 1603.05681.

[161]  Kole T. Roybal,et al.  Precision Tumor Recognition by T Cells With Combinatorial Antigen-Sensing Circuits , 2016, Cell.

[162]  Seth Lloyd,et al.  Quantum algorithms for topological and geometric analysis of data , 2016, Nature Communications.

[163]  Laxmi Parida,et al.  Characterizing redescriptions using persistent homology to isolate genetic pathways contributing to pathogenesis , 2016, BMC Systems Biology.

[164]  O. Troyanskaya,et al.  Predicting effects of noncoding variants with deep learning–based sequence model , 2015, Nature Methods.

[165]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[166]  F. Petruccione,et al.  An introduction to quantum machine learning , 2014, Contemporary Physics.

[167]  Shawn M. Gillespie,et al.  Single-cell RNA-seq highlights intratumoral heterogeneity in primary glioblastoma , 2014, Science.

[168]  Marco Cuturi,et al.  Sinkhorn Distances: Lightspeed Computation of Optimal Transport , 2013, NIPS.

[169]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[170]  Wendell A. Lim,et al.  Cell-Based Therapeutics: The Next Pillar of Medicine , 2013, Science Translational Medicine.

[171]  K. Dill,et al.  The Protein-Folding Problem, 50 Years On , 2012, Science.

[172]  J. Scannell,et al.  Diagnosing the decline in pharmaceutical R&D efficiency , 2012, Nature Reviews Drug Discovery.

[173]  Jóhannes Reynisson,et al.  Serendipity in anticancer drug discovery. , 2012, World journal of clinical oncology.

[174]  G. Carlsson,et al.  Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival , 2011, Proceedings of the National Academy of Sciences.

[175]  Ned Stafford,et al.  Science in the digital age , 2010, Nature.

[176]  Wendell A. Lim,et al.  Designing customized cell signalling circuits , 2010, Nature Reviews Molecular Cell Biology.

[177]  Aram W. Harrow,et al.  Quantum algorithm for solving linear systems of equations , 2010 .

[178]  L. Guibas,et al.  Topological methods for exploring low-density states in biomolecular folding pathways. , 2008, The Journal of chemical physics.

[179]  C. Villani Optimal Transport: Old and New , 2008 .

[180]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[181]  Andrew M. Childs,et al.  Universal computation by quantum walk. , 2008, Physical review letters.

[182]  Naren Ramakrishnan,et al.  Redescription Mining: Structure Theory and Algorithms , 2005, AAAI.

[183]  F. Sams-Dodd Target-based drug discovery: is something wrong? , 2005, Drug discovery today.

[184]  M. Szegedy,et al.  Quantum Walk Based Search Algorithms , 2008, TAMC.

[185]  Leonidas J. Guibas,et al.  Persistence barcodes for shapes , 2004, SGP '04.

[186]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[187]  M. Sadelain,et al.  Antigen-dependent CD28 Signaling Selectively Enhances Survival and Proliferation in Genetically Modified Activated Human Primary T Lymphocytes , 1998, The Journal of experimental medicine.

[188]  B. Boghosian,et al.  Simulating quantum mechanics on a quantum computer , 1997, quant-ph/9701019.

[189]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[190]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[191]  S. Lloyd Quantum-Mechanical Computers , 1995 .

[192]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[193]  Jerome Percus,et al.  Correlation inequalities for Ising spin lattices , 1975 .

[194]  T. D. Lee,et al.  Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .

[195]  N. Gulbahce,et al.  Network medicine: a network-based approach to human disease , 2010, Nature Reviews Genetics.

[196]  Freeman J. Dyson,et al.  Mathematics as metaphor : selected essays of Yuri I. Manin , 2007 .

[197]  E. Villaseñor,et al.  CHAPTER 1 – AN INTRODUCTION TO QUANTUM MECHANICS , 1981 .