1y ago

25 Views

2 Downloads

1.80 MB

14 Pages

Transcription

Exploring Quantum Computingfor Machine LearningIstvan Barabasi, Charles C. Tappert, Daniel Evans, and Avery M. LeiderSeidenberg School of CSIS, Pace University, Pleasantville, New York 10570{ibarabasi, ctappert, devans, aleider}@pace.eduIn the following sections, this paper provides a background forreaders not familiar with quantum computing, describes earlywork on using quantum computers for machine learning,discusses the new area of quantum machine intelligence,describes additional quantum machine learning algorithms,presents the methodology our students used to implementquantum programs, describes in detail programs coded and runby our faculty and students on quantum simulators or actualquantum computers, and finally draws conclusions andindicates future work.Abstract—(This paper explores the use of quantum computingfor solving machine learning problems more efficiently. Today’squantum computers are rather primitive, so only relatively smallmachine learning problems can be solved at this time.Nevertheless, the machine learning problems described here thathave been solved on quantum simulators or actual quantumcomputers indicates the potential power of quantum computersfor solving computationally intensive machine learning problemssuch as the deep learning multi-layer neural networks.Keywords—machine learning, quantum computing, deeplearning, quantum machine intelligenceII. QUANTUM COMPUTING BACKGROUNDI. INTRODUCTIONFor the reader unfamiliar with quantum computing, we providesome background material as an introduction to the conceptsdiscussed in this paper (Evans, 2019). Others may wish to skipthis section.There is currently considerable interest in quantum computing.In the U.S. in January 2019, the National Quantum InitiativeAct authorized 1.2 billion investment over the next 5-10 years(Rep Smith, 2019). A quantum computing race is ongoingamong the tech giants Google, IBM, and Microsoft, Amazon,and China’s Alibaba. IBM emphasizes heavy usage on their QExperience quantum simulator with more than 90,000 userswho have run 5,000 experiments and published 110 papers.Governments, particularly America and China, are fundingwork in the area with the concern that quantum-computers maysoon become large enough to crack current encryptionmethods, giving the country that gets there first a majoradvantage (Economist, 2018). At the 2019 ConsumerElectronics Show, IBM announced for sale – or, moreaccurately, calculation time on it – the IBM Q System One, theworld's first commercial quantum computer (IBM, 2019b).Although quantum programs can be written in a quantumprogramming language, they are often shown in a circuitdiagram (Fig. 1). The circuit diagram is close to universal inthe field, and concisely represents quantum computingconcepts.Fig. 1: A Quantum Circuit: A Hadamard Gate followed by aConditional NOT Gate and Measurements.Circuit diagrams are stacked horizontal lines (wires) withvarious connections between them (Fig. 1). Each single wireline represents a single qubit, a quantum state. Double wirelines represent classical bits. Circuits are read from left to rightcorresponding to the sequential execution of the gates in thecircuit, and to the movement of time. Gates are rectangles,labeled for the type of gate, although some common gates, likeConditional NOT, have special representations. Measurementsets a classical bit from a qubit. Measurement is indicated in aquantum circuit by a meter symbol, and usually appears at theend of the circuit. Elements that are vertically aligned areconsidered to happen simultaneously. Qubits operands are readfrom top to bottom in the circuit. Individual qubit lines arenamed on the left, with optional initial values. The final resultsIn MIT News, a recent article interviewed William Oliver, theprincipal investigator in both the Engineering QuantumSystems Group at MIT and the Quantum Information andIntegrated Nanosystems Group at MIT Lincoln Laboratory. Henoted that MIT’s quantum computing effort was beinginhibited by a shortage of quantum knowledge workers(Leddy, 2019). To fill this gap Pace University in teachingquantum computing at the PhD and advanced Master’s level,in particular teaching the students how to become softwaredevelopers for these quantum computers, and has even startedexperimenting with a high school level orientation course.Funded, in part, by an IBM faculty award.1

matrix. A single-qubit 2 2 gate matrix tensor product withthe 2 2 identity gate matrix will create a 4 4 two-qubitgate. In a quantum circuit diagram, tensor products are impliedwhen it is necessary to match gate and qubit dimensions.are shown in labels on the right. See the tensor productdescription below for how qubits are combined in a circuit.The data of quantum computing is the qubit, representing aquantum state. A single qubit is a probabilistic combination ofits basis states, 0⟩ and 1⟩. The bracket notation derives fromquantum mechanics, and is an abstraction of subatomiccharacteristics related by uncertainty. Mathematically, a qubit𝜓 is a vector 𝜓 𝛼 0⟩ 𝛽 1⟩. The values of 𝛼 and 𝛽 arelimited by the probability relation 𝛼 2 𝛽 2 1 . Whenmeasured, a qubit's state will be 0 with a probability of 𝛼 2 or1 with a probability of 𝛽 2 . The coefficients 𝛼 and 𝛽 arecomplex numbers, 𝛼 𝑎0 𝑎1 i and 𝛽 𝑏0 𝑏1 i . Themagnitude of a complex number is real, so the probabilitiesrepresented by 𝛼 and 𝛽 are real numbers. If either 𝛼 or 𝛽 is 1,the other must be 0. A qubit with only a single non-zero basiscoefficient is a pure qubit – for example, 0 0⟩ 1 1⟩ 1⟩.A qubit with neither coefficient equal to 1 is said to be insuperposition and will be probabilistically 1 or 0 whenmeasured. Measurement collapses the probabilistic quantumstate into one of its pure states: the probabilistic information islost, and subsequently, the qubit always measures in thatcollapsed state.With the foregoing information and a knowledge of the relevantquantum gate matrices, the operation of the quantum circuit(quantum program) in Fig. 1 can be modeled by the equation:𝐶( 0⟩ 𝐻( 0⟩)).1.Apply the H-gate to the 0⟩ qubit on the first wire11122.1 111 0212Expand the single qubit result to a 2-qubit operand usingthe tensor product with the value on the second wire112123.4.20120Apply the Conditional NOT gate to the result1000Qubits are manipulated by quantum gates, representingquantum state transformations. Mathematically, gates aremodeled by square matrices that satisfy the conditions ofunitarity. The application of a gate to a qubit is equivalent tomatrix multiplication of the qubit by the gate matrix.Multiplication by a unitary matrix preserves the magnitude ofthe vector, and thus the probability relation.1 00100000100101122012 0010211The 2-qubit output is the vector, 00⟩ 11⟩ .22When measured, it will yield 00 50% of the time and 111150% of the time. Note that 2 2 1.2Although there are an infinite number of quantum gates,arbitrary gates can be composed using only a small set of gatesas building blocks. This is analogous to classical computingwhere, for example, AND, OR, and NOT gates form a universalbasis for building any classical circuit.2The result is known as a Bell state, after the physicist John Bell,and represents entangled qubits. With entangled qubits, themeasurements are correlated, even if the qubits are separated.Entanglement is the basis for "quantum teleportation", whatEinstein famously called "spooky action at a distance." Itunderlies such algorithms as quantum key distribution. Onemay wonder at the usefulness of the probabilistic behavior of aquantum program such as Fig. 1. The following sections showa number of quantum computing applications that intersectmachine learning.One of the postulates of quantum mechanics states that "Thestate space of a composite physical system is the tensor productof the state spaces of the component physical systems" (Nielsen& Chuang, 2010). Among other things, this means that thetensor product is used to match smaller qubit gates to largerqubit operands, and vice versa. Specifically, the tensor product 0⟩ 0⟩ 00⟩ creates a two qubit operand from two onequbit operands. In general, a two qubit quantum state isrepresented by a vector 𝜓2 𝑎00 00⟩ 𝑎01 01⟩ 𝑎10 10⟩ 𝑎11 11⟩. The probability relation must hold, 𝑎00 2 𝑎01 2 𝑎10 2 𝑎11 2 1. When a gate is applied to a qubit operand,the qubit is represented as a column vector, with the basis vectororder implied by the binary numerical order. The dimension ofthe general single qubit vector 𝜓 is 2 1. The dimension ofthe two-qubit vector 𝜓2 is 4 1. As the number of qubits in anoperand increases, the dimension increases by a power of 2.The tensor product reflects this because it multipliescorresponding dimensions. The tensor product of a two qubitquantum state (4 1) and a one-qubit quantum state (2 1) isa three-qubit (8 1) quantum state. Similarly, a quantum gatecan be extended by a tensor product of the gate and the identityIII. EARLY THEORETICAL ADVANCES AND EXPERIMENTS USINGQUANTUM COMPUTERS FOR MACHINE LEARNINGDuring 2018, Google published early articles about machinelearning algorithms using Quantum Neural Networks: Classification with Quantum Neural Networks on NearTerm Processors by Edward Farhi1,2 and Hartmut Neven1 Barren plateaus in quantum neural network traininglandscapes by Jarrod R. McClean1, Sergio Boixo 1, VadimN. Smelyanskiy1, Ryan Babbush1 & Hartmut Neven12

conventional SVM methods. It optimizes a parameterizedquantum circuit to provide a solution that cleanly separates thedata.Fig. 2. Google’s approach to QNNs, where in contrast to hiddenlayers in classical deep neural networks, the boxes represententangling actions, or “quantum gates”, on qubitsFig. 3. MIT and IBM researches implemented a sample VQCalgorithm on IBM’s 5-Qubit machine (Supervised learning withquantum-enhanced feature spaces)In March 2019, IBM and Intel reported breakthroughexperiments using quantum algorithms for deep learning. IBM announced the development of QC4ML algorithmswhich “demonstrate how noisy quantum computers cansolve machine learning classification problems thatclassical computers cannot” Intel reported about “mathematically proven that artificialintelligence can help us understand currently unreachablequantum physics phenomena”, publishing QuantumEntanglement in Deep Learning Architectures. Within thisarticle, Intel confirms that “highly entangled many-bodywave functions can be efficiently represented by deeplearning architectures, such as convolutional neuralnetworks (CNNs) and recurrent neural networks (RNNs).Our students performed multiple tutorials for VQC classifier,using platforms from IBM and Xanadu.AI: IBM Quantum Computer with Qiskit SDK: studentsreviewed the VQC tutorial for breast -cancer imagesclassification and evaluated its applicability for a 2018Chest Xray Images Classification Project previouslyimplemented classically using neural networks andTensorflow. Xanadu.AI PennyLane Platform: students reviewed theVQC tutorial for IRIS dataset classification andimplemented it via GPU simulator on Google Colab.B. Quantum kernel estimator or Quantum Support VectorMachine (QSVM)IV. QUANTUM MACHINE INTELLIGENCEQuantum machine intelligence is a new approach to artificialintelligence and machine learning. Machine learning andquantum computing are two technologies that have substantialimpact on how we use computer science to solve artificialintelligence problems. Based on a new study by IBM and MITresearchers, quantum computing can extend how to applycomputation to solve complex machine learning problemsmore efficiently at a fraction of time. Classical computers usekernel methods for common pattern recognition algorithms,such as for example implementing support vector machines(SVMs) to solve classification problems. When SVMconsidered feature space becomes large, kernel methods willbecome computationally expensive. Such algorithms can beefficiently speeded up by mapping out the combinations ofthese features into a “feature space” represented viaexponentially large number of quantum states of a multi-qubitquantum computer.QSVMs estimate kernel functions on quantum computers andoptimizes a classical SVM. Solves classification problems thatrequire a feature map for which computing the kernel is notefficient classically. QSVM solves the problem by performingdirect estimation of the kernel within the quantum featurespace. Students reviewed the IBM Qiskit QSVM tutorial forbreast-cancer images classification and comparedresults with earlier tutorial results that used VQC.Giovanni Acampora from University of Naples Federico II,Italy, launched the first journal dedicated to Quantum ArtificialIntelligence. The section named Quantum Machine Learning,edited by Seth Lloyd from MIT, publishes papers aboutquantum implementation of ML algorithms such as quantumperceptrons, quantum neural networks, and quantum clustering.According to Giovanni, within the last 8 year there was a 4xgrowth within the number of papers published in the area ofquantum machine intelligence, with the biggest jump ofapproximate 2x in 2018.Using quantum-enhanced feature space, efficientlyimplemented on quantum computers enables quantumadvantage for efficiently solving considerable number ofmachine learning problems. Here are two examples forquantum enabled machine learning.A. Variational Quantum Classifiers (VQC)VQC implemented using variational quantum circuits canclassify data with complex features set in a similar wat as3

Fig. 6. High-level architecture of the proposed QKNN solution.B. Quantum K-Means (QKM) AlgorithmQuantum Computing can be used for distance estimationwithin k-means clustering. Shan Jin, Xi He, Xiaokai Hou, LiSun, Dingding Wen, Shaojun Wu and Xiaoting Wang fromUniversity of Electronic Science and Technology of China,designed a quantum circuit below or Euclidian distancecalculation and implemented it using IBM Qiskit:Fig. 4. Number of published quantum machine intelligence papers.This journal published a number of interesting articles in thearea of applying Quantum Computing for Machine Learning(QC4ML), such as for example: Bayesian deep learning on a quantum computer byZhikuan Zhao, Alejandro Pozas-Kerstjens, PatrickRebentrost, with sample code for IBM and RigettiQuantum Computers, that can be implemented andtested with students during class (see tutorial). A hybrid machine learning algorithm for designingquantum experiments by L. O’Driscoll, R. Nichols, P.A. Knott, with an implemented example of a neuralnetwork for classifying quantum states, with samplecode for classifying quantum states of lights viaQuTIP framework.Fig. 7. Quantum K-Means circuit to find the Euclidian distance.C. Quantum Generative Adversarial Networks (qGANs)GANs represent a class of algorithms that employ two neuralnetworks - a generator and a discriminator - to solve agenerative task, namely the creation of random samples of adistribution that is implicitly given by the training data. Asshown in Fig. 8: The generator creates data samples which appear to beindistinguishable from the training data. The discriminator tries to differentiate between thegenerated samples and the training samples. The generator and discriminator are trained alternately.Fig. 5. Neural network for classifying quantum statesV. ADDITIONAL QUANTUM MACHINE LEARNING ALGORYTHMSA. Quantum KNN (QKNN) AlgorithmClassic K Nearest-Neighbor algorithm has high complexity,because similarity computing and searching are timeconsuming. This becomes challenging when the number ofimages to be classified is high. Within “Image ClassificationBased on Quantum KNN Algorithm” article, Dang at.al.proposed a QKNN where complexity is only quantumalgorithm is onlyFig. 8. Generative Adversarial Network.4

qGAN use a quantum generator and a classical discriminator tocapture the probability distribution of classical trainingsamples. A quantum channel, i.e., the quantum generator, istrained to transform a given n-qubit input state ψin toB. JupyterHubThe benefits of using the JupyterHub type deployment of theteaching environment were the following: Leveraged enhanced IDE using JupyterLAB and a numberof extensions, such as Google Drive, Github and otherplugins. We have pre-installed multiple Quantum ComputingScience Kits, such as Qiskit, QuTIP and others. We have pre-installed additional required python libraries,such as matplotlib draw, LaTex draw, IBMQ provider,PDF exporters and other circuit visualization add-ons. Simplified faculty’s work to assist and help students withtheir Jupyter notebooks, python programs and codeartifacts. This platform empowered students become selfsufficient with QC science kits, creating quantum circuitsand developing programs for implementing specializedalgorithms in context of the studied class topics.an n-qubit output state, wheredescribe the resultingoccurrence probabilities of the basis states j .IBM Qiskit SDK provides a tutorial for applying qGANs inFinancial Industry for Options Pricing.VI. IMPLEMENTING ALGORITHMS ON QUANTUM COMPUTERSOur quantum computing graduate course has student projectsthat utilize hands-on labs with simplified quantum programdevelopment, live code executions and student projectsperformed using IBM’s Quantum Experience Platform withaccess to real Quantum Computers (Tappert, et al., 2019). Weuse the IBM Cloud to connect to the IBM Q Network with livequantum computers in the USA as well as in Japan, Australia,and Spain.C. IBM ComposerThe benefits of IBM Composer used with the high schoolteaching environment were the following: IBM Composer is all on the web, so it took only the onestep of having the high school technical support securitypolicy decision maker to make the URL available. Thestudents could get hands-on with the tool right away afterIBM registration, which took only minutes. IBM Composer includes descriptions of the gates,includes QASM, and includes a diagram of thearrangement of the qubits in the quantum computer beingprogrammed. The User Interface is intuitive, at least, to ahigh school student. Well-placed error messages, such asa reminder to save the program before running it, pop-upto assist.Quantum programs written in IBM Composer can be run oneither real quantum computers or on the simulator. Sometimesat periods of high traffic, the real quantum computers delayedgiving their results by a few hours or even a day. Also, oncommon programs (such as those following the online IBMComposer tutorials), an option to accept the results of previousidentical code that was run on the quantum computer, that is stillin cache, will be offered. Simulator results are instantlydelivered. For the classes given to the high school students,running the programs on the real machine were limited to whereit made a significant difference in the results, such as Grover’sAlgorithm. The simulator also offers a range of configurationoptions and that can be designed by the student to try differentideas.We used multiple Quantum Computing Science Kits to teachstudents quantum computing technology. The objective was tohelp the students to gain practical experience via lab exercisesand to develop projects to solve relevant and practicalproblems using quantum computing algorithm and programs.While initially we used Watson Studio within IBM Cloud, welater deployed a simplified shared development platform basedon an integrated JupyterHub/JupyterLab virtual machinerunning within a public cloud service.A. QC Science KitsThese QC Science Kits include: IBM contributed and moderated community projectQuantum Information Science Kit (Qiskit) available athttps://github.com/Qiskit Quantum Toolbox in Python (QuTIP) moderated byQuSTaR (www.qustar.org) Investigated Rigetti’s SDK package, with focus on itsPython pyQuil package and Quantum VirtualMachine (QVM), which is an open-source implementationof simulator as a quantum abstract machine (QAM) usingclassical computer hardware.In addition to Quantum Computers, we used multiple QuantumComputing simulators provided by IBM: The 32-qubit IBMQ-QASM-Simulator via IBM Cloud Custom deployed HPC-Quantum-Simulator and made itavailable for students with the goal to help them avoid jobqueue wait times for having their code be processed byIBMQ devices. We have custom implemented thissimulator using a large-size virtual machine, available24/7 for students use.Local simulators available within Qiskit, such as simplifiedtraditional simulator and the experimental release of the QiskitAer high-performance circuit simulator frameworkThe layout of the Composer is shown in Fig. 9 and the user canselect whether to run the program on the simulator or on oneof the real quantum computers that IBM has made available.5

Fig. 10. Five Qubit IBM Quantum Computer.VII. SUMMARY OF MACHINE LEARNING ALGORITHMIMPLEMENTATIONS ON QUANTUM COMPUTERSFig 9. User interface of the IBM Composer.The quantum registers with the qubits in them are listed on theleft side, initialized with zero kets,The following subsections contain descriptions of the quantumcomputer programs implemented and run by our students andfaculty on the IBM quantum simulator.0 , which is the groundstate of a qubit. The qubits are also depicted in relationship toeach other on the actual quantum circuit chip in the diagram inthe upper left side of Fig. 9. The gate selection menu on thelower right hand side is where the programmer chooses the gatethey need and drags it onto the appropriate wire in ‘the score’.The selection buttons, for running the program on either thesimulator or the actual quantum computing machine are on theright hand side above the gate selection area. The system onwhich to run the program is selected after the program has beenbuilt, named, and saved.A. Quantum War (Barabasi, et al., 2019)The first programming example is the quantum version of thechildren’s card game “War.” This program demonstrates apractical application for the quantum principle of superposition,and it shows how a small number of qubits can do the work ofmany classical bits. It also illustrates how to create and measuretwo quantum circuits.To play the game, a deck of playing cards is divided evenlyamong two players, then each player simultaneously draws acard and the player with the card of the highest order wins thebattle and claims the losing player’s card. The first player torun out of cards loses. After drawing, the cards are removedfrom the deck. Traditionally, the rules of War state that thelosing player’s cards are added to the winning player’s deck.This study has opted to forego this portion of the rules to keepthe example simple for those first learning about quantumprogramming. For simplicity, this program also omits the threecard WAR draw for a tie.After this orientation, the students went hands-on. The studentsran programs demonstrating the X gate which is the quantumequivalent to the classical NOT gate. If the qubit is in a groundstate with value 0, then putting it through an X gate flips it intothe 1 state, the activation state, and vice versa. Studentsreviewed the results – the zeros and ones – which were readfrom right to left, as if they were Chinese characters. Alsoimportant was the understanding that the results in a quantumprogram are delivered in probabilities. Quantum programmingdoes not deliver exact results, so each quantum program is runmany times in order to give a probability distribution. On asimulator, a program might be run 100 times to give a goodresult, whereas on the real machine, it may take 1,024 or moreexecutions to give a reasonable distribution.A traditional deck of cards contains fifty-two unique cards. Aclassical computer requires 312 bits (six bits per card times 52cards) to represent all fifty-two card options simultaneously. Incontrast, a quantum computer requires only 6 qubits torepresent the 52 cards by using the principle of superposition, alinear combination of both 0⟩ and 1⟩. This means that the qubitrepresents all possible values simultaneously. Thus, six qubits,all in a state of superposition, represent all fifty-twopossibilities when drawing from a deck of playing cards.The hands-on portion of the class was to make 6 CNOTconnections in the IBM Composer, use X gates (X gates flipvalues from zero to one and one to zero), to predict theiranswers, and run the program. To do this, the students had tostudy the diagram that accompanies the programming interfaceof the Composer, to identify legitimate paths for entanglementof qubits, see Fig. 10. A legitimate path of qubit entanglementgoes from qubit 1 to qubit 0 or 2 or from qubit 3 to qubit 4 or2. An attempt to put a CNOT gate between other combinationsof qubits, such as between 1 and 3, will not be allowed and inthe Composer, the disappearance of the incorrect CNOT fromthe program.This study slightly modifies the rules of War to illustrate morefully the quantum principles at play. Each player plays with afull deck of fifty-two cards. Each deck is represented by sixqubits, twelve qubits in total.The program begins with two classes that are used to keep trackof the cards in each player’s deck. The Card class holdsinformation about each playing card including, the suit, name,and value of the card. The Deck class contains logic for creatinga deck of cards containing 52 cards with values 2-10, Jack,Queen, King and Ace with suits Clubs, Diamonds, Hearts, and6

Spades. It also contains the logic for drawing a card andremoving it from the deck.simulation employs qubits in a practical situation that requirestruly random results.Following the class definitions, the user chooses to run theprogram on a local quantum simulator or IBM’s IBMQX5, a 16qubit chip. The simulator runs faster than making a connectionto the IBMQX5 and is guaranteed to produce a result. Due tohigh volume of usage, a request to use the IBMQX5 cansometimes timeout.B. Random Password Generator (Barabasi, et al., 2019)The second programming example is the quantum version of arandom password generator. This program demonstrates howto use superposition to generate ASCII characters. It also showshow a small number of qubits can do the work of many classicalbits and uses a practical example to increase user engagement.It also shows how to use a single measurement to get multipleresults and illustrates how to account for noise when measuringa quantum circuit.Next, the program creates two quantum circuits to representeach deck. Each circuit contains six qubits. All six qubits havean H gate applied to them to induce a state of superposition.This allows the six qubits to represent any of the 52 cards in thedeck. The program now contains two quantum circuits, each ofwhich represents a deck of 52 playing cards.This program uses a quantum circuit to create a truly randompassword using English ASCII characters. The program uses an8 qubit quantum circuit to generate a variable length randompassword. A single ASCII character, represented on a classicalcomputer, uses 8 bits. In the classical implementation, 8 bitsrepresents a single character, and only that character. In orderfor the classical machine to represent a different character, thevalue of one or more bits must be changed or more bits must beused. The quantum implementation can utilize superposition tocreate multiple characters using only 8 qubits by measuringeach qubit multiple times. Thus, the quantum circuit representsall ASCII characters simultaneously when in a state ofsuperposition.Next, the battle between players begins. Player One's quantumcircuit is measured. This represents drawing a card from the topof the deck. Then, player Two's quantum circuit is measured.The measurement returns the probability of drawing any one ofthe 52 cards from the top of the deck. The card drawn isdetermined by the measurement taken of the state of the qubits.The six qubits representing each deck are measured 1024 times.Each measurement is referred to as a “shot”. In a single shot,the probability that a qubit is equal to 0⟩ or 1⟩ is measured andrecorded. After all 1024 shots, a dictionary is returned thatcontains the number of times all sixty-four combinations of thesix qubits were measured. The value between 000000 and110011 that is measured with the highest frequencycorresponds to the card that the player drew. The drawn card isthen removed from the deck and cannot be drawn again.Finally, python logic compares the two cards and determines awinner for the battle.The quantum computer has two advantages over the classicalcomputer when it comes to password generation. The firstadvantage is that because quantum computers use qubits withsuperposition, they can generate longer passwords in less timethan a classical computer. The second advantage is that thequantum computer is capable of generating a truly randompassword while the classical computer is not. While theclassical computer utilizes pseudorandom functions to produceresults that seem random, only qubits can produce truly randomresults. As with the Quantum War program, the motion ofquantum particles is unpredictable. Thus, using qubits canproduce a password that is truly random and thus stronger thana random password generated on a classical computer.The program then presents the players with the cards that theydrew and the likelihood that the qubits represented that card atthe time of measurement. The likelihood is calculated bydividing the number of times the value was measured by thetotal number of shots and represented as a percentage in theoutput. Sample output is presented in Fig. 11.The program begins by creating an 8 qubit quantum circuit.Next, the program uses gates to set the qubits to the properstates for execution. All English ASCII characters begin withthe leading bits 01. The following six bits are variable and canbe set to either 0 or 1 depending on the character beingrepresented. Thus, to represent an AS

Keywords—machine learning, quantum computing, deep learning, quantum machine intelligence I. INTRODUCTION There is currently considerable interest in quantum computing. In the U.S. in January 2019, the National Quantum Initiative Act authorized 1.2 billion investment over the next 5-10 years (Rep Smith, 2019). A quantum computing race is ongoing

Related Documents: