Exploring Quantum Computing For Machine Learning - Pace

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