Simulation of Electronic Structure Hamiltonians Using Quantum Computers
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Free and Open Source Software for Computational Chemistry Education
Free and Open Source Software for Computational Chemistry Education Susi Lehtola∗,y and Antti J. Karttunenz yMolecular Sciences Software Institute, Blacksburg, Virginia 24061, United States zDepartment of Chemistry and Materials Science, Aalto University, Espoo, Finland E-mail: [email protected].fi Abstract Long in the making, computational chemistry for the masses [J. Chem. Educ. 1996, 73, 104] is finally here. We point out the existence of a variety of free and open source software (FOSS) packages for computational chemistry that offer a wide range of functionality all the way from approximate semiempirical calculations with tight- binding density functional theory to sophisticated ab initio wave function methods such as coupled-cluster theory, both for molecular and for solid-state systems. By their very definition, FOSS packages allow usage for whatever purpose by anyone, meaning they can also be used in industrial applications without limitation. Also, FOSS software has no limitations to redistribution in source or binary form, allowing their easy distribution and installation by third parties. Many FOSS scientific software packages are available as part of popular Linux distributions, and other package managers such as pip and conda. Combined with the remarkable increase in the power of personal devices—which rival that of the fastest supercomputers in the world of the 1990s—a decentralized model for teaching computational chemistry is now possible, enabling students to perform reasonable modeling on their own computing devices, in the bring your own device 1 (BYOD) scheme. In addition to the programs’ use for various applications, open access to the programs’ source code also enables comprehensive teaching strategies, as actual algorithms’ implementations can be used in teaching. -
Quantum Computing Overview
Quantum Computing at Microsoft Stephen Jordan • As of November 2018: 60 entries, 392 references • Major new primitives discovered only every few years. Simulation is a killer app for quantum computing with a solid theoretical foundation. Chemistry Materials Nuclear and Particle Physics Image: David Parker, U. Birmingham Image: CERN Many problems are out of reach even for exascale supercomputers but doable on quantum computers. Understanding biological Nitrogen fixation Intractable on classical supercomputers But a 200-qubit quantum computer will let us understand it Finding the ground state of Ferredoxin 퐹푒2푆2 Classical algorithm Quantum algorithm 2012 Quantum algorithm 2015 ! ~3000 ~1 INTRACTABLE YEARS DAY Research on quantum algorithms and software is essential! Quantum algorithm in high level language (Q#) Compiler Machine level instructions Microsoft Quantum Development Kit Quantum Visual Studio Local and cloud Extensive libraries, programming integration and quantum samples, and language debugging simulation documentation Developing quantum applications 1. Find quantum algorithm with quantum speedup 2. Confirm quantum speedup after implementing all oracles 3. Optimize code until runtime is short enough 4. Embed into specific hardware estimate runtime Simulating Quantum Field Theories: Classically Feynman diagrams Lattice methods Image: Encyclopedia of Physics Image: R. Babich et al. Break down at strong Good for binding energies. coupling or high precision Sign problem: real time dynamics, high fermion density. There’s room for exponential -
Simulating Quantum Field Theory with a Quantum Computer
Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. -
Quantum Clustering Algorithms
Quantum Clustering Algorithms Esma A¨ımeur [email protected] Gilles Brassard [email protected] S´ebastien Gambs [email protected] Universit´ede Montr´eal, D´epartement d’informatique et de recherche op´erationnelle C.P. 6128, Succursale Centre-Ville, Montr´eal (Qu´ebec), H3C 3J7 Canada Abstract Multidisciplinary by nature, Quantum Information By the term “quantization”, we refer to the Processing (QIP) is at the crossroads of computer process of using quantum mechanics in order science, mathematics, physics and engineering. It con- to improve a classical algorithm, usually by cerns the implications of quantum mechanics for infor- making it go faster. In this paper, we initiate mation processing purposes (Nielsen & Chuang, 2000). the idea of quantizing clustering algorithms Quantum information is very different from its classi- by using variations on a celebrated quantum cal counterpart: it cannot be measured reliably and it algorithm due to Grover. After having intro- is disturbed by observation, but it can exist in a super- duced this novel approach to unsupervised position of classical states. Classical and quantum learning, we illustrate it with a quantized information can be used together to realize wonders version of three standard algorithms: divisive that are out of reach of classical information processing clustering, k-medians and an algorithm for alone, such as being able to factorize efficiently large the construction of a neighbourhood graph. numbers, with dramatic cryptographic consequences We obtain a significant speedup compared to (Shor, 1997), search in a unstructured database with a the classical approach. quadratic speedup compared to the best possible clas- sical algorithms (Grover, 1997) and allow two people to communicate in perfect secrecy under the nose of an 1. -
Quantum Machine Learning: Benefits and Practical Examples
Quantum Machine Learning: Benefits and Practical Examples Frank Phillipson1[0000-0003-4580-7521] 1 TNO, Anna van Buerenplein 1, 2595 DA Den Haag, The Netherlands [email protected] Abstract. A quantum computer that is useful in practice, is expected to be devel- oped in the next few years. An important application is expected to be machine learning, where benefits are expected on run time, capacity and learning effi- ciency. In this paper, these benefits are presented and for each benefit an example application is presented. A quantum hybrid Helmholtz machine use quantum sampling to improve run time, a quantum Hopfield neural network shows an im- proved capacity and a variational quantum circuit based neural network is ex- pected to deliver a higher learning efficiency. Keywords: Quantum Machine Learning, Quantum Computing, Near Future Quantum Applications. 1 Introduction Quantum computers make use of quantum-mechanical phenomena, such as superposi- tion and entanglement, to perform operations on data [1]. Where classical computers require the data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states. These computers would theoretically be able to solve certain problems much more quickly than any classical computer that use even the best cur- rently known algorithms. Examples are integer factorization using Shor's algorithm or the simulation of quantum many-body systems. This benefit is also called ‘quantum supremacy’ [2], which only recently has been claimed for the first time [3]. There are two different quantum computing paradigms. -
User Manual for the Uppsala Quantum Chemistry Package UQUANTCHEM V.35
User manual for the Uppsala Quantum Chemistry package UQUANTCHEM V.35 by Petros Souvatzis Uppsala 2016 Contents 1 Introduction 6 2 Compiling the code 7 3 What Can be done with UQUANTCHEM 9 3.1 Hartree Fock Calculations . 9 3.2 Configurational Interaction Calculations . 9 3.3 M¨ollerPlesset Calculations (MP2) . 9 3.4 Density Functional Theory Calculations (DFT)) . 9 3.5 Time Dependent Density Functional Theory Calculations (TDDFT)) . 10 3.6 Quantum Montecarlo Calculations . 10 3.7 Born Oppenheimer Molecular Dynamics . 10 4 Setting up a UQANTCHEM calculation 12 4.1 The input files . 12 4.1.1 The INPUTFILE-file . 12 4.1.2 The BASISFILE-file . 13 4.1.3 The BASISFILEAUX-file . 14 4.1.4 The DENSMATSTARTGUESS.dat-file . 14 4.1.5 The MOLDYNRESTART.dat-file . 14 4.1.6 The INITVELO.dat-file . 15 4.1.7 Running Uquantchem . 15 4.2 Input parameters . 15 4.2.1 CORRLEVEL ................................. 15 4.2.2 ADEF ..................................... 15 4.2.3 DOTDFT ................................... 16 4.2.4 NSCCORR ................................... 16 4.2.5 SCERR .................................... 16 4.2.6 MIXTDDFT .................................. 16 4.2.7 EPROFILE .................................. 16 4.2.8 DOABSSPECTRUM ............................... 17 4.2.9 NEPERIOD .................................. 17 4.2.10 EFIELDMAX ................................. 17 4.2.11 EDIR ..................................... 17 4.2.12 FIELDDIR .................................. 18 4.2.13 OMEGA .................................... 18 2 CONTENTS 3 4.2.14 NCHEBGAUSS ................................. 18 4.2.15 RIAPPROX .................................. 18 4.2.16 LIMPRECALC (Only openmp-version) . 19 4.2.17 DIAGDG ................................... 19 4.2.18 NLEBEDEV .................................. 19 4.2.19 MOLDYN ................................... 19 4.2.20 DAMPING ................................... 19 4.2.21 XLBOMD .................................. -
Python Tools in Computational Chemistry (And Biology)
Python Tools in Computational Chemistry (and Biology) Andrew Dalke Dalke Scientific, AB Göteborg, Sweden EuroSciPy, 26-27 July, 2008 “Why does ‘import numpy’ take 0.4 seconds? Does it need to import 228 libraries?” - My first Numpy-discussion post (paraphrased) Your use case isn't so typical and so suffers on the import time end of the balance. - Response from Robert Kern (Others did complain. Import time down to 0.28s.) 52,000 structures PDB doubles every 2½ years HEADER PHOTORECEPTOR 23-MAY-90 1BRD 1BRD 2 COMPND BACTERIORHODOPSIN 1BRD 3 SOURCE (HALOBACTERIUM $HALOBIUM) 1BRD 4 EXPDTA ELECTRON DIFFRACTION 1BRD 5 AUTHOR R.HENDERSON,J.M.BALDWIN,T.A.CESKA,F.ZEMLIN,E.BECKMANN, 1BRD 6 AUTHOR 2 K.H.DOWNING 1BRD 7 REVDAT 3 15-JAN-93 1BRDB 1 SEQRES 1BRDB 1 REVDAT 2 15-JUL-91 1BRDA 1 REMARK 1BRDA 1 .. ATOM 54 N PRO 8 20.397 -15.569 -13.739 1.00 20.00 1BRD 136 ATOM 55 CA PRO 8 21.592 -15.444 -12.900 1.00 20.00 1BRD 137 ATOM 56 C PRO 8 21.359 -15.206 -11.424 1.00 20.00 1BRD 138 ATOM 57 O PRO 8 21.904 -15.930 -10.563 1.00 20.00 1BRD 139 ATOM 58 CB PRO 8 22.367 -14.319 -13.591 1.00 20.00 1BRD 140 ATOM 59 CG PRO 8 22.089 -14.564 -15.053 1.00 20.00 1BRD 141 ATOM 60 CD PRO 8 20.647 -15.054 -15.103 1.00 20.00 1BRD 142 ATOM 61 N GLU 9 20.562 -14.211 -11.095 1.00 20.00 1BRD 143 ATOM 62 CA GLU 9 20.192 -13.808 -9.737 1.00 20.00 1BRD 144 ATOM 63 C GLU 9 19.567 -14.935 -8.932 1.00 20.00 1BRD 145 ATOM 64 O GLU 9 19.815 -15.104 -7.724 1.00 20.00 1BRD 146 ATOM 65 CB GLU 9 19.248 -12.591 -9.820 1.00 99.00 1 1BRD 147 ATOM 66 CG GLU 9 19.902 -11.351 -10.387 1.00 99.00 1 1BRD 148 ATOM 67 CD GLU 9 19.243 -10.169 -10.980 1.00 99.00 1 1BRD 149 ATOM 68 OE1 GLU 9 18.323 -10.191 -11.782 1.00 99.00 1 1BRD 150 ATOM 69 OE2 GLU 9 19.760 -9.089 -10.597 1.00 99.00 1 1BRD 151 ATOM 70 N TRP 10 18.764 -15.737 -9.597 1.00 20.00 1BRD 152 ATOM 71 CA TRP 10 18.034 -16.884 -9.090 1.00 20.00 1BRD 153 ATOM 72 C TRP 10 18.843 -17.908 -8.318 1.00 20.00 1BRD 154 ATOM 73 O TRP 10 18.376 -18.310 -7.230 1.00 20.00 1BRD 155 . -
Clustering by Quantum Annealing on the Three–Level Quantum El- Ements Qutrits V
CLUSTERING BY QUANTUM ANNEALING ON THE THREE–LEVEL QUANTUM EL- EMENTS QUTRITS V. E. Zobov and I. S. Pichkovskiy1 Abstract Clustering is grouping of data by the proximity of some properties. We report on the possibility of increasing the efficiency of clustering of points in a plane using artificial quantum neural networks after the replacement of the two-level neurons called qubits represented by the spins S = 1/2 by the three-level neu- rons called qutrits represented by the spins S = 1. The problem has been solved by the slow adiabatic change of the Hamiltonian in time. The methods for controlling a qutrit system using projection operators have been developed and the numerical simulation has been performed. The Hamiltonians for two well-known cluster- ing methods, one-hot encoding and k-means ++, have been built. The first method has been used to partition a set of six points into three or two clusters and the second method, to partition a set of nine points into three clusters and seven points into four clusters. The simulation has shown that the clustering problem can be ef- fectively solved on qutrits represented by the spins S = 1. The advantages of clustering on qutrits over that on qubits have been demonstrated. In particular, the number of qutrits required to represent N data points is smaller than the number of qubits by a factor of log23NN / log . Since, for qutrits, it is easier to partition the data points into three clusters rather than two ones, the approximate hierarchical procedure of data partition- ing into a larger number of clusters is accelerated. -
An Introduction to Quantum Computing
An Introduction to Quantum Computing CERN Bo Ewald October 17, 2017 Bo Ewald November 5, 2018 TOPICS •Introduction to Quantum Computing • Introduction and Background • Quantum Annealing •Early Applications • Optimization • Machine Learning • Material Science • Cybersecurity • Fiction •Final Thoughts Copyright © D-Wave Systems Inc. 2 Richard Feynman – Proposed Quantum Computer in 1981 1960 1970 1980 1990 2000 2010 2020 Copyright © D-Wave Systems Inc. 3 April 1983 – Richard Feynman’s Talk at Los Alamos Title: Los Alamos Experience Author: Phyllis K Fisher Page 247 Copyright © D-Wave Systems Inc. 4 The “Marriage” Between Technology and Architecture • To design and build any computer, one must select a compatible technology and a system architecture • Technology – the physical devices (IC’s, PCB’s, interconnects, etc) used to implement the hardware • Architecture – the organization and rules that govern how the computer will operate • Digital – CISC (Intel x86), RISC (MIPS, SPARC), Vector (Cray), SIMD (CM-1), Volta (NVIDIA) • Quantum – Gate or Circuit (IBM, Rigetti) Annealing (D-Wave, ARPA QEO) Copyright © D-Wave Systems Inc. 5 Quantum Technology – “qubit” Building Blocks Copyright © D-Wave Systems Inc. 6 Simulation on IBM Quantum Experience (IBM QX) Preparation Rotation by Readout of singlet state 휃1 and 휃2 measurement IBM QX, Yorktown Heights, USA X X-gate: U1 phase-gate: Xȁ0ۧ = ȁ1ۧ U1ȁ0ۧ = ȁ0ۧ, U1ȁ1ۧ = 푒푖휃ȁ1ۧ Xȁ1ۧ = ȁ0ۧ ۧ CNOT gate: C ȁ0 0 ۧ = ȁ0 0 Hadamard gate: 01 1 0 1 0 H C01ȁ0110ۧ = ȁ1110ۧ Hȁ0ۧ = ȁ0ۧ + ȁ1ۧ / 2 C01ȁ1100ۧ = ȁ1100ۧ + Hȁ1ۧ = ȁ0ۧ − ȁ1ۧ / 2 C01ȁ1110ۧ = ȁ0110ۧ 7 Simulated Annealing on Digital Computers 1950 1960 1970 1980 1990 2000 2010 Copyright © D-Wave Systems Inc. -
Using Machine Learning for Quantum Annealing Accuracy Prediction
algorithms Article Using Machine Learning for Quantum Annealing Accuracy Prediction Aaron Barbosa 1, Elijah Pelofske 1, Georg Hahn 2,* and Hristo N. Djidjev 1,3 1 CCS-3 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA; [email protected] (A.B.); [email protected] (E.P.); [email protected] (H.N.D.) 2 T.H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA 3 Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria * Correspondence: [email protected] Abstract: Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem Citation: Barbosa, A.; Pelofske, E.; will be solvable to optimality with the D-Wave 2000Q. -
Computational Chemistry
G UEST E DITORS’ I NTRODUCTION COMPUTATIONAL CHEMISTRY omputational chemistry has come of chemical, physical, and biological phenomena. age. With significant strides in com- The Nobel Prize award to John Pople and Wal- puter hardware and software over ter Kohn in 1998 highlighted the importance of the last few decades, computational these advances in computational chemistry. Cchemistry has achieved full partnership with the- With massively parallel computers capable of ory and experiment as a tool for understanding peak performance of several teraflops already on and predicting the behavior of a broad range of the scene and with the development of parallel software for efficient exploitation of these high- end computers, we can anticipate that computa- tional chemistry will continue to change the scientific landscape throughout the coming cen- tury. The impact of these advances will be broad and encompassing, because chemistry is so cen- tral to the myriad of advances we anticipate in areas such as materials design, biological sci- ences, and chemical manufacturing. Application areas Materials design is very broad in scope. It ad- dresses a diverse range of compositions of matter that can better serve structural and functional needs in all walks of life. Catalytic design is one such example that clearly illustrates the promise and challenges of computational chemistry. Al- most all chemical reactions of industrial or bio- chemical significance are catalytic. Yet, catalysis is still more of an art (at best) or an empirical fact than a design science. But this is sure to change. A recent American Chemical Society Sympo- sium volume on transition state modeling in catalysis illustrates its progress.1 This sympo- sium highlighted a significant development in the level of modeling that researchers are em- 1521-9615/00/$10.00 © 2000 IEEE ploying as they focus more and more on the DONALD G. -
Quantum Algorithms
An Introduction to Quantum Algorithms Emma Strubell COS498 { Chawathe Spring 2011 An Introduction to Quantum Algorithms Contents Contents 1 What are quantum algorithms? 3 1.1 Background . .3 1.2 Caveats . .4 2 Mathematical representation 5 2.1 Fundamental differences . .5 2.2 Hilbert spaces and Dirac notation . .6 2.3 The qubit . .9 2.4 Quantum registers . 11 2.5 Quantum logic gates . 12 2.6 Computational complexity . 19 3 Grover's Algorithm 20 3.1 Quantum search . 20 3.2 Grover's algorithm: How it works . 22 3.3 Grover's algorithm: Worked example . 24 4 Simon's Algorithm 28 4.1 Black-box period finding . 28 4.2 Simon's algorithm: How it works . 29 4.3 Simon's Algorithm: Worked example . 32 5 Conclusion 33 References 34 Page 2 of 35 An Introduction to Quantum Algorithms 1. What are quantum algorithms? 1 What are quantum algorithms? 1.1 Background The idea of a quantum computer was first proposed in 1981 by Nobel laureate Richard Feynman, who pointed out that accurately and efficiently simulating quantum mechanical systems would be impossible on a classical computer, but that a new kind of machine, a computer itself \built of quantum mechanical elements which obey quantum mechanical laws" [1], might one day perform efficient simulations of quantum systems. Classical computers are inherently unable to simulate such a system using sub-exponential time and space complexity due to the exponential growth of the amount of data required to completely represent a quantum system. Quantum computers, on the other hand, exploit the unique, non-classical properties of the quantum systems from which they are built, allowing them to process exponentially large quantities of information in only polynomial time.