Camberley U3A Science & Technology. Quantum Computing

Transcription

1 Camberley U3A Science & Technology Quantum Computing 1

2 Traditional Computing! Digital computing 1s and 0s binary! A sequence of arithmetic or logical operations which can be changed readily, allowing the computer to solve more than one kind of problem! A series of instructions that act upon data not known in full until the programme is run.! Turing machine - a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a computer s central processor.! Van Neumann architecture a conceptual model of a computer architecture! This PC can play HD videos. It has to process 1920 pixels (dots) on each of 1080 lines. Each pixel can be any one of about 250,000 colours. And it has to do this at least 25 times per second. That is up to12,000,000,000,000 possible combinations a second.!! So, what s the problem? 2

3 Why quantum computing?!! Traditional computing is nearing the limits of what is possible using current semiconductor manufacturing technology! Moore's law - Gordon Moore, co-founder of Intel, observed in a 1965 paper that the number of transistors in a dense integrated circuit doubles approximately every two years! Although this trend has continued for half a century, Moore's law may soon not apply it is predicted that growth will slow from the end of 2014, when transistor counts and densities are to double only every three years, with further slowdown soon thereafter. 3

4 Semiconductor development! Existing PC chips are manufactured at atomic levels of scale! The typical half-pitch on most new computers (i.e., half the distance between identical features in an array) for a memory cell on current microprocessors is 22 nanometres. Intel have just (September 2014) introduced 14nm processors! Just how small is nano? In the International System of Units, the prefix "nano" means one-billionth, or 10-9 ; therefore one nanometre is one-billionth of a metre. It s difficult to imagine just how small that is, so here are some examples:! A sheet of paper is about 100,000 nanometres thick! A strand of human DNA is 2.5 nanometres in diameter! There are 25,400,000 nanometres in one inch! A human hair is approximately 80, ,000 nanometres wide! A hydrogen atom is about 0.1 nanometres in diameter, and a gold atom is around 0.3nm. The atoms used in silicon chip fabrication are around 0.2nm.! So current technology 14nm - is working at detail levels of around 70 silicon atoms, and 4000 memory cells (each comprising several transistors) is equivalent the width of a human hair. 4

5 Semiconductor manufacturing processes! 10 µm 1971 Integrated circuits! 3 µm 1975! 1.5 µm 1982 IBM PC! 1 µm 1985! 800 nm 1989! 600 nm 1994! 350 nm 1995! 250 nm 1997! 180 nm 1999! 130 nm 2002! 90 nm 2004! 65 nm 2006! 45 nm 2008! 32 nm 2010! 22 nm 2012 Intel Core i5 and i7, up to 9 million transistors per mm 2! 14 nm 2014 Intel Broadwell processor family (was delayed by manufacturing difficulties)! 10 nm 2016! 7 nm 2018! 5 nm 2020 may never be reached due to cost, complexity and quantum effects at the subatomic level. 5

6 Why do we need more powerful computers?! Examples:! Making sense of trends in huge volumes of data! Optimisation of large databases! Best fit solutions! Cryptography and security; factoring large numbers eg x3907! Weather forecasting! Medical data! Radiotherapy ; calculating how to treat the problem whilst minimising damage to surrounding tissues! Modelling proteins! Machine learning, recurring patterns in data, images etc.! Modelling atomic physics! Simulation of chemical processes! Complex space, astronomy and engineering simulations! Database searches! Video compression! Air traffic control! Positioning systems like GPS but better! Courier and post routing optimisation!... 6

7 What does Quantum mean?! In Latin, quantum is the neuter form of quantus, or "how much."! The word entered the English language in the 16th century, meaning a discrete amount of something! It became almost permanently associated with physics when Max Planck, Albert Einstein and their colleagues began developing the field of quantum mechanics.! Those scientists even invented the verb, "quantize," which they introduced in 1922 to describe the process of subdividing energy into small, measurable increments. 7

8 Subatomic weirdness! What we think of as solid is in fact mostly empty space! Physical laws we are familiar with do not necessarily apply at the subatomic level! Particle = wave = particle! An electron can be in many different places simultaneously! Particles can spring in and out of existence! There could even be multiple parallel universes... 8

9 Subatomic particles & Newton s laws! In general, the behaviour of the sub-atomic particles cannot be described by Netwon's Laws, which in the larger-scale world that we know describe the relationship between a body and the forces acting upon it, and its motion in response to these forces.! Newton's Second Law states that force = mass x acceleration. Knowledge of the positions and the velocities of all the relevant particles at a specific moment of time allows to predict the positions and the velocities at any other time.! The laws which govern the behaviour of sub-atomic particles are completely different. It is impossible to assign a specific position and velocity to a particle.! Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.! Stuff that makes up the universe is only brought into existence when you observe it (interact with it).! Each particle can be in a superposition of different states, which means that in some sense it is located at the same time in a whole region of space and has a whole range of velocities. If you measure the position (or the velocity) of the particle, you just get one of the values from that range, at random (possibly with different probabilities for each value). However, this is NOT because the particle actually HAD that position and you just hadn't known that, but the particle really HAD a whole range of positions the moment before the measurement. 9

10 Quantum mechanics! A particle can be in several different states simultaneously! Wave-particle duality: sub-atomic particles (electrons, neutrons and others) can behave like waves and show interference.! Consider a particle source aimed towards a wall with two slits through which the particles can pass, and a detecting screen beyond this wall. First we allow the particles to pass only through one of the slits, and then only through the second one. In a third experiment, the particles can pass though both the slits. When looking at the results, the results of the last experiment seem to be completely unrelated to the results of the first two. This happens because when particles are allowed to pass through both slits it's not that some of them pass through the first slit and some of them through the second one, but in some sense each particle passes through both of them. On the detecting screen we see a picture identical to one which is obtained from interference of waves.! Behaviour of sub-atomic particles is described by the theory of Quantum Mechanics.! A system (sometimes a single particle) can be described by a wave function (or by a vector in a multi-dimensional space). The information contained in the wave function is just the weight of each possible state of the system (actually there is something more: the phase of each state). The wave function allows us to calculate the possible results (and their probabilities) of any measurement which can be performed on the system. The development of the wave function in time is described by Schroedinger's Equation. 10

11 Scary stuff, but is it relevant?! Actually, it is, very... All of the following make use of or depend on quantum effects:! Lasers! X-rays! Semiconductors! Mobile phones! MRI scans! PET scans! Light-emitting diodes, hence televisions! Electrical conductors! Nuclear power! Nuclear fusion! Radioactivity! Superconductors!... 11

12 OK, so what about computers?! Some of this weirdness is potentially really useful.! Superposition of states where a particle can be in multiple states simultaneously! Entanglement two or more particles can be entangled together so that if you know the state of one, you automatically know the state of the other! Teleportation quantum information can be communicated at the speed of light 12

13 How might a quantum computer work?!! Qubits!! Unit of quantum information, the quantum analogue of the classical 1 or 0 bit.! A qubit is a two-state quantum-mechanical system, such as the polarization of a single photon where the two states are vertical polarization and horizontal polarization. In a classical system, a bit would have to be in one state or the other, but quantum mechanics allows the qubit to be in a superposition of both states at the same time, a property which is fundamental to quantum computing.! This gives inherent parallelism and means massive scalability when compared with traditional binary! Qubits processing capacity increases exponentially 3 bits, 8 states, 100 Qubits, 1267 billion billion billion. (1 billion = 10 9 or 1,000,000,000)! 250 Qubits could store more bits of information than there are particles in the universe, AND perform logic operations on all of the bits simultaneously.! Bits power of ! 6 Gbyte memory = 8 x 6 x 10 9 or 48,000,000,000 bits of storage. Processing is separate. 13

14 Exponential growth!! If I offered you (this is hypothetical!!) one penny today, and doubled the amount I gave you each day for 30 days, (2p tomorrow, 4p the day after, and so-on) or alternatively offered you 10,000 as a lump sum which would you take? 14

15 Go for the first one! After 30 days you would have!!! 10,737,418 15

16 And in a bit more detail...! A classical computer has a memory made up of bits, where each bit represents either a one or a zero.! A quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or any quantum superposition of these two qubit states! A pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8. In general, a quantum computer with n qubits can be in an arbitrary superposition of up to 2 n different states simultaneously (this compares to a normal computer that can only be in one of these states at any one time).! A quantum computer operates by setting the qubits in a controlled initial state that represents the problem at hand and by manipulating those qubits with a fixed sequence of quantum logic gates. The sequence of gates to be applied is called a quantum algorithm. The calculation ends with a measurement, collapsing the system of qubits into one of the 2 n pure states, where each qubit is purely zero or one. The outcome can therefore be at most n classical bits of information. Quantum algorithms are often non-deterministic, in that they provide the correct solution only with a certain known probability. 16

17 Additional notes ( ed following the presentation)! It is rather difficult to best understand the computational advantages offered by superposition. Since any qubit can contribute both 0 and 1 to any given state, each time a single qubit is added to the computer the number of contributions to the total state doubles - effectively, the quantum computer acts like a number of traditional computers all calculating at once.! In a quantum computer, entangled states using many qubits are used. The computer is first prepared with all qubits in a simple state such a 0 (e.g., spinning one way, up or down). The qubits are then linked to one another via quantum 'logic gates' which cause the spin of one qubit to become entangled with another, the details being set by the algorithm or programme which the machine is running. The process continues, but the programme / algorithm is carefully designed so that when it is finished the qubits are once again disentangled - that is, they are in a simple state such as down or up (0 or 1). The final state of the whole collection gives the outcome of the computation. It can be read by making measurements on the qubits.! An example. In Shor's factoring algorithm, entanglement is used to allow two groups of qubits to store two sets of correlated numbers, Each number in the second group is given a fixed mathematical operation (such as exponentiation, the repeated multiplication of a base number) on the corresponding number in the first group. The quantum programme instructs the computer, through entanglement, to reveal a shared property of all the numbers in the second group - e.g., when they are all even, or all multiples of some unknown number. This information can be used to identify the prime factors of any integer.! Quantum algorithms such as Shor and Grover rely on the order in which operations are performed on two or more qubits.! In traditional silicon-based processors, current passes through semiconductor diodes and transistors. In a quantum computer, the superposition of quantum states are typically manipulated using lasers or magnetic fields.! What is an Algorithm?! Cambridge dictionary definition of 'algorithm':! A set of mathematical instructions that must be followed in a fixedorder, and that, especially if given to a computer, will help to calculate an answer to a mathematical problem! From Wikipedia:! 'Algorithm' stems from the name of a Latin translation of a book written by al-khwārizmī, a Persian mathematician, astronomer and geographer,. Al-Khwarizmi wrote a book titled 'On the Calculation with Hindu Numerals' in about 825 AD, and was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum (in English, "Al-Khwarizmi on the Hindu Art of Reckoning"). The term "Algoritmi" in the title of the book led to the term "algorithm" 17

18 Quantum computing - history of an idea! The 15 years after physicist Richard Feynman first floated the idea of a quantum computer saw the theory of quantum information advance.! 1981 Feynman argues that modelling the correlations and interactions of particles in complex quantum physics problems can only be tackled by a universal quantum simulator that exploits those same properties.! 1982 The no cloning theorem threatens hopes for quantum computing. It states that you cannot copy quantum bits, so there is no way to back up information. The plus side is that this makes intercepting data difficult a boon for secure transmission of quantum information.! 1984 Charles Bennett of IBM and Gilles Brassard of the University of Montreal in Canada develop BB84, the first recipe for secure encoding and transfer of information in quantum states (see "Quantum security", below).! 1985 David Deutsch at the University of Oxford shows how a universal quantum computer might, in theory, emulate classical logic gates and perform all the functions of quantum logic.! 1992 Superdense coding theory shows how a sender and receiver can communicate two classical bits of information by sharing only one entangled pair of quantum states.! 1993 Quantum teleportation protocols prove that you do not need to transmit quantum states at all to exploit their power: it is sufficient to possess entangled quantum states and communicate using classical bits.! 1994 Shor's algorithm indicates how a quantum computer might factorise numbers faster than any classical computer.! 1995 US physicist Benjamin Schumacher coins the term qubit for a quantum bit.! 1996 Grover's algorithm gives a recipe by which quantum computers can outperform classical computers in an extremely common task: finding an entry in an unsorted database.! 1996 Quantum error correction theory finally overcomes the no-cloning problem. Quantum information cannot be copied but it can be spread over many qubits.! With the problem of copying quantum bits finally solved, the main theoretical tools for quantum information processing were in place but the theories still had to be put into practice. 18

19 Algorithms make quantum effects usable!! Feynman! Shors algorithm! Grovers algorithm! Others!! All quantum computing algorithms could, it is believed, be implemented on classical computers. But they would require impractically large computing resources to run effectively. 19

20 So, important Quantum features are:! Superposition! Entanglement! Teleportation 20

21 Superposition! Quantum superposition is a fundamental principle of quantum mechanics! A physical system - such as an electron or a photon - exists partly in all it s theoretically possible states simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations 21

22 Quantum entanglement! Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a whole.! Measurements of physical properties, eg position, momentum, spin, polarization, etc., performed on entangled particles are found to be appropriately correlated.! For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counter-clockwise.! Because of the nature of quantum measurement, however, this behaviour gives rise to effects that can appear paradoxical: any measurement of a property of a particle can be seen as acting on that particle (e.g. by collapsing a number of superimposed states); and in the case of entangled particles, such action must be on the entangled system as a whole.! It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances. 22

23 Quantum teleportation! These phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen, describing what came to be known as the EPR paradox, and several papers by Erwin Schrödinger shortly thereafter.! Einstein & others considered such behaviour to be impossible, as it violated the local realist view (Einstein referred to it as "spooky action at a distance"), and argued that the accepted theories of quantum mechanics must be incomplete.! Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally.! Experiments have been performed involving measuring the polarization or spin of entangled particles in different directions, which demonstrate statistically that the local realist view cannot be correct. This has been shown to occur even when the measurements are performed more quickly than light could travel between the sites of measurement: there is no light-speed or slower influence that can pass between the entangled particles.! Recent experiments have measured entangled particles within less than one part in 10,000 of the light travel time between them. According to quantum theory, the effect of measurement happens instantly. It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds.! In May 2014, researchers from the Delft University of Technology in the Netherlands managed to teleport quantum information between two diamonds that were 3 metres apart. This is an early step towards quantum computing in the cloud and a quantum internet. 23

24 So that s easy then.! When can I buy one?!! Well, there are a few minor problems...!! Decoherence!! Engineering complexity, temperatures 24

25 Decoherence! One of the greatest challenges is controlling quantum decoherence collapse of the quantum state to classical behaviour.! This usually means isolating the system from its environment as interactions with the external world would cause the system to decohere.! However, other sources of decoherence also exist. Examples include the lattice vibrations and background nuclear spin of the physical system used to implement the qubits.! Decoherence is irreversible and must be tightly controlled, or avoided.! Decoherence times typically range between nanoseconds and seconds at low temperatures 25

26 Qubit examples! Ion traps use optical or magnetic fields (or a combination of both) to trap ions.! Optical traps use light waves to trap and control particles.! Quantum dots are made of semiconductor material and are used to contain and manipulate electrons.! Semiconductor impurities contain electrons by using "unwanted" atoms found in semiconductor material.! Superconducting circuits allow electrons to flow with almost no resistance at very low temperatures.! Photons! The position, polarisation or just number of photons in a given space can be used to encode a qubit. Though initialising their states is easy, photons are slippery: they are easily lost and do not interact very much with each other. That makes them good for communicating quantum information, but to store that information we need to imprint photon states on something longer-lived, such as an atomic energy state.! If we can nail that, quantum computing with photons is a promising concept, not least because the processing can be done at room temperature. In 2012, a team at the University of Vienna, Austria, used four entangled photons to perform the first blind quantum computation. Here a user sends quantum-encoded information to a remote computer that does not itself "see" what it is crunching. This may be a future model totally secure quantum cloud computing.! Cold atoms! Collections of many hundreds of atoms might make usable qubits when trapped, cooled and arranged using lasers in a two-dimensional array known as an optical lattice. The energy states of these atoms can encode information that can be manipulated using further lasers, as with trapped ions (see below). We've mastered the basic techniques, but making a true quantum computer from cold atoms awaits establishing reliable entanglement. 26

27 Qubits more examples! Nuclear spins! Nuclear spin states manipulated using magnetic fields were among the first qubits explored. In 1998, the first implementation of Grover's algorithm used two nuclear magnetic resonance qubits to seek out one of four elements in a database.! The great advantage of spin states is that they make qubits at room temperature, albeit with a very low initialisation accuracy of about one in a million. But the disrupting effects of thermal noise on entanglement means that nuclear-spin computers are limited to about 20 qubits before their signal becomes washed out.! A variant on the spin theme exploits nitrogen impurities in an otherwise perfect diamond (carbon) lattice. These introduce electrons whose spin can be manipulated electrically, magnetically or with light but scaling up to anything more than a couple of spins has proved difficult.! Atom-light hybrids! Cavity electrodynamics is a quantum computing approach that aims to combine stable cold atoms with agile photons. Light is trapped inside a micrometre-scale cavity and atoms sent flying through, with logical operations performed through the interactions of the two.! Initialisation is highly efficient, and the decoherence time allows 10 or so gate operations to be performed although scaling the technology up awaits reliable ways of entangling trapped cold atoms. Serge Haroche of the Collège de France in Paris, one of the pioneers of this approach, shared the 2012 Nobel prize in physics with trapped-ion researcher David Wineland! Topological states! This promising basis for a quantum computer has yet to get off the theoretical drawing board, because it depends on the existence of particles confined to two dimensions called anyons. These "topological" particles are peculiarly impervious to environmental noise, in principle making them excellent qubits. Particles such as Majorana fermions that fulfil some of the requirements of anyons have been fabricated in certain solids, but whether they are useful for practical quantum computing is still debatable. 27

28 Theory to practice! 1998! Los Alamos and MIT researchers managed to spread a single qubit across three nuclear spins in each molecule of a liquid solution of alanine (an amino acid used to analyze quantum state decay) or trichloroethylene (a chlorinated hydrocarbon used for quantum error correction) molecules. Spreading out the qubit made it harder to corrupt, allowing researchers to use entanglement to study interactions between states as an indirect method for analyzing the quantum information. 2000! In March, scientists at Los Alamos National Laboratory announced the development of a 7- qubit quantum computer within a single drop of liquid. The quantum computer uses nuclear magnetic resonance (NMR) to manipulate particles in the atomic nuclei of molecules of transcrotonic acid, a simple fluid consisting of molecules made up of six hydrogen and four carbon atoms. The NMR is used to apply electromagnetic pulses, which force the particles to line up. These particles in positions parallel or counter to the magnetic field allow the quantum computer to mimic the information-encoding of bits in digital computers.! Researchers at IBM-Almaden Research Centre developed what they claimed was the most advanced quantum computer to that date. The 5-qubit quantum computer was designed to allow the nuclei of five fluorine atoms to interact with each other as qubits, be programmed by radio frequency pulses and be detected by NMR instruments similar to those used in hospitals. Led by Dr. Isaac Chuang, the IBM team was able to solve in one step a mathematical problem that would take conventional computers repeated cycles. The problem, called orderfinding, involves finding the period of a particular function, a typical aspect of many mathematical problems involved in cryptography. 28

29 ... continued! 2001! Scientists from IBM and Stanford University successfully demonstrated Shor's Algorithm on a quantum computer. Shor's Algorithm is a method for finding the prime factors of numbers (which plays an intrinsic role in cryptography). They used a 7-qubit computer to find the factors of 15. The computer correctly deduced that the prime factors were 3 and 5.! 2005! The Institute of Quantum Optics and Quantum Information at the University of Innsbruck announced that scientists had created the first qubyte, or series of 8 qubits, using ion traps.! 2006! Scientists in Waterloo and Massachusetts devised methods for quantum control on a 12- qubit system! Quantum control becomes more complex as systems employ more qubits.! 2007! Canadian startup company D-Wave demonstrated a 16-qubit quantum computer. The computer solved a sudoku puzzle and other pattern matching problems.! Sceptics believed that practical quantum computers are still decades away, that the system D- Wave has created isn't scalable, and that many of the claims on D-Wave's Web site are simply impossible (or at least impossible to know for certain given our understanding of quantum mechanics). 29

30 ... and more! 2009! A team at Yale created a basic solid-state quantum processor.! They used a two-qubit superconducting chip to successfully run simple algorithms. An important advancement was that before this, scientists didn t manage to get a qubit to last longer than a nanosecond, but the Yale qubit lasted a microsecond. The quantum processor was made using solid state electronics, unlike the NMR implementations. Artificial atoms were used, which could be placed in the superpositional state that quantum computers need.! 2011! D-Wave Systems announced a ten-million dollar commercial quantum computer, with a 128-qubit chipset that performs a task known as discrete optimization. At the time the company received much criticism from scientists, who argued that the computer isn t really a quantum device, due to the lack of demonstrations of the inner workings of the computer.! 2014! Two research teams working in the same laboratories at UNSW Australia have found distinct solutions to a critical challenge that has held back the realisation of super powerful quantum computers.! The teams created two types of qubits that each process quantum data with an accuracy above 99%.! A group of UC Santa Barbara physicists has moved one step closer to making a quantum computer a reality by demonstrating a new level of reliability in a five-qubit array. 30

31 Error correction! Current computers make mistakes - a bit can be buffeted by a voltage spike or a passing cosmic ray, changing it from a 0 to a 1, say. Processors deal with this by keeping copies! This isn't an option for qubits, thanks to a law called the no-cloning theorem.! Fortunately there are error correction algorithms to get around this. The drawback is that these need a lot of qubits, anything between 100 and 10,000 times as many as needed for the actual computation you're trying to perform.! The ability to assemble arrays of qubits for error correction has come on leaps and bounds. And error rates have been creeping downwards too. In June 2014, IBM unveiled error correcting code that is well suited to the large arrays of qubits expected to outperform regular machines. Essentially we're where we need to be to start building interesting quantum computers. 31

32 D:Wave! 2013! Google bought one. So did Lockheed Martin, one of the world s largest defence contractors. And NASA.! D:Wave calls their system the world s first quantum computer that will lead to huge advances in mathematical calculation. But many of the world s experts argued that the D-Wave machine was something other than the computing holy grail the scientific community has sought since the mid-1980s.! The argument will continue. But in 2013, researchers at the University of Southern California published a paper that comes that much closer to showing the D:Wave is indeed a quantum computer. USC houses and operates the D:Wave system owned by Lockheed, and the researchers led by Daniel Lidar, a professor of electrical engineering, chemistry, and physics say they have at least shown the machine is not using a computing model known as simulated annealing, which obeys the laws of classical physics (the physics of everyday life) rather than the more elusive properties of quantum physics.! [Our research] rules out one type of classical model that has been argued as a proper description of the D:Wave machine, Lidar says. A lot of people thought that when D:Wave came on the market their machine was just doing that, [but] we ruled that out. 32

33 The future! Currently, it s research so no definite timescales for volume commercial systems. But see the next slide!! Personally, I hope that I will see commercial realisation in my lifetime. (Same for fusion)! Fusion has always seemed to be 30 years away but Lockheed Martin has just announced a technology which it says can be viable and commercially available within 10 years.! So, we ll see! 33

34 Quantum computer buyer s guide (from New Scientist) 34

35 D:Wave respond to New Scientist...! Quantum computing From Colin Williams, D-Wave The world of quantum computing is complex, and while we appreciate Michael Brooks educating audiences on the various efforts, there were some misconceptions made about the D-Wave system in his article (18 October, p 43).! In particular, the article's table "Which quantum computer is right for you?" indicates that the D-Wave machine is only suitable for optimisation finding the best solution to a given problem and cannot perform other computations such as integer factorisation.! In fact, our machine has been used to perform optimisation, sampling, machine learning and constraint satisfaction. Although our machine cannot run Shor's algorithm, it has factorised integers tens of thousands of times larger than the integers factored by any other quantum computer currently available.! We were also given the lowest score on your "quantumness" category despite the fact that we recently published a peer reviewed paper (Physical Review X, doi.org/w46) demonstrating a world record for the number of superconducting qubits entangled. It was said that we cannot perform error correction, when, in fact, we can.! Finally, suggesting that the other quantum computers are all "easier to use" than our computer is a significant stretch. Our machines come with an interface that allows them to be programmed in Python, MATLAB, or C++ from any internet-connected computer in the world, and our users have harnessed this interface to demonstrate by far the widest range of applications yet achieved on any type of quantum computer.! Although quantum computing is still in its infancy, D-Wave has been a leader in the field, driving forward innovation on a scale that most said was impossible. Our technology is being used by commercial customers today something that cannot be said about any of the other efforts reflected on in the article. Vancouver, Canada 35

36 Useful links! Station Q Microsoft! Google and NASA's Quantum Artificial Intelligence Lab! D:Wave! IBM! Quantum: A Guide For The Perplexed! Quantum Life: How physics can revolutionise biology! Both by Jim Al-Khalili and others! 36

37 Thanks for listening!! Any questions? 37