EP1836628A1 - Architecture d'ordinateur classique-quantique hybride pour le modelage moleculaire - Google Patents

Architecture d'ordinateur classique-quantique hybride pour le modelage moleculaire

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Publication number
EP1836628A1
EP1836628A1 EP05754940A EP05754940A EP1836628A1 EP 1836628 A1 EP1836628 A1 EP 1836628A1 EP 05754940 A EP05754940 A EP 05754940A EP 05754940 A EP05754940 A EP 05754940A EP 1836628 A1 EP1836628 A1 EP 1836628A1
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EP
European Patent Office
Prior art keywords
molecular system
qubits
quantum
computer
ground state
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Ceased
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EP05754940A
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German (de)
English (en)
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EP1836628A4 (fr
Inventor
Jeremy Hilton
Geordie Rose
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D Wave Systems Inc
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D Wave Systems Inc
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Publication of EP1836628A1 publication Critical patent/EP1836628A1/fr
Publication of EP1836628A4 publication Critical patent/EP1836628A4/fr
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
    • G16C20/90—Programming languages; Computing architectures; Database systems; Data warehousing

Definitions

  • the present invention relates to quantum computing. More specifically, the present invention relates to the application of a quantum computer to molecular modeling, and a hybrid classical-quantum architecture to accomplish this task.
  • Problems of interest in this field include calculating the ground-state coordinates of atoms in a molecule, calculating the ground-state energy of a molecule given a particular set of atomic coordinates, and predicting which chemical compounds are likely to bind with a high degree of affinity to a target receptor (e.g., a protein)
  • a target receptor e.g., a protein
  • QM quantum mechanics
  • a classical computer is a computer that represents information by numerical binary digits known as "bits," where each bit has a value of "0" or "1.”
  • bits binary digits
  • the digital computer time and memory resources required to simulate a physical system on a quantum mechanical basis scales exponentially with the number of electrons in a molecule.
  • classical computers do not have the necessary physical resources to solve.
  • the general problem of finding the naturally occurring three-dimensional structure of a molecule given its chemical composition includes the problem of finding the natural ground state of the structure. For example, identifying the naturally occurring three-dimensional structure of a protein given its sequence of amino acids is known as the protein folding problem and is one of the fundamental problems in biophysical science.
  • United States Patent 6,226,603 to Freire et al entitled “Method for the Prediction of Binding Targets and the Design of Ligands,” hereby incorporated by reference in its entirety, describes an algorithm for identifying the location or identity of natural binding sites on a protein, termed active sites, using a high resolution structure of the protein. The algorithm further determines the identity of ligands that can potentially bind to those active sites.
  • the algorithm relies on conventional algorithms such as the predicted Gibbs free energy of binding of each atom in the protein structure in order to identify binding sites and predict protein-ligand binding energies. Such methods are limited in their accuracy and are resource-intensive. There are a number of additional programs and algorithms in the art.
  • Affinity is a docking-program that computes interactions between bulk (non-flexible) and moveable atoms using a molecular mechanical/grid (MM/Grid) approximation method developed by Luty et al, 1995, J. Computational Chemistry 16, 454-464, hereby incorporated by reference in its entirety, while interactions among moveable atoms are treated using a full force field representation.
  • AutoDock The Scripps Research Institute, La Jolla, San Diego
  • AutoDock is a suite of automated docking tools designed to predict how small molecules, such as substrates or drug candidates, bind to a receptor of known three-dimensional structure.
  • the program uses a free-energy scoring function that is based on a linear regression analysis, the AMBER force field, and a large set of diverse protein-ligand complexes with known inhibition constants. See, for example, Morris et al, 1998, J. Computational Chemistry 19, 1639-1662, which is hereby incorporated by reference in its entirety.
  • Still another program is DockVision (University of Alberta). DockVision computes binding energies using a pairwise calculation between atoms in the ligand and the protein with terms for van der Waals and electrostatics. A distance cutoff is employed and atoms in both the ligand and the protein are organized into charge groups. Intramolecular energies for the ligand are optional.
  • MMFF94 Two force fields are used by DockVision, namely "Research” and "MMFF94.”
  • the MMFF94 force field is described in Halgren, 1996, J. Computational Chemistry 17, 490-519, hereby incorporated by reference.
  • the Research force field uses a Lennard- Jones 6-12 function together with a standard electrostatic function. All charge groups are neutralized to reduce long range ionic interactions. Intramolecular energies include torsion and van der Waals terms and no electrostatic terms are included. A dielectric constant of 1.0 is used. Charges and atom types for the ligand and protein are automatically assigned within the program.
  • Still another program for receptor-ligand docking is FRED (OpenEye, Sante Fe, New Mexico), which provides docking features using Gaussian potentials.
  • FlexiDock Tripos, Saint Lois, Missouri
  • FlexX BioSolvelT GmbH, Germany
  • FlexX BioSolvelT GmbH, Germany
  • GLIDE uses a scoring function to rank the receptor binding potential of individual members of a ligand library.
  • Still other programs include, but are not limited to, GOLD (Cambridge Crytallographic Data Centre, Cambridge, England), HINT! (Virginia Commonwealth University), LigPlot (University College of London), Situs (Scripps Research Institute, La Jolla, California), and Vega (Milan University), DOCK (University of California, San Francisco, Molecular Design Institute), GRAMM (SUNY, New York), and ICM-Dock (MolSoft LLC, La Jolla, California).
  • AMBER 4.1 An exemplary force field is AMBER 4.1, described in Georgia et al, 1995, J. Am. Chem. Soc. 117, 5179, hereby incorporated by reference in its entirety. AMBER was originally parameterized against a limited number of organic systems. AMBER is used to provide approximations of gas-phase model geometries, solvation free energies, vibrational frequencies, and conformational energies. Still another force field used in the art is CHARMM22, described in Mackerall and Karplus, 1995, J. Am. Chem. Soc.
  • MMFF94 Another force field used in the art is MMFF94, which is described in Halgren, 1996, J. Computational Chemistry 17, 490-586, hereby incorporated by reference in its entirety. MMFF94 was developed through ab initio approximation techniques using quantum-mechanical principles and verified by experimental data sets.
  • a qubit is a well-defined physical structure that (i) has a plurality of quantum states, (ii) can be isolated from its environment and (iii) permits quantum tunneling between two or more quantum states associated with the qubit.
  • quantum bits There are many types of implementations of qubits of which superconducting qubits are just one. Implementations of qubits include ion traps, cavity quantum electrodynamics (QED), nuclear magnetic resonance (NMR), quantum dots, silicon-based, electrons-on- helium, and optical.
  • the five requirements for the implementation of quantum computation are: i) a scalable physical system with well characterized qubits; ii) the ability to initialize the state of the qubits to a simple fiducial state, such as
  • Control of a qubit includes performing single qubit operations as well as operations on two or more qubits.
  • this set of operations is typically a universal set.
  • a universal set of quantum operations is any set of quantum operations that permits all possible quantum computations.
  • Many sets of gates (operations) are universal.
  • One example of a set of gates that is universal is the complete set of single qubit gates plus a CNOT gate.
  • Quantum computing hardware proposals Several quantum computing hardware proposals have been made. Of these hardware proposals, one of the most scalable types of physical systems appear to be those that are superconducting structures. Superconducting material is a material that has no electrical resistance below critical levels of current, magnetic field and temperature. Josephson junction based qubits are examples of devices made using superconducting materials.
  • the Josephson energy Ej is significantly larger, e.g., in some embodiments 10 times, between 10 to 100 times, or greater than 100 times larger, than the charging energy Ec- In charge qubits, the charging energy Ec is significantly larger than the Josephson energy Ej.
  • Superconducting qubits include devices that are well known in the art, such as Josephson junctions.
  • a qubit The feature that distinguishes a qubit from a bit is that, according to the laws of quantum mechanics, the permitted states of a single qubit occupy a two-dimensional complex vector space.
  • the general state of a qubit is written ⁇
  • a classical computer CC
  • QC quantum computer
  • a QC is a computer that stores or manipulates information in a quantum mechanical fashion. This allows a QC to simulate a physical system with quantum properties more efficiently than a CC can.
  • the QC is more efficient than the CC because the QC is a type of analog computer.
  • the storage and evolution of data under a QC can occur by quantum mechanical rules, with QM effects such as superposition, states having phases, entanglement, tunneling, etc.
  • 00) + b ⁇ 0l) + c ⁇ 10) + d ⁇ 11) is a four-dimensional state vector, one dimension for each distinguishable state of the two qubits.
  • the general state of n qubits is therefore specified by a 2"-dimensional complex state vector. For more information on qubits, see Braunstein and Lo.
  • One embodiment provides a method adapted for use on a hybrid computer.
  • the method is for simulating a molecular system.
  • the hybrid computer comprises classical and quantum components.
  • the method provides input to a classical computer.
  • the input comprises atomic coordinates R n , atomic charges Z n , and one or more parameters for the molecular system.
  • the input is sent to the quantum computer where a ground state energy of the molecular system is determined based on the input nuclear coordinates. This ground state energy is represented by an R-bit binary number.
  • the ground state energy is returned to the classical computer and the nuclear coordinates are geometrically optimized on the classical computer based on information about the ground state energy of corresponding nuclear coordinates to produce new nuclear coordinates R n .
  • One aspect of the invention provides a method of simulating a molecular system for use on a hybrid system, where the hybrid system comprises a classical computer and a quantum computer.
  • the hybrid system comprises a classical computer and a quantum computer.
  • an input from the classical computer is sent to the quantum computer.
  • This input comprises a set of atomic coordinates R n of the molecular system and a set of atomic charges Zgan for the set of atomic coordinates.
  • the quantum computer is used to determine a ground state energy of the molecular system based on the input set of atomic coordinates.
  • This ground state energy of the molecular system is returned to the classical computer, which uses this information to optimize the set of atomic coordinates thereby producing a new set of atomic coordinates R n for the molecular system. These steps are repeated. In each repetition, the new set of atomic coordinates R n from the last iteration of the method become the set of atomic coordinates
  • the ground state energy of the molecular system returned to the classical computer in step (C) is represented by a binary number.
  • the input to the quantum computer further comprises a number specifying a number of electrons N in the molecular system.
  • the input further comprises a set of one or more parameters of the molecular system (e.g., a set of ground state atomic coordinates of the molecular system and a ground state energy of the molecular system as determined by the quantum computer).
  • the quantum computer comprises a superconducting quantum processor.
  • the method further comprises sending the ground state atomic coordinates from the classical computer to the quantum computer, along with the parameter Uof the molecular system for which a quantum calculation is sought; and then causing the quantum computer to solve for ⁇ 7 and return the output to the classical computer. In some embodiments, these steps are repeated once for each parameter C/in a plurality of parameters U.
  • the predetermined termination condition is any combination of: (i) a time when the ground state energy of the molecular system falls below a specified value; (ii) a predetermined number of repetitions of the method; (iii) a time when the ground state atomic coordinates of the molecular system has been reached; (iv) the atomic coordinates of the molecular system for the ground state has been reached within a predetermined accuracy; and (v) the achievement of a predetermined condition of a general optimization algorithm run on the classical computer.
  • the input to the quantum computer further comprises a request for the calculation of an unknown value and the output from the quantum computer further comprises a particular value of the unknown value.
  • the output further comprises an updated value for an additional output parameter for the molecular system.
  • molecular system comprises a first molecule and a second molecule and the second molecule is noncovalently bound to the first molecule.
  • the atomic coordinates for the first molecule in the set of atomic coordinates R n of the molecular system have been experimentally determined (e.g., by X-ray crystallography, nuclear magnetic resonance, or mass spectrometry).
  • the first molecule is a protein having a molecular weight of 1000 Daltons or greater.
  • the second molecule binds to the first molecule thereby inhibiting an enzymatic activity associated with the first molecule.
  • Another aspect of the present invention provides a method of determining the ground state energy of a molecular system.
  • an initial electron distribution is determined for a plurality of electrons in the molecular system based on a set of atomic coordinates for the molecular system.
  • a nucleus charge of a first nucleus in the set of atomic coordinates is set to a large magnitude such that all of the electrons in the plurality of electrons are localized around the first nucleus.
  • the method continues by assigning each respective electron in the plurality of electrons to a corresponding grid register in a plurality of grid registers. Each respective electron in the plurality of electrons is initialized in its corresponding grid register according to the initial electron distribution.
  • the method continues with the adiabatic reduction in the nuclear charge on the first nucleus in a series of steps until the first nucleus has reached its natural charge value.
  • the reduction is simulated by a sequence of operators applied to qubits in each of the grid registers in the plurality of grid registers.
  • the ground state energy of the molecular system is then computed using the Eigenvalue finding algorithm. Finally, the ground state energy of the molecular system is transferred to a readout register using a measurement algorithm.
  • the initializing comprises representing a state of an electron in the plurality of electrons is by a superposition of grid register states for the grid register corresponding to the electron.
  • the plurality of grid registers can be of equal size.
  • the initializing step includes initializing the readout register in a ground state.
  • the transferring step further comprises providing the ground state electron distribution energy to the readout register.
  • the plurality of grid registers and the readout register are comprised of superconducting qubits.
  • the initializing step causes a grid register in the plurality of grid registers to encode an eigenstate of a corresponding electron in the plurality of electrons.
  • the eigenstate can be a position eigenstate.
  • the computer program product comprises a computer readable storage medium and a computer program mechanism embedded therein.
  • the computer program mechanism is for simulating a molecular system and comprises instructions for sending an input from the classical computer system to a quantum computer. This input comprises a set of atomic coordinates R n of the molecular system and a set of atomic charges Z Center for the set of atomic coordinates.
  • the computer program mechanism further comprises instructions for determining, using the quantum computer, a ground state energy of the molecular system based on the input set of atomic coordinates as well as instructions for receiving the ground state energy of the molecular system from the quantum computer.
  • the computer program mechanism further comprises instructions for optimizing the set of atomic coordinates based on information about the ground state energy of the molecular system provided by the instructions for receiving, thereby producing a new set of atomic coordinates R n for the molecular system.
  • the computer program mechanism further comprises instructions for repeating the foregoing instructions, where the new set of atomic coordinates R n from the last instance of the instructions for optimizing becomes the set of atomic coordinates R n used in the repeated instructions for sending, until a predetermined termination condition is reached.
  • the ground state energy of the molecular system returned to the classical computer system by the instructions for receiving are represented by a binary number.
  • the input further comprises a number specifying a number of electrons N in the molecular system.
  • the computer program mechanism further comprises instructions for sending the ground state atomic coordinates from the classical computer system to the quantum computer, along with a parameter U of the molecular system for which a quantum calculation is sought as well as instructions for causing the quantum computer to solve for U and return the output to the classical computer system.
  • Such instructions can be repeated once for each parameter ⁇ 7 in a plurality of parameters U.
  • the predetermined termination condition is any combination of (i) a time when the ground state energy of the molecular system falls below a specified value; (ii) a predetermined number of repetitions of the method; (iii) a time when the ground state atomic coordinates of the molecular system has been reached; (iv) the atomic coordinates of the molecular system for the ground state has been reached within a predetermined accuracy; and (v) the achievement of a predetermined condition of a general optimization algorithm run on the classical computer.
  • Still another aspect of the present invention provides a computer program product for use in conjunction with a classical computer system.
  • the computer program product comprises a computer readable storage medium and a computer program mechanism embedded therein.
  • the computer program mechanism is for determining the ground state energy of a molecular system and comprises instructions for determining an initial electron distribution of a plurality of electrons in the molecular system based on a set of atomic coordinates for the molecular system, where a nucleus charge of a first nucleus in the set of atomic coordinates is set to a large magnitude such that all of the electrons in the plurality of electrons are localized around the first nucleus.
  • the computer program mechanism further includes instructions for assigning each respective electron in the plurality of electrons to a corresponding grid register in a plurality of grid registers.
  • the computer program mechanism further includes instructions for initializing each respective electron in the plurality of electrons in its corresponding grid register according to the initial electron distribution.
  • the computer program mechanism further includes instructions for adiabatically reducing the nuclear charge on the first nucleus in a series of steps until the first nucleus has reached its natural charge value. This reduction is simulated by a sequence of operators applied to qubits in each of the grid registers in the plurality of grid registers.
  • the computer program mechanism further includes instructions for computing the ground state energy of the molecular system using the Eigenvalue finding algorithm and instructions for transferring the ground state energy of the molecular system to a readout register using a measurement algorithm.
  • Still another embodiment of the present invention provides a method of calculating the energy of a molecular system comprising initializing a plurality of qubits, where the plurality of qubits comprises a set of readout qubits and a set of evolution qubits. Each qubit in the plurality of qubits has a state, the set of readout qubits is initialized in a vacuum state, and the set of evolution qubits is initialized in a predetermined state.
  • each qubit in the set of readout qubits is rotated by an angle of about ⁇ /2 radians around the x-axis and the plurality of qubits is evolved with a unitary operator.
  • a quantum Fourier transform is performed on the set of readout qubits; and the set of readout qubits is measured.
  • the predetermined state of the set of evolution qubits is computed by a step for determining the predetermined state.
  • the rotating step comprises applying a plurality of ⁇ x pulses, each of area ⁇ /2, to each of the qubits in the set of readout qubits.
  • the plurality of pulse are applies in parallel or series.
  • the initializing step occurs before the rotating.
  • the rotating step transforms the state of a qubit in the plurality of qubits from a first state:
  • the evolving step comprises repeatedly applying a second unitary operator U to the set of evolution qubits.
  • the unitary operator is time independent.
  • the quantum Fourier transform causes interference between states of the qubit in the set of readout qubits.
  • the readout step includes measuring the state of the set of readout qubits.
  • the readout step comprises computing an eigenvalue encoded in the state of the readout register, and the eigenvalue corresponds to an eigenvector stored in the set of evolution qubits after the measuring step.
  • the state of the set of evolution qubits is an eigenvector corresponding to an eigenvalue just measured in the state of the set of readout qubits.
  • the eigenvalue is a ground state of the molecular system being emulated.
  • the predetermined state is an approximate ground state of a molecular system being emulated.
  • Still another aspect of the invention provides a method of calculating an energy of a molecular system. In the method, a plurality of qubits is initialized.
  • the plurality of qubits comprises a set of readout qubits in a first predetermined state and a set of evolution qubits in a second predetermined state.
  • the second predetermined state is computed by adiabatically varying the magnitude of a set of nuclear charges in the molecular system and the second predetermined state is a quantum state of the molecular system.
  • the method continues by computing the energy of the second predetermined state by performing an eigenvalue finding algorithm on the plurality of qubits.
  • the eigenvalue finding algorithm comprises (i) applying a plurality of ⁇ x pulses each of area about ⁇ /2 to each of the qubits in the set of readout qubits, (ii) evolving the plurality of qubits with repeated application of a time independent operator, (iii) performing a quantum Fourier transform on the set of readout qubits; and (iv) measuring the state of the set of readout qubits.
  • the first predetermined state is a vacuum state.
  • FIG. 1 illustrates a black box apparatus in accordance with an embodiment of the present invention.
  • FIG. 2 illustrates more details of a black box apparatus in accordance with an embodiment of the present invention.
  • FIG. 3 illustrates a hybrid algorithm for molecular modeling in accordance with an embodiment of the present invention.
  • FIG. 4 illustrates a hybrid algorithm for molecular modeling in accordance with another embodiment of the present invention.
  • FIG. 5 illustrates a quantum algorithm for molecular modeling in accordance with still another embodiment of the present invention.
  • FIG. 6 illustrates a four by four by four grid in which the x -direction is horizontal to the page, the y -direction is vertical to the page, the z -direction is positioned perpendicularly to the x - and y -directions, and the state [111010 011111] is shown explicitly, in accordance with an embodiment of the present invention.
  • FIG. 7 illustrates a schematic diagram of a computer system for modeling molecular systems in accordance with an embodiment of the present invention.
  • Like reference numerals refer to corresponding parts throughout the several views of the drawings.
  • one embodiment of the present invention provides a specific- purpose machine 110 that overcomes the exponential scaling of QM by employing a programmable QM system, called a quantum computer, to solve the QM equations for a set of desired parameters (e.g., a molecular system).
  • a programmable QM system called a quantum computer
  • This strategy reduces the physical resources required to solve the full QM equations from an exponential function of the number of electrons to a polynomial function of the number of electrons.
  • the inputs to machine 110 are aspects of a molecular system or systems such as: (1) an initial "best guess" of the atomic coordinates and charges; (2) optionally, the number of electrons to be modeled; and (3) physical parameters of the system requested as output (e.g., ground states and/or ground state energies, ground state or near-ground state atomic coordinates, estimates of the potential energy required to adopt such ground or near-ground states, binding energies between receptor/ligand pairs, or best guess estimates of any of the foregoing, etc.).
  • a molecular system or systems such as: (1) an initial "best guess" of the atomic coordinates and charges; (2) optionally, the number of electrons to be modeled; and (3) physical parameters of the system requested as output (e.g., ground states and/or ground state energies, ground state or near-ground state atomic coordinates, estimates of the potential energy required to adopt such ground or near-ground states, binding energies between receptor/ligand pairs, or best guess estimates of any of the foregoing, etc.).
  • Machine 100 acts to return all requested parameters, which can include, for example, the ground state nuclear positions, ground state or excited energies, charge density distributions, correlation functions, momentum distributions, and polarization.
  • FIG. 1 illustrates a black box schematic of machine 110 in an embodiment of the present invention.
  • Inputs 130 comprise an initial atomic configuration 130-1, represented as R n ! , for the molecular system to be used for the calculation; the number of electrons
  • input 130 can comprise the coordinates of more than one molecular entity.
  • input 130 can comprise the atomic coordinates of a receptor (e.g., a protein) and a ligand that potentially binds to the receptor. Proteins are described in Stryer, Biochemistry, W.H. Freeman and Company, New York, 1988, Chapter 2, which is hereby incorporated by reference in its entirety.
  • Machine or black box 110 calculates the ground state atomic configuration of the input molecular system 130 and returns the output 140. The details of this calculation are described below.
  • Output 140 comprises the calculated parameters as specified by a user (130-4).
  • output parameters 140 comprise the ground state atomic coordinates and/or the ground state energy of the molecular system under study.
  • any observable of the molecular system can be specified in parameters to output 130-4 and provided as result of the computation in output 140.
  • a molecular system is any molecular entity.
  • a molecular system is one or more organic compounds, where at least one of the organic compounds in the molecular system has a molecular weight of more than 100 Daltons, more than 200 Daltons, more than 300 Daltons, more than 400 Daltons, more than 1000 Daltons, between 1000 Daltons and 5000 Daltons, or between 2000 Daltons and 100,000 Daltons.
  • One Dalton equals 1 atomic mass unit (a.m.u.) or 1.66 x 10 "27 kilograms, atomic mass units and Daltons may be used interchangeably herein.
  • the two or more compounds are typically bound to each other by molecular interactions that are typically not covalent (e.g., electrostatic interactions).
  • Black box 110 comprises a hybrid computer architecture that combines a classical computer with one or more quantum processors.
  • FIG. 2 illustrates a schematic of the main components of black box 110 in one embodiment of the present invention.
  • Classical computer 111 functions as a manager of the computational resources of the quantum processors.
  • Classical computer 111 accepts inputs 130 from a user or other entity and returns output 140.
  • classical computer 111 is a supercomputer capable of processing large amounts of data.
  • Exemplary supercomputers include, but are not limited to, the Cray SX- 6, XI, and XDl (Cray Inc., Seattle Washington) and the Hitachi SRI 1000 (Tokyo, Japan).
  • Classical computer 111 interfaces with the quantum computer 112 via quantum computer input 131 and quantum computer output 141. In accordance with the present invention, interfaces 131 and 141 permit certain aspects of the calculation to be performed on quantum computer 112.
  • the interfaces 131 and 141 operate as digital to analog converters, and analog to digital converters. However, these interfaces 131 and 141 are designed to minimize their effect on the quantum computer. Because quantum computers need to be isolated from their environment embodiments interfaces 131 and 141 have appropriate shielding and filtering to isolate the quantum computer 112 from noise and other effects. In one embodiment of the present invention, interfaces 131 and 141 operate as serial or as parallel communication channels. In embodiments of the present invention where quantum computer 112 operates at low temperature, interfaces 131 and 141 can be embodied in a series of devices existing at low temperature and the temperature of the classical computer 111, and temperatures between.
  • interfaces 131 and 141 are means for transferring information from classical computer 111 to quantum computer 112 or the reverse.
  • Interfaces 131 and 141 can be composed of semiconductor circuits, superconductor circuits, optical devices and channels, digital circuits, and analog circuits.
  • the embodiments of interfaces 131 and 141 vary with the embodiments of classical computer 111 and quantum computer 112. Examples of control systems include, but are not limited to, United States Patent Number 6,803,599, entitled “Quantum processing system for a superconducting phase qubit," issued October 12, 2004, United States Patent Number 6,897,468, entitled “Resonant controlled qubit system,” issued May 24, 2005; WIPO Patent Publication Number
  • FIG. 7 illustrates more details of a system for molecular modeling in accordance with one embodiment of the present invention.
  • the system depicted in FIG. 7 can be used to perform any of the algorithms and methods disclosed herein.
  • Classical computer 111 functions as a manager of the computational resources of the quantum processors.
  • Classical computer 111 accepts inputs from a user or other entity and returns output.
  • Classical computer 111 is preferably a computer system having: • a central processing unit 22; • a main non-volatile storage unit 14, for example, a hard disk drive, for storing software and data, the storage unit 14 controlled by controller 12; • a system memory 36, preferably high speed random-access memory (RAM), for storing system control programs, data, and application programs, comprising programs and data loaded from non-volatile storage unit 14; system memory 36 may also include read-only memory (ROM); • a user interface 32, comprising one or more input devices (e.g., keyboard 28) and a display 26 or other output device; • communication circuitry 20 described herein for interfacing with quantum computer 112; • an internal bus 30 for interconnecting the aforementioned elements of the system; and • a power source 24 to power the aforementioned elements.
  • ROM read-only memory
  • Operation of computer 111 is controlled primarily by operating system 40, which is executed by central processing unit 22.
  • Operating system 40 can be stored in system memory 36.
  • system memory 36 includes: • file system 42 for controlling access to the various files and data structures used by the present invention; • atomic coordinates 44 of a molecular system to be modeled; • atomic charges 46 of the atoms in the atomic coordinates; • a conventional refinement algorithm 48 for refining the atomic coordinates of the molecular system; and • a refinement coordination program 50 for interfacing with quantum computer 112.
  • An embodiment of the present invention provides a computer program product for use in conjunction with a classical computer system 111.
  • the computer program product comprises a computer readable storage medium (e.g., memory 36, a DVD, a computer media tape, or other device) and a computer program mechanism embedded therein (e.g., refinement coordination program 50).
  • the computer program mechanism is refinement coordination program 50.
  • refinement coordination program 50 comprises instructions for sending an input from classical computer system 111 to a quantum computer 112.
  • the input comprises a set of atomic coordinates R n 44 of the molecular system and a set of atomic charges Zgan 46 for the set of atomic coordinates 44.
  • the refinement coordination program 50 further comprises instructions for determining, using the quantum computer 112, a ground state energy of the molecular system based on the input set of atomic coordinates 44.
  • the refinement coordination program 50 further comprises instructions for receiving the ground state energy of the molecular system from the quantum computer.
  • the refinement coordination program 50 further comprises instructions for optimizing the set of atomic coordinates based on information about the ground state energy of the molecular system provided by the instructions for receiving, thereby producing a new set of atomic coordinates R n , optionally stored as atomic coordinates 44, for the molecular system.
  • the refinement coordination program 50 further comprises instructions for repeating the foregoing instructions, where the new set of atomic coordinates R n from the last instance of the instructions for optimizing become the set of atomic coordinates R n used in the repeated instructions for sending, until a predetermined termination condition is reached.
  • Another embodiment of the present invention provides a computer program product for use in conjunction with a classical computer system 111.
  • the computer program product comprises a computer readable storage medium (e.g., memory 36, a DVD, a computer media tape, or other device) and a computer program mechanism embedded therein (e.g., refinement coordination program 50) for determining the ground state energy of a molecular system.
  • the computer program mechanism is a refinement coordination program 50.
  • refinement coordination program 50 comprises instructions for determining an initial electron distribution of a plurality of electrons in the molecular system based on a set of atomic coordinates for the molecular system where a nucleus charge of a first nucleus in the set of atomic coordinates is set to a large magnitude such that all of the electrons in the plurality of electrons are localized around the first nucleus.
  • refinement coordination program 50 further comprises instructions for assigning each respective electron in the plurality of electrons to a corresponding grid register in a plurality of grid registers.
  • Refinement coordination program 50 further comprises instructions for initializing each respective electron in the plurality of electrons in its corresponding grid register according to the initial electron distribution.
  • Refinement coordination program 50 further comprises instructions for adiabatically reducing the nuclear charge on the first nucleus in a series of steps until the first nucleus has reached its natural charge value, where the reduction is simulated by a sequence of operators applied to qubits in each of the grid registers in the plurality of grid registers.
  • Refinement coordination program 50 further comprises instructions for computing the ground state energy of the molecular system using the Eigenvalue finding algorithm.
  • Refinement coordination program 50 further comprises instructions for transferring the ground state energy of the molecular system to a readout register using a measurement algorithm.
  • machine 110 iterates through different molecular configurations to find a particular molecular configuration of the molecular system under study that minimizes the ground state energy of the molecular system.
  • machine 110 Once machine 110 has determined the coordinates of the molecular system leading to this lowest ground state energy, it returns the coordinates along with the corresponding output parameters 140. In some embodiments, rather than finding the minimum ground state energy of the molecular system machine 110 iterates through successive molecular configurations of the molecular system until a molecular configuration having less than a specified energy is identified. In one application of the present invention, the binding affinity between a small molecule and a macromolecular receptor binding site is calculated. In some embodiments, the hybrid computer architecture can model the optimal binding configurations between a small molecule and a macromolecular receptor and minimize their corresponding intermolecular binding energies.
  • the black-box technology fits into existing schemes for computational drug discovery and development while providing increases in computational speed and accuracy that cannot be achieved with classical computers.
  • the specific details of the classical computer 111 and quantum computing 112 aspects of the hybrid computer architecture are flexible as long as pertinent information is exchanged between the classical computer and the quantum computer.
  • the algorithm run on the quantum processor can vary depending on the power and capacity of the quantum processor being used.
  • the quantum processor is one or more superconducting quantum computing chips. However, different functional quantum processors can be used for performing these tasks.
  • a hybrid algorithm takes as input an approximation of the atomic coordinates of a molecular system and finds the ground state atomic coordinates, or 'natural' coordinates of the system and returns these new coordinates along with a quantity or set of observables for that state, such as the ground state energy.
  • the hybrid algorithm specifies the manner of function of the machine described in FIG. 1 and FIG. 2, and uses a novel architecture that combines classical and quantum computing resources.
  • the hybrid algorithm works by solving Schr ⁇ dinger's equation given a coordinate set. In conventional modeling applications, the interaction between objects in a molecular system is described either by a force field, a quantum chemical model, or a mix between the two.
  • a force field also called a forcefield
  • a forcefield is a loosely defined term and refers to the functional form and parameter sets used to describe the interactions (potential, forces) within a system of particles (atoms, ions, or similarly sized objects) as well as the interaction with electrons, or similarly charged leptons. It is independent of the system's configuration and is not a numerical field as in the above context.
  • a force field can be empirical, derived from higher-level modeling (e.g. quantum chemical studies), or even heuristic.
  • the present invention thus provides an advantageous feature in which a molecular system is refined on a digital computer using known geometric restraints of the molecular system and, at intervals specified by known global optimization algorithms, the ground state energy of the molecular system is updated in order to identify candidate structures that represent the naturally occurring state of the molecular system.
  • the software packages for molecular dynamic simulation of biological molecules cited in the preceding paragraphs are further described in the following references. For AMBER see Pearlman, et al, 1995, "AMBER, a computer program for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to elucidate the structures and energies of molecules," Computer Physics Communications 91, pp. 1-41.
  • AMBER is available from the Department of Pharmaceutical Chemistry, University of California, San Francisco, Box 2280, 600 16 th Street, San Francisco, California 94143-2280.
  • CHARMM is available from the CHARMM Development Project, Department of Chemistry and Chemical Biology, 12 Oxford Street, Harvard University, Cambridge, Massachusetts 02138.
  • GROMACS is available online at http://www.gromacs.org/.
  • GROMOS is available from BIOMOS b.v, Laboratory of Physical Chemistry, ETH H ⁇ nggerberg, HCI, CH-8093 Zurich, Switzerland.
  • a hybrid algorithm 300 for determining the ground state coordinates, or naturally occurring coordinates of a molecule comprises the steps detailed in FIG. 3: step 302: nuclear coordinates R n , nuclear charges Z n and, optionally, the number of electrons N in a molecular system of interest are sent from a classical computer (CC) to a quantum computer (QC); step 304: quantum computer 112 solves for the ground state energy
  • step 306 quantum computer sends the R-bit number E(R n ,Z n ,N) to the CC;
  • step 308 the classical computer uses a global optimization algorithm to update
  • step 310 new coordinates R ⁇ n ' are sent from the classical computer to the quantum computer; step 312: steps 302 through 310 are repeated until the energy E of the molecular system is either minimized or until the difference between the energy E(R n ,Z n ,N) and the energy of new coordinates E(R n ' , Z n , N) is less than a threshold value in order to obtain ground state coordinates R * ,f and the corresponding ground state energy step 340: calculated parameters comprising the final ground state coordinates ⁇ ?,f and the corresponding ground state energy E(R ⁇ ,Z n ,N) are returned to a user.
  • the hybrid algorithm 300 is described in further detail below.
  • Step 302. The hybrid algorithm starts by accepting as input an estimate of the nuclear coordinates (coordinates) R n for each atom in the molecular system, along with the nuclear charges Z n and, optionally, the number of electrons, N.
  • the subscript n is an integer that identifies an atom and goes from 1 to Z, where Z is the number of atoms in the molecular system.
  • this estimate for the initial nuclear coordinates is determined based on well known algorithms such as Hartree-Fock, for example.
  • the essence of the Hartree-Fock approximation is to replace the complicated many-electron problem by a one-electron problem in which electron-electron repulsion is treated in an average way.
  • Algorithms for estimating the nuclear coordinates of a molecular system can be performed efficiently but have limited accuracy.
  • the role of the hybrid algorithm is to increase this accuracy in order to accurately simulate the molecular systems.
  • the molecular system for which the naturally occurring three-dimensional coordinates are sought includes more than 10 electrons, more than 20 electrons, more than 30 electrons, more then 40 electrons, more than 50 electrons, more than 100 electrons, more than 500 electrons, more than 1000 electrons, more than 10,000 electrons, or between 10 and 15,000 electrons.
  • the molecular system is a protein, polypeptide, D ⁇ A, R ⁇ A, a polymer, or an organic molecule having a molecular weight that is less than 1000 Daltons.
  • information comprising the estimate of the nuclear coordinates (coordinates) R n for each atom in the molecular system, along with the nuclear charges Z n and, optionally, the number of electrons, Nare transferred from the classical computer to the quantum computer using a communication channel.
  • the number of electrons N in a molecular system of interest is inferred from nuclear coordinates R n .
  • the molecular system comprises two or more molecules that are noncovalently bound to each other.
  • the molecular system comprises a single molecule.
  • the molecular system has a molecular mass of greater than 100 Daltons, greater than 200 Daltons, greater than 300 Daltons, or greater than 1000 Daltons.
  • the coordinates for at least a portion of the molecular system that is sent in step 302 are derived from high resolution X-ray crystal structure, mass spectrometry, or nuclear magnetic resonance.
  • the molecular system comprises a receptor having coordinates determined by X-ray crystallography as well as the coordinates of a ligand, not determined by X-ray crystallography, that have been docked onto the receptor using a conventional modeling program run on a digital computer.
  • the term receptor refers to any type of protein that has an active site (e.g., kinases, phosphodiesterases, metalloproteases, and the like).
  • Step 304 the corresponding energy E(R n ,Z n ,N) of the estimated coordinates passed from CC to QC is calculated by the quantum processor by performing a quantum algorithm (see e.g., Section 5.3, Quantum Algorithm).
  • a quantum algorithm see e.g., Section 5.3, Quantum Algorithm.
  • This aspect of the hybrid algorithm is advantageous because the quantum algorithm has substantially reduced ' complexity over any classical algorithm.
  • the use of the quantum processor permits the machine to obtain results that are otherwise not possible using classical resources (which includes both memory and time resources).
  • the term quantum algorithm refers to an algorithm that computes the energy of the molecular system using the full form of Schr ⁇ dinger's equation or, optionally, using the Born-Oppenheimer approximation.
  • a quantum algorithm is an algorithm that models quantum behavior of a quantum system without incurring an exponential cost in time or space resources. Step 306.
  • R n (coordinates of the molecular system of interest) is returned to the classical computer and becomes a comparison point for the next iteration of the calculation.
  • Step 308 The coordinates of the system are modified by the CC using a global optimization algorithm, a subset of a global optimization algorithm, or a refinement algorithm that can be implemented in a number of ways.
  • refinement algorithms refine the potential energy of the molecular system (from instances of step 306) subject to known geometric restraints associated with the molecular system. Typical geometric restraints include acceptable bond lengths and bond angles between each of the nuclei in the molecular system as well as acceptable torsion angles.
  • the global optimization algorithm produces a new set of coordinates and sends them to the quantum processor in step 310, which then calculates and returns the ground state energy for comparison.
  • step 308 is a refinement of the coordinates of the molecular system subject to known geometric restraints. In such embodiments, step 308 ends when the root mean square difference between the coordinate set of step 302 and the refined coordinate set of step 308 is less than some threshold value such as 0.01 Angstroms, 0.05 Angstroms, 0.1 Angstroms, 0.2 Angstroms, or greater than 0.3 Angstroms.
  • Step 310 the modified nuclear coordinates R n ' are passed back to the quantum computer and the algorithm iterates.
  • the global optimization algorithm takes further advantage of one or more quantum processors by stepping the system coordinates forward a number of iterations for each degree of freedom of the molecular system, where each respective step uses the quantum processor to determine the energy state of the molecular system at the respective step. For each degree of freedom each step yields a difference in energy, and after a number of steps the configuration has rendered enough information for the global optimization algorithm to process and optimize the appropriate path.
  • the algorithm can be parallelized across quantum processors to further increase efficiency. In this manner, the global optimization algorithm rapidly traces a path toward the lowest energy configuration of the molecular system.
  • Step 312. each subsequent iteration of the calculation will determine the energy for a different atomic configuration and each energy will be compared until a terminal point in the algorithm is realized.
  • a terminal point in the algorithm is realized when the ground state configuration of the molecular system has been achieved with a high probability.
  • the algorithm iterates until the ground state energy is minimized, subject to any other termination criteria of the global optimization algorithm. See, e.g., Press et al, 1992, Numerical Recipes in C: the Art of Scientific Computing, 2 n Ed., Cambridge University Press, ISBN 0521431085, which is incorporated herein by reference in its entirety.
  • a terminal point in the algorithm is realized when the threshold energy level of the molecular system falls below a specified value. In still other embodiments, a terminal point in the algorithm is realized when steps 302 through 310 have been repeated a predetermined number of times (e.g., once, twice, three times, four times, between five and 1000 times, between 1000 and 10,000 times, or more than 10,000 times). In some embodiments, steps 302 through 310 are not repeated. In some embodiments, a number of quantum co-processors can be used in parallel to accelerate the iteration process. In typical embodiments, steps 302 through 310 are repeated in accordance with the global optimization algorithm.
  • Such embodiments can reject a structure from an instance of step 308 if the energy of the new structure obtained in step 308 is higher than the energy of the structure from the previous instance of step 308.
  • the manner in which steps 302 through 310 are repeated is in accordance with a global optimization algorithm refinement schedule.
  • Such refinement schedules can perturb the state of the molecular system in order to identify a global minimum.
  • steps 302 through 310 represent one step in a simulated annealing schedule in which the molecular system is set at a given temperature and the structure to be sent to the quantum computer at step 310 is accepted with some probability that is a function of (i) the energy of the coordinates at step 310 versus the energy of the coordinates prior to step 308, and (ii) the current temperature in the annealing schedule.
  • Each successive repetition or set of repetitions of steps 302 through 310 then represents the molecular structure at successively cooler temperatures until the system reaches a global minimum.
  • steps 302 through 312 can represent a genetic algorithm in which randomized changes in the coordinates of the molecular system are introduced at step 308 and such structures are accepted or rejected at step 312 with some probability in accordance with the genetic algorithm.
  • steps 302 through 312 can represent a least squares minimization, a Bayesian decision theory approach, a maximum- likelihood approach, a linear discriminate function, a neural network, algorithm- independent machine learning, or another refinement algorithm. See, for example, Duda, Pattern Classification, Second Edition, 2001, John Wiley & Sons, Inc., New York and Pearl, Probabilistic Reasoning In Intelligent Systems: Networks of Plausible Inference, Morgan Kauffmann Publishers, Inc., San Francisco, each of which is hereby incorporated by reference in its entirety.
  • Step 340 Once the natural ground-state configuration R is identified, other parameters of the molecular system are calculated by the quantum processor, and the output, which comprises the ground state coordinates along with system observables as specified in the input is transferred from the quantum computer to the classical computer. In some cases, the output coordinates and the corresponding energy of the system can be returned as soon as the answer has been calculated, and the algorithm will then continue to calculate the other desired observables U of the system.
  • U include the time evolution operator in of any local Hamiltonian. See, for example, Lloyd, 1996, Science 273, pp. 1073-1078, which is incorporated herein by reference in its entirety. Further examples of U include charge density distributions, correlation functions, momentum distributions, and the like.
  • step 407 send the coordinates ⁇ from the classical computer to the quantum computer, along with a request for the output parameter to calculate C/(R,f ,Z cuisine,N) ;
  • step 408 quantum computer solves for C/(i?,f ,Z contour,N) and returns it to CC; and
  • step 409 repeat steps 407 and 408 for as many desired output parameters as are requested.
  • the calculated parameters are then returned as output of the calculation in step 440.
  • each parameter to be calculated is returned as output in 440 once each iteration is complete.
  • the hybrid algorithm is illustrated by way of example for a hydrogen molecule
  • the quantum processor will calculate the ground state energy for the given coordinates. Variations of the above-described hybrid algorithm can be realized depending on the computational capability of the quantum processor and the nature of the problem to be solved. In some embodiments, if the target molecular system is too large for complete modeling with the quantum processor, then quantum effects of the system can be localized and the molecular system can be broken into components and modeled separately, a method known as domain decomposition. Such methods are well known and characterized in the field. See, e.g., Yang, 1991, Physical Review Letters. 66, p.
  • the classical computer transfers each of these components separately to the quantum processor (or processors) and then combines the resulting energies to form an estimate of the energy of that configuration.
  • the usefulness of such an approximation depends on the nature of the system.
  • the quantum mechanical aspects of the molecular system can be simplified, in order to make larger problems tractable for the quantum processor.
  • Such simplifications can include, for example, freezing out the core electrons and treating only the valence electrons of each atom. Whether such approximations are useful depends on the nature of the problem being solved.
  • Quantum algorithm An overview of the methods of the present invention have been presented. What follows is a more detailed description of a quantum computing algorithm for determining a ground state of a molecular system in accordance with an aspect of the present invention. This more detailed algorithm is one implementation of Fig. 3, in accordance with an aspect of the present invention. The invention is by no means limited to such an algorithm. Many other examples of suitable quantum computing algorithms and their application, including receptor / ligand docking, have been described in above.
  • a quantum algorithm is described herein that combines a method for efficiently determining the ground state of a molecular system with a measurement algorithm described by Abrams and Lloyd for extracting the value of an observable from that ground state. See, for example, Abrams and Lloyd, 1999, Physical Review Letters 83, pp. 5162-5165, which is hereby incorporated by reference in its entirety, for a description of the measurement algorithm.
  • the quantum processor component of the quantum computer comprises a quantum register with a specified number of available quantum bits, or qubits, to perform the operations.
  • the quantum register is divided into one or more grid registers and a readout register, where each register is interconnected via quantum information channels.
  • the grid registers define and encode a set of eigenstates. This set is used to define the molecular system's wavefunction as an expansion over these eigenstates.
  • a grid register encodes electronic position eigenstates. It is shown that this algorithm scales, at most, linearly in the number of electrons, and that the execution time is also linear in the number of electrons.
  • each electron in the system is assigned a separate grid register.
  • the number of qubits required can then be defined as NDQ + R , where N is the number of electrons in the system, D is the number of dimensions to be used for the computation, Q is the number of qubits used to define the grid size (giving a total of 2 s grid points per dimension), and R is the number of qubits in the readout register.
  • the readout register is used to store the output of the computation. In most cases the number of dimensions D will be three, and the grid resolution will depend on the type of molecular system to be modeled. Without taking into account qubit encoding and error correction, which is linear in the number of qubits, the NDQ + R number of qubits represents an upper limit for solving these problems.
  • Table 1 provides a list of exemplary molecules with approximate scaling features for the example of the quantum algorithm that uses separate grid registers for each electron in the system. Table 1 illustrates that the maximum number of qubits required scales linearly in the number of electrons in the system. Table 1 is viewed as a nonlimiting and exemplary values for the conditions and assumptions given herein.
  • Protein-ligand docking site 1,000 3 10 128 30,128 — Actual grid size is defined as 2 N for each dimension, where N is the number of qubits.
  • the quantum algorithm takes as inputs the nuclear configuration for the molecular system, and then calculates and returns the ground state energy for that configuration.
  • the quantum algorithm simulates an adiabatic transition in the molecule, in which all the electrons are initially highly localized around a nucleus by artificially setting the nuclear charge of the nucleus to a large magnitude (large enough to localize all of the electrons in the system around the one nucleus). Without loss of generality, this nucleus is chosen to be nucleus 1 at position ⁇ ?, with nuclear charge Z;, and the nuclear charge is then artificially set to value Z[ that is large enough to localize all of the electrons in the system around nucleus 1.
  • the electronic distribution for such a system of many electrons and one nucleus can easily be calculated using a conventional method such as Hartree-Fock on a conventional computer.
  • This pre-processing results in an electron distribution that is then initialized in the grid registers.
  • the quantum algorithm then models a process of slowly reducing the artificial nuclear charge for nucleus 1, and increasing the nuclear charge of the other nuclei, such that the electrons slowly become delocalized and are influenced more and more by other nuclei and electrons.
  • the nuclear charge on nucleus 1 is reduced until the nucleus has reached the natural value of Z x atomic units of charge.
  • the quantum algorithm simulates this process of varying the nuclear charge.
  • changes in the nuclear charge are discretized and each step is converted into a sequence of quantum gates.
  • the quantum processor then simulates the evolution of the actual molecular system and yields the required ground state energy.
  • Section 5.5 includes a detailed description of this algorithm for the hydrogen molecule (H 2 ).
  • FIG. 5 illustrates the quantum algorithm for an embodiment of the present invention.
  • Step 5 presents a case where one grid register is assigned to each electron, resulting in the necessity for N grid registers to carry out this aspect of the invention.
  • step 502 the system is pre-initialized to prepare N grid registers of equal size and a readout register all in the ground state
  • step 504 the pre-processed electron distribution is initialized for each electron in its respective grid register.
  • Each electron's state is represented by a superposition of grid register states. For example, if the grid states represent position eigenstates, and an electron is in a particular superposition of position eigenstates initially, then the grid register is prepared in that superposition of grid states corresponding to the desired superposition of position eigenstates.
  • Step 506 Artificial nuclear charge on nucleus one is adiabatically reduced in a series of discretized steps from a sufficiently large starting value, which are simulated by a sequence of operators applied to the qubits in each of the grid registers. Once the artificial nuclear charge reaches the atomic unit value of Z 7 , the electrons have assumed the ground state distribution. Step 508. The ground state energy is transferred to the readout register, using the Abrams and Lloyd technique, and is read out.
  • Step 510 energy of the ground state electron distribution is returned to the CC.
  • step 506 involves simulating the Hamiltonian of the molecular system with the Hamiltonian of the quantum processor. This can be realized by applying the Trotter approximation and decomposition technique to form a sequence of elementary quantum logic gates. Quantum registers capable of universal quantum computation are described in detail below. Also see, e.g., Somma et al, 2001, arXiv:quant-ph/0108146, hereby incorporated by reference in its entirety.
  • steps 508 and 510 for transferring and reading out the ground state energy of the system can be performed according to the Abrams and Lloyd measurement algorithm, which provides a method for reading out a ground state observable of a QM system once a ground state has been determined.
  • the classical computer component comprises a primary computational resource that processes the bulk of the classical algorithm and that interfaces with a classical node, where each classical node represents a specialized device for controlling a quantum processor.
  • the primary computational resource is abstracted from the details of the quantum computer. This type of configuration can help enhance the efficiency of the hybrid computer architecture.
  • the classical computer is capable of implementing the hybrid algorithm, coordinating one or more quantum processors, and comparing the results for each iteration.
  • the classical computer is a grid of nodes, where the number of nodes are used to perform the classical aspects of the algorithm while some of the nodes are used to control and operate the quantum processors.
  • the specific combination of nodes is chosen to optimize the computational efficiency of the architecture, by balance between parallelization of the problem versus data transfer overhead between the nodes.
  • Classical computers useful for performing the front-end aspects are commercially available.
  • Exemplary classical supercomputers useful for the classical component of the present invention include, but are not limited to, the Cray SX- 6, XI, and XD1 (Cray Inc., Seattle Washington) and the Hitachi SRI 1000 (Tokyo, Japan), and other combined vector/parallel machines.
  • vector computers that manipulate two sets of registers rather than two registers at a time, are used.
  • the quantum computer comprises a quantum processor.
  • the quantum computer further comprises an interface classical computer (ICC) that controls one or more quantum processors.
  • ICC is a commercially available classical computer.
  • the quantum processor is any quantum computing architecture that can perform universal quantum computation. Examples of quantum computer architectures useful for this purpose include superconducting, ion-trap, or optical quantum computers. Methods for programming and controlling quantum computers are known. See, for example, United States Patent Publication Number 20030121028 to Coury et al, entitled “Quantum Computing Integrated Development Environment,” published June 26, 2003, which is hereby incorporated by reference in its entirety.
  • the quantum processor is a superconducting quantum computer chip.
  • superconducting quantum computing chips In order for superconducting quantum computing chips to function they are placed at sufficiently low temperatures, which typically range from about 5 milliKelvin (mK) to about 80 mK. Cryogenic equipment for achieving these temperatures is well known and commercially available.
  • Control electronics for performing quantum logic on the superconducting quantum computer chip typically run in the room temperature environment, and other aspects of the control electronics run in the low temperature environment.
  • the use of control electronics includes application of currents and voltages to the superconducting quantum computer chip, and are generated by commercial devices and manipulated appropriately.
  • control electronics are coordinated by the ICC, which translates machine input into machine language instructions for the superconducting quantum computer chip.
  • the machine language is then expressed by the control electronics as currents and voltages applied to appropriate components of the superconducting quantum computer chip.
  • the currents and voltages can have direct and/or alternating components.
  • the alternating components have frequencies ranging from 100 megahertz (MHz) to 50 gigahertz (GHz).
  • the currents can have magnitudes (post-filtering) ranging from 1 microampere (pA) to 1 milliampere (mA) on the actual superconducting quantum computer chip and the voltages can have magnitudes ranging from 1 picovolt (pV) to 1 millivolt (mV) on the actual superconducting quantum computer chip.
  • the currents and voltages are sufficiently filtered and the wires are sufficiently cooled in order to be useful at the operational temperatures of the superconducting quantum computer chip. Methods for filtering and cooling these electronics are known.
  • Output from the superconducting quantum computer chip returns to room temperature in the form of currents or voltages, or both. These are detected by the classical computer and converted to an informational result that is returned as the output of the program.
  • the molecular system is subject to a common approximation, the nuclei do not move under effect of electrons, and then modeled quantum mechanically.
  • the algorithm of Abrams and Lloyd is applied to load the ground state energy eigenvalue into a second register of the quantum computer.
  • N (2) is the number of electrons in a hydrogen molecule
  • D (3) is the number of spatial dimensions (3)
  • R (7) is the number of qubits in the second (readout) register.
  • This strategy requires NDQ qubits in a first register, the evolution register, and R qubits in a second register, the readout register.
  • the readout register holds the energy eigenvalue ⁇ Q that is to be calculated.
  • N 1000
  • D 3
  • Q 10. Therefore 30,000 qubits are needed for the evolution register. Taking R to be 128 qubits, a total of 30,128 qubits is needed. Note that even if a 7:1 ratio of physical to logical qubits is required (for error correction), this last case gives about 250,000 physical qubits. If each qubit and associated hardware takes up 100 ⁇ m 2 , this gives an area of 25 mm 2 , which is in line with the current size of conventional microchips. The calculation the ground state energy of H 2 involves a low mass molecular system H 2 .
  • nuclear coordinates can be used in place of atomic coordinates, and atomic mass units used in place of Daltons.
  • atomic coordinates and nuclear coordinates are interchangeable.
  • FIG. 6 illustrates a three-dimensional grid, or a subset thereof, 650 for an embodiment of the present invention.
  • FIG. 6 A shows a subset of three-dimensional space, with circles denoting points in this three-dimensional space. Each point has x, y, and z Cartesian coordinates. Each electron in the molecular system under study is assigned to a unique register of DQ qubits. D is three since there are three dimensions (x, y, and z), and ⁇ is 2 since there are 2 s grid points per dimension.
  • DQ qubits is three since there are three dimensions (x, y, and z)
  • each possible state of the register in equation (2) corresponds to a state where electron one is at a specific point on the grid 650 (denoted by the six rightmost qubits) and electron two is at the grid point denoted by the six leftmost qubits. It covers all possible electron configurations for a two election system.
  • the register state [l 11010 011111] corresponds to the situation where electron one (labeled as element 651 in FIG. 6B) is at gridpoint [011111] and electron two (labeled as 652) is at [lllOlO] (see FIG. 6B).
  • the operator y f acting on the wavefunction gives the position in the y-direction of electron : For electron one, the terms on the diagonal of operator y ; . read [0,...,0] with 2 s terms, followed by [1,...,1] with 2 s terms, etc. up to [2 ⁇ _1 ,...,2 ⁇ _I ] with 2 s terms, repeated until full.
  • the operator z ; . acting on the wavefunction gives the position in the z-direction of electron /:
  • the U matrices effect a transformation of the p operators from their original momentum basis defined by px,py, and pz to the positional basis defined by x, y, and z.
  • the QFT matrices are readily obtained. See, Nielsen and Chuang, 2000, Quantum Computation and Quantum Information, pp. 204-215 as well as United States Patent Publication Number 2003/0164490 Al, to Blais, published September 2, 2003, each of which is hereby incorporated by reference in its entirety. 5.5.3 Getting to the ground state by varying nuclear charges adiabatically
  • Embodiments of the present invention include steps and/or means for adiabatically varying the parameters of the system being emulated.
  • the algorithm of Abrams and Lloyd is an example of an eigenvalue finding algorithm.
  • the algorithm begins by considering a quantum computer with two registers containing R and NDQ qubits respectively. These two registers serve two different purposes in this algorithm.
  • the R qubit register is used to do a quantum Fourier transform and read out the desired energy eigenvalue at the end of the computation.
  • the R qubit register is also called the readout register.
  • the NDQ qubit register encodes the Hubert space in which the quantum evolution operator U - Qxp ⁇ itH fmal ) acts.
  • the Hamiltonian used here is the t — » ⁇ version, after the system has settled into its ground state and is not explicitly time dependent anymore.
  • the NDQ qubit register is also called the evolution register.
  • the eigenvalues o ⁇ H fiml is extracted by measuring the state of the R qubit register. Since there are T - 2 R possible states in this register, the accuracy of the result scales as l/r .
  • the size of register R is not a function of the size of the molecular system being simulated because it is an "output method" whose size is chosen based on the accuracy desired for the answer.
  • the algorithm in accordance with this embodiment of the invention proceeds as described below. This description is one embodiment of step 508 of FIG. 5, other embodiments may vary or omit steps.
  • Step 1 Initialization. First, all R qubits are initialized into state 10 . Second, the NDQ qubit register is initialized into the
  • ⁇ >
  • Step 2 Rotation of the readout register qubits.
  • a ⁇ /2 rotation is performed on each of the R qubits. This can be done by applying a ⁇ x pulse of area ⁇ 12 to each of the R qubits in parallel. This transforms the system state to
  • Step 3 Evolve the system with U in ⁇ specific way. Next the quantum evolution operator is used to create the state
  • This transformation is accomplished by applying the operation U to the NDQ qubit register y times.
  • Step 4 Perform a quantum Fourier transform on the R qubit register.
  • the state of the system is rewritten.
  • label the exact eigenvectors of U which are unknown, by states
  • the quantum Fourier transform acts as
  • Step 5 Measure the state of the R qubit register. A measurement on this register selects one of the states, which will be the k" 1 eigenvalue with probability Denoting the state measures as
  • Step I Initialization of the input state.
  • the user defines three registers A, B, and C, each consisting of n quwords.
  • a quword is a string of qubits of length log 2 ; where one quword represents any integer in the range 1, ... , m and, consequently, the state of one particle; hence n quwords are n log 2 m qubits.
  • the qubits in register A are initialized to the unsymmefrized input state
  • the algorithm is unaffected if this state is a superposition of several ordered w-tuples.
  • the correspondence between an ordered w-tuple of quwords and an antisymmefrized superposition is one to one.
  • Step II Generating n! states.
  • the user creates the following state in register B:
  • Step III Transform into permutations of natural numbers.
  • the goal of this third step is to transform register B into the state
  • S n is the symmetric group of permutations on n objects.
  • a permutation of a plurality of objects is a "shuffling" of them, that is, the objects exchange places with each other. Shuffling a deck of cards permutes their order.
  • the state of register B is now an equal superposition of the states representing all the permutations of the first n natural numbers. This can be done in the following manner.
  • Step IV Sorting and unsorting.
  • the algorithm for antisymmetrization proceeds with a series of sorting and unsorting operations.
  • a string of "scratch" qubits is required so that the sorting operations are reversible.
  • Any sorting algorithm can be used.
  • An exemplary sort is Heap sort, because it requires about n In n operations in all cases and only n log 2 n scratch qubits.
  • the first sort orders register B with a series of exchanges and scrambles A and C with the same series of exchanges. There it is exactly known how registers A and C are scrambled. At this point, one has already obtained a symmetrized superposition of the input states, but it is entangled with many other qubits.
  • the term "about” is the typical range of values about the stated value that one of skill in the art would expect for the physical parameter represented by the stated value.
  • a typical range of values about a specified value can be defined as the typical error that would be expected in measuring or observing the physical parameter that the specified value represents.
  • the te ⁇ n "about” means the stated value + 0.10 of the stated value.
  • the present invention can be implemented as a computer program product that comprises a computer program mechanism embedded in a computer readable storage medium.
  • the computer program product could contain the program modules shown in Fig.
  • the computer program product could contain program modules that encode any of the algorithms or methods disclosed herein. These program modules can be stored on a CD-ROM, DVD, magnetic disk storage product, or any other computer readable data or program storage product.
  • the software modules in the computer program product can also be distributed electronically, via the Internet or otherwise, by transmission of a computer data signal (in which the software modules are embedded) either digitally or on a carrier wave. While the present invention has been described with reference to a few specific embodiments, the description is illustrative of the invention and is not to be construed as limiting the invention. Various modifications may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined by the appended claims. This patent specification concludes with the appended claims.

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Abstract

L'invention concerne un procédé de simulation d'un système moléculaire utilisant un ordinateur hybride. Cet ordinateur hybride comprend un ordinateur classique et un ordinateur quantique. Ce procédé utilise des coordonnées atomiques Rn et des charges atomiques Zn d'un système moléculaire afin de calculer une énergie à l'état fondamental du système moléculaire au moyen de l'ordinateur quantique. Cette énergie à l'état fondamental est renvoyée vers l'ordinateur classique et les coordonnées atomiques sont géométriquement optimisées sur l'ordinateur classique en fonction des informations relatives à l'énergie d'état fondamental renvoyée des coordonnées atomiques afin de produire un nouvel ensemble de coordonnées atomiques R n pour le système moléculaire. Ces étapes sont facultativement répétées conformément à un algorithme d'affinage jusqu'à ce qu'une condition de conclusion soit obtenue.
EP05754940A 2004-06-05 2005-06-06 Architecture d'ordinateur classique-quantique hybride pour le modelage moleculaire Ceased EP1836628A4 (fr)

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