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REPORT EXCERPTTable of Contents1. Introduction to Quantum Computing 1Schrödinger’s Cat 1The Quantum Treasure Chest 1Figure 1: Brute-Force Problem-Solving Approach 2Figure 2: Quantum Problem-Solving Approach 3Getting Down to Qubits 4Quantum Gates: The Standard Universal Computer Architecture 5Quantum Annealing: A Specific Architecture for Specific Problems 62. Success Factors 7Benchmark Use Cases 7Figure 3: Most Overhyped Security Buzzwords 7Role of Economics 8Figure 4: A Minority of Providers Are Considering Quantum Computing 10Measuring Success 103. Types of Qubit 13Superconducting 13Trapped Ion 13Spin Qubits/Quantum Dots 14Topological 144. Hardware Is the Battleground 15IBM 16D-Wave 17Rigetti Computing 18Honeywell 19IonQ 19Quantum Circuits, Inc 20Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPT5. Development and Services Open the Door 21Qiskit 21Q# 22Amazon Braket 22Azure Quantum 231QBit 236. Big Tech Companies Research in the Background 24Microsoft 24Amazon 24Google 24Intel 257. The Post-Quantum Era 26Security Threat 26Quantum Key Distribution 278. Recommendations 309. Further Reading 31Appendix A – Companies Primarily Developing Quantum Computing Hardwareand/or Systems 32Appendix B – Companies/Projects Primarily Focusing on Quantum ComputingSoftware Development 39General 39Vertical-Specific 44Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPT1. Introduction toQuantum ComputingSchrödinger’s CatConsider a thought experiment involving a cat – Schrödinger’s cat. The cat is placed in a box,along with a radioactive material. When a sensor detects the radioactive material has radiated aparticle, a device releases toxic gas into the box, killing the poor cat. We put the cat into the boxalive, close the lid and wait. Is the cat alive or dead?There is no way of knowing unless we measure the cat’s state. We could open the box,acoustically listen for movements or x-ray the box. But these are all measurements, and wegenuinely have no way of knowing if the cat is alive or dead unless we penetrate the box usingsuch measurements. We can determine the probability of the cat being alive or dead after acertain time, but we can never be certain. Even if we knew everything about the state of theradioactive element before the cat goes in, we would not be able to know for sure when thefatal radioactive particle is released – in other words, the atomic and subatomic particles thatdetermine when a radioactive particle is released have inherent unpredictability. In essence, untilwe measure, the cat is both alive and dead, in a state of what is called superposition.At the subatomic level, this is actually the case – some particles don’t necessarily have anabsolute state, which prompted Einstein’s famous quote, “God does not play dice.” He couldn’taccept that some things are just inherently unpredictable. Even if we have all the data there is,we cannot determine what will come next. In the vacuum of space, particles can appear out ofnowhere and disappear within millionths of a second because of this inherent unpredictability. Itis this superposition of all possibilities due to inherent uncertainty that gives quantum computingits potential.The Quantum Treasure ChestImagine we have an impenetrable chest, in which lies a treasure of vast importance – perhapsa cure for cancer, or the key to nuclear fusion. To access the chest, we must find the correctthree-number combination of the padlock. If we don’t know the combination, the only way toaccess the chest is to try every possible combination from 000 to 999. But our chest is milesunderground, and not easily accessible. In fact, to test every single combination, it takes a wholeyear of planning and implementation. In the worst case, if the code were 999, we’d have to wait1,000 years to access the secrets inside (see Figure 1).Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPTFigure 1: Brute-Force Problem-Solving ApproachSource: 451 Research, 2020598 YEARS1 YEAR0 0000260 100 11 YEARSUCCESSBuilding a business case for investing in opening the chest is not feasible. Who would make aninvestment now for a return in – potentially – a thousand years? The payback period simply isn’tworth the effort.But imagine we have a magic box – Schrödinger’s box. The box is special because it can makevirtual ‘copies’ of the chest padlock, which represents inherent uncertainty. When we put thepadlock in the box, 1,000 copies of the padlock are made – not real copies that we can access, butvirtual padlocks encoded in the uncertainty of tiny particles. Now imagine we can manipulate thebox: fire lasers at it or expose it to magnetic fields such that we can simultaneously manipulateall these copies, without actually opening the box or examining the inside. In our scenario, wecould perhaps manipulate the combinations of the padlocks, such that each virtual padlock has adifferent code. This is akin to a quantum algorithm or ‘circuit.’ If we correctly manipulate the box,when we open it, these virtual copies disappear and all we see is the single padlock with the correctcombination (see Figure 2). If we keep opening and closing the box and sample the results, we canbecome increasingly confident that the combination is the correct result.Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPTFigure 2: Quantum Problem-Solving ApproachSource: 451 Research, 2020MANIPULATIONS1 YEAR0 0039899960 100 1?60 1SUCCESSThe crucial point about the box is we don’t have to test every combination. The box takesadvantage of the uncertainty of the position and movement of subatomic particles to test everycombination for us. So rather than having to do 1,000 tests, each taking a year, we can do a singletest that simultaneously looks at all combinations. The speed-up here is effectively from 1,000years to 1 year – is it worth investing in opening the padlock to cure cancer? Yes, it is likely thisinvestment would make a significant return.This is the quantum computer. In a nutshell, a quantum computer allows us to exploit uncertaintyin the characteristics of a subatomic particle by performing operations on this uncertainty. Oncethese operations are performed, the characteristics of the particle can be measured, and a resultobtained. The key part to remember is that a quantum computer allows all states to encodedin this uncertainty and then evaluated once, as opposed to a traditional computer where eachstate must be encoded and evaluated separately. This provides a huge (in fact, exponential)improvement in the time required to solve a problem.Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPTWhen the numbers get bigger, so too does the benefit of quantum computing. If the combinationlock is eight digits, it would take us 9,999,999 years to brute force every combination. In thequantum computer ‘box,’ it would take a year. But the problem is the box has to be able to handleso many combinations. This is the challenge facing quantum computing – making it powerfulenough to solve bigger combinations such that it provides a return on the investment.Getting Down to QubitsIn computing, binary digits (or bits) are used to represent data: 0 or 1. In quantum computing, qubitsare used, and these can represent 0, 1 or a superposition of 0 and 1. Until a qubit is measured, itis both 0 and 1, just like our cat is both alive and dead. It is this superposition that gives quantumcomputing an advantage over traditional computing (or Turing machines, more technically).If we have to store the state of all three-bit numbers in a register to be processed, then we needto store and process all successive states: [000,001,010, etc., to 111], which in decimal represents[0,1,2.7] on traditional computers – essentially, we have to store all of them in the same way wehave to look through all the padlock combinations, and then process each one individually. Thesame situation for three qubits is simply [?], with ‘?’ representing a superposition of both 0 and 1(i.e., hidden in the box with its state unknown). We put the unknown [?] in the box so that the boxmakes virtual copies of all the possible combinations from [000] to [111], and then manipulate thebox to solve our problem. When we open the box, the [?] becomes a definite answer.If we are trying to hack security keys, for example, rather than going through every possiblebit combination using a Turing machine, we can simply determine it once from the superposedqubits. We just need to manipulate the box in the right way (akin to an algorithm).A qubit is physically a subatomic particle, perhaps a photon (a packet of light) or an electron (thebasis of electricity). In the case of an electron, angular momentum, or ‘spin,’ is typically used todifferentiate between 0 and 1, typically ‘up’ spin and ‘down’ spin. In most Turing computers today,five volts represents 1, and 0 volts represents 0; there is no ambiguity between these states. Inquantum computing, we don’t know if the electron has up or down spin until it is measured, thusit has the ability to be in both states at the same time. This isn’t a trick – it is impossible to knowits exact state, and thus it represents all states. Crucially, we can affect the characteristics of theparticle without having to measure its state through microwave radiation or lasers or magneticfields. The qubits allow us to store all possibilities in a single register. Quantum ‘gates’ allow us tochange the characteristics of these particles, without us having to measure them directly, whichmeans the gates can perform operations on all possibilities at once. Many gates together make a‘circuit’ or algorithm.This physical basis of quantum computing is less important to understanding its potential than isits theoretic basis.Quantum Computing: Countdown to a Quantum Leap C O P Y R I G H T 2 0 2 0 4 5 1 R E S E A R C H . A L L R I G H T S R E S E R V E D.

REPORT EXCERPTLet’s say we are solving for the factors of a number (what numbers divide leaving no remainder)– for example, 10. Using a Turing machine, one way of finding factors is to continually dividethe number to see if it divides with no remainders – does nine fit? No. Does eight fit? No. Doesfive fit? Yes. So, it is a factor. etc. This is a computational challenge because for each numberwe are evaluating, we have to cycle through many other numbers to process. Using a quantumcomputer that has been superposed with all possible states, we can essentially run functions onall possibilities using these gates and determine the output all at once. It’s akin to working witha single row on an Excel spreadsheet compared with a chart of all the outcomes – if we wanta quick answer, do we glance at the chart or work through all the rows one by one? In a Turingmachine, the function rotates through all the rows; in a quantum machine, the function works ona space that can be visualized as almost a chart of all the possibilities at once.A quantum algorithm can be thought of as a series of logic gates, with each performingoperations on this ‘chart,’ similar to the way an electronic logic gate outputs a single 0 or 1depending on the state of all the inputs. In reality, each gate is a mathematical function based onimaginary numbers, but the specifics are unimportant for understanding the basic premise.We can’t see this chart directly. It is an analog of all the choices coded into the superposed stateof the subatomic particles. As soon as we try to measure it, just as we measure if the cat is aliveor dead, we get a definite output. Of course, at different times, the [?] will be a different value– just like if we measure the state of our cat at the beginning of the experiment, it is more likelyto be alive compared with later, when it is more likely to be dead. As such, we must sample thestate – we measure it repeatedly and derive a probability distribution. We might find that duringour sample, the answer was [101] 80% of the time and [100] 20% of the time. The answer to ourproblem is thus [101] on average.Quantum Gates: The Standard Universal Computer ArchitectureThe common approach to building a quantum computer is gate-based. This approach iscommonly called ‘universal,’ as it can be programmed to solve a wide variety of problems and isprogrammed through the use of quantum gates in a circuit. In traditional computers, operationsare performed on binary digits – a NOT gate, for example, turns 0 into 1 and 1 into 0. In gatebased quantum computers, similar operations are performed on the characteristics of the qubitwhile in a state of superposition. The qubit is yet to have a state when it is processed via thealgorithm; rather it is a set of probabilities for what the qubit could be when it is measured. Thequantum gates change the characteristics of the particle, without requiring direct measurementof the particle. Put a number of these gates together, and we get a circuit – essentially, analgorithm. Once the gates have operated on the qubit, the qubit is measured so that the rangeof probabilities collapses to provide an answer. Crucially, these gates must be reversible. In aclassic gate, two inputs might lead to one output – for example, in an AND gate, 0 and 0 outputs1; and 1 and 1 outputs 1. All other combinations output 0. But if we know an output is

Quantum Leap Dr. Owen Rogers, Research Vice President, Cloud Transformation James Sanders, Analyst, Cloud Transformation Rachel Dunning, Research Associate Matthew Utter, Research Associate Quantum computing would make a profound impact to society’s viewpoint of what is possible, pa