
CHAPTER TWO – WHAT IS QUANTUM COMPUTING?
Terminology
Before delving into the intricacies of quantum computing, we must first address a matter pertaining to the nomenclature utilised in this text. At various points, by way of comparison, we will refer to a “classical computer”, meaning the computers that we are familiar with and use day to day (which includes supercomputers). These are distinct from quantum computers. You may find when you read more widely on the topic of quantum computers various terms are used to refer to a classical computer – digital, conventional and even analogue. There is much discussion over the appropriate term to use. Some argue that “digital computers” are a misnomer, given the computers we use day to day have not worked in standard digital form since the 1940s as modern computers use binary rather than decimal form. Strictly speaking “quantum” is the opposite of “analogue” but in the context of quantum computing it refers to specifically to computers which harness the power of quantum particles. In this book, we assign no significance to the use of the term classical computer, save to denote the kind of machines with which we are all familiar.
This book focuses on quantum computers specifically.[1] In various pieces of legislation, which we will explore in greater detail later in this book, “quantum technologies” are referred to. Quantum technology is a much broader term which does not yet have a universally accepted meaning.[2] Quantum computing is a branch of quantum technology. Quantum technology more broadly refers to a field of engineering and computer science which harnesses the power of quantum mechanics but results in a broader range of technologies than just computers, for example creating quantum batteries or sensors. Therefore, while quantum technology encompasses quantum computing, the terms should not be used interchangeably.
What is a quantum computer?
A classical computer is a device that, by virtue of being dependent on electronics (which focuses on the behaviour of electrons), is dependent on quantum physics. However, largely they do not harness the power of quantum particles in the way that quantum computers do.[3]
On the other hand, a quantum computer harnesses the special properties of quantum particles in order to perform certain operations. As a result of those special properties, it is possible to not only perform computational calculations faster than a classical computer, but also to carry out tasks that would not be possible with a classical computer.
This history of quantum computing, how a quantum computer is built and how they might work in practice, is addressed in greater detail below. It is worth noting at the outset that the below is intended to give a sense of how quantum computers may be designed and operate, in order to grasp a little of how they differ from classical computers. This is done at a high-level not only because as lawyers we are not trying to design quantum computers ourselves, but more importantly because the rate of development is quick. What is intended to be current as at the time of writing, will likely be different in the months and certainly years that follow.
Therefore, we hope the following discussion gives an insight into the differences between classical and quantum computers and, by virtue of how they are designed and may operate, the legal issues which arise in respect of quantum computers that may differ from classical computers.
Short history
We live in a quantum world. Quantum physics and quantum mechanics shed a light on our understanding of how our world operates. Quantum theory or quantum mechanics developed in part for scientists to be able to account for some physical phenomena that were inherently uncertain. This context is an important backdrop to the development of quantum computers.
In 1981 Professor Richard Feynman gave a keynote at MIT.[4] Feynman suggested that a computer could be built to simulate the probabilistic nature of quantum interactions which would make it a more realistic model for quantum behaviour. Classical computers struggle in simulating quantum behaviour partly because of the difficulty in reproducing randomness. Feynman’s lecture therefore proved an important point in the development of quantum computing.
Fast forward to 2018 onwards and many companies are competing for what is known as quantum supremacy or quantum advantage. We return to this concept later in this chapter.
Therefore, in understanding what quantum computers are, and how they work, it is important to remember that quantum computers were conceived of, at least initially, as a way to understand quantum physics itself. This is therefore relevant to considering not only how they work but how users can utilise these computers and their capabilities.
Benefits
Before addressing how a quantum computer may be built, we address at a high level what the benefits are. The practical significance and use cases of quantum computers are explored in greater detail later in this next chapter of this book.
It is worth noting the limits on the exponential growth possible with classical computers. Those familiar with Moore’s Law will know it states that the number of transistors that can fit on a silicon chip doubles every two years. Quite simply, there are limits on the exponential improvement possible with classical computers. Therefore, it is worth keeping in mind as we address the benefits of quantum computers, this general context that there is a limit on how much classical computers will ever be able to develop and improve.
At a high level there are two key advantages to quantum computers. The first, is the ability to carry out a computational task far quicker than a classical computer and the second is the ability to perform tasks that are beyond the capability of a classical computer. The line between the two can, on occasion, be hard to distinguish i.e. can a quantum computer perform a task because: (i) it is able to perform a task exponentially faster (i.e. making intractable problems tractable); or (ii) because quantum computers are actually performing the task in a different way.
It would be a mistake to believe that quantum computers can perform a task that classical computers cannot merely because they are faster. That is not the case. Quantum computers can also perform tasks that classical computers cannot by virtue of the fact they harness the power of quantum particles and therefore are better suited to certain tasks. It is not the case with comparing a computer that merely has greater computational power by virtue of enhanced speed. We address each benefit in turn below.
Turning to the first key benefit – speed. For certain problems, digital computers are unable to give a useful answer in a realistic time scale because the number of possibilities to assess are too great. However, quantum computers can represent multiple states at once and therefore provide answers in a realistic and useful timeframe in response to those questions.
There is of course a drawback to speed, which many readers will be aware of, which is the impact on internet security. This point is explored in greater detail in Chapter Five, which covers security breaches and data protection.
The second key benefit is solving problems that are beyond the reach of classical computers. Simulations are one example where quantum computers offer the potential for significant advances. For example, the European Patent Office commented in its decision in Pedestrian Simulation [2021] E.P.O.R. 30, which relating to the patentability of computer-implemented simulation of pedestrian flows in architectural designs, at paragraph 115 that “[s]imulations may even require computer power which is not available from a standard computer (for example, quantum computing could be necessary for turbulence or molecular simulations).” It is worth adding that it is not just a question of computational power but also the distinct way in which quantum computers approach simulations of, for example, molecules, which make them better suited to these tasks. For example, classical computers cannot accurately calculate how atoms combine to create important chemical reactions. Robert Sutor, vice president of IBM, often makes the following comparison: for a classical computer to re-create a one-to-one simulation of a simple molecule, like caffeine, it would require 1048 bits of information. To put that figure in context, that represents 10% of the number of atoms making up planet earth.
Hence, classical computers cannot successfully simulate even simple molecules. Classical computers often rely on approximations to simulate complex systems like atoms. While a single hydrogen atom can be solved relatively easily, adding more electrons, like in helium, makes the calculations exponentially more complex. Quantum computers, like Google’s Sycamore, have shown promise in simulating these systems more accurately, as demonstrated by its simulation of a 12-atom hydrogen chain.[5] At scale, it is anticipated that fully operational quantum computers could be 100 million times faster than today’s classical computers and even taking supercomputers, at least 3,500 times more powerful.[6]
The use cases are wide including in pharmaceuticals (addressed in Chapter Three on the practical significance of quantum computers below) where simulating complex biological and chemical processes. For example, trying to model the penicillin molecule with a classical computer would take 1086 bits of computer memory. This is beyond the capability of a classical computer but within the capability of a quantum computer.
Finally, it is worth noting that quantum computers are not intended to replace classical computers. They are not being designed to have that effect. The first point is that classical computers are relatively robust machines that execute well the tasks we require. Even turning to specialist functionality, quantum computers will most likely require classical computers to support their specialised abilities and so classical computers, even in the dominion of the quantum computer will remain important and relevant. For example, a research group at IBM is collaborating with bankers JPMorgan Chase & Co.[7] The objective is to develop a quantum algorithm in order to accelerate pricing options. While it utilises quantum computing, it is based on IBM’s cloud-based computing service. It is therefore a combination of classical and quantum computing.
Furthermore, IBM Quantum Platform (previously known as IBM Q Experience) is a publicly available service whereby users can access quantum computers via a cloud-based service.[8] Readers of this book may be interested in trying out the IBM Quantum Platform to browse tutorials but also to run experiments and explore use cases. However, again the pertinent point is that this indicates at least in the near to middle future access may be via the cloud for quantum computing where the quantum computer itself is located in a specialist environment (with appropriate cooling and vibration controls).
Qubits and building a quantum computer
John Preskill asked two key questions in 1998: [1] do we want to build quantum computers and [2] can we build them?[9] This section deals with that second question. There is not a universal method of building a quantum computer. However, from the point of view of lawyers, what this section seeks to achieve is an understanding of the basic building blocks and methods that are being explored to answer Preskill’s second question.
Fundamental unit – quantum/bit
Bits in classical computers are binary in nature in that they are represented by either a “0” or a “1” (“classic bits”). Classic bits are therefore open or closed and are a traditional logic gate. Each bit is a small circuit. These circuits are typically comprised of one or more transistors and a capacitor (a component that holds an electrical charge which represents 1, or no charge which represents 0).
Quantum computers are constructed using a basic unit of operation which is not limited in the way that classic bits are. A quantum bit, known as a qubit,[10] is based on a quantum particle for example an electron or photon. Typically it is measured in terms of spin or polarisation. In contrast to classic bits, a qubit is not binary, it can be a 0 or 1 (as with a classical computer) but can also be any linear combination of the two (superposition). It is therefore in an intermediate state with a potentially infinite set of possibilities of which state it is in. This is a fundamental and crucial difference between a classical and quantum computer.
The practical significance of this difference is that a quantum computer can conceive of more than one result at any particular moment in time. Three conventional bits can store any one number between 0 and 7 (binary 000 to 111). However, three qubits can make use of all eight numbers simultaneously. A binary string of eight bits, also called a byte, can represent any of 256 possible values. We will return to the number of possible values that classic bits can hold versus quantum bits in the context of superposition.
While currently quantum computers are largely used as effectively a compute unit for classical computers, it is possible to programme a quantum computer and therefore utilise the unique logic gates that go beyond the capability of a classical computer.
Those familiar with the workings of classical computers will wonder what coding language a quantum computer uses. In short, in classical computers, source code is run through a compiler (a program which converts source code into assembly language). The result is then run through another program which generates executable code. In quantum computers no standardised program has emerged. It may be that given quantum computers can be neatly represented by matrices that there may be resurgence in a variant of APL, as some commentators in the industry have speculated, but this is yet to be seen.
Quantum theory
At a high level, the theory behind quantum computers is that storing information in a superposition of states and manipulating their value (using quantum interactions such as entanglement) allows for new types of algorithms.
Understanding the theory behind how quantum computers work is difficult and in itself merits a book, indeed many books. As a lawyer, it is not necessary in order to explore the issues below to understand the theory behind quantum computers in granular detail. However, there are a number of key concepts which are useful to understand, even at a high level, in order to understand why quantum computers are different to classical computers and accordingly, the distinct legal issues that stem from them.
There are a number of key concepts that underpin how quantum computers work and how they differ from classical computers, these are [1] superposition, [2] entanglement, [3] sum over paths and [4] tunnelling. The first two are particularly important and therefore are addressed in greater detail below.
Superposition
A key element of classical computers is that they analyse information in a binary way using either ones or zeros. This is a fundamental difference to the way that quantum computers operate and is crucial in understanding the potential power of a quantum computer.
In a quantum computer the range of possibilities for the state of a qubit is greater before it is measured. When the quantum spin of a particle is measured, it only be either “up” or “down”. However, the before the particle is measured, it is in a superposition of states – it is therefore both up and down at the same time. Therefore, only probabilities exist.
Many readers will be familiar with Schrodinger’s Cat and therefore the idea, at a very high level, that it is not possible to know the state of something (in that case a cat) until a measurement is made. Perhaps an easier way to conceptualise superposition is to imagine a spinning coin; before the coin is observed and a measurement made, all that exists are possibilities as to what state the coin is in.
Logic gates operate in a different way in quantum computers versus classical computers. Classical computers have circuits that as act as logical gates performing a function such as NOT or AND. Quantum gates are more complex, as they operate on multiple possibilities at any one time. However, quantum gates can perform many calculations at once and, unlike classic logic gates (apart from NOT), quantum gates are reversible.
Entanglement
Entanglement is an important part of connecting a quantum computing system. In short, a change in one particle is instantly reflected in another particle. This occurs even if the particles are separated by large distances. For example, if one particle is measured as spin down, the other particle would instantly become spin up.
Accordingly, each time another qubit is added, it interacts with the previous qubit and so the number of possible interactions doubles. The practical impact is an exponentially powerful computer.
Entanglement improves the processing speed of quantum computers because it allows them to manipulate many qubits in a single operation, instead of manipulating each qubit individually.
It is worth mentioning that entanglement is often misunderstood and often explained incorrectly in articles. It does not allow actual information to be transmitted faster than the speed of light because the results of quantum measurements are random, so it will never be able to overcome the delays involved in contact with deep space missions. For example, if communications are being sent as between Earth and Mars the results will not be instantaneous and will take around twenty minutes depending on the relative positions of Earth and Mars in their orbits.[11]
Methods of building a quantum computer
In theory any quantum particle could be used. However, in practice simple particles are selected on the basis that they are easier to deal with. For example, photons and electrons as opposed to a water molecule. A few benefits of photons are that they are relatively easy to produce in controlled environments, are plentiful and are the easiest to get into an entangled state. Electrons are also a good choice as we are familiar with electrons (given our knowledge of electronics). However, each have their drawbacks in practice. Larger quantum particles have also been used including ions. IonQ system makes using of ytterbium ions.[12]
In terms of specific methods based on the above:[13]
- Superconducting quantum computers. An example is Sycamore, which is discussed in the section below in the context of the race for quantum supremacy. The advantage is that they use silicon as a base, which has been used in industry for decades. By cooling circuits to near absolute zero, they enter a quantum state where electrons can exist in multiple states simultaneously. When these circuits are connected, they can become entangled, enabling quantum calculations. A major drawback of this method is the complex system of tubes and pumps required to cool the machine to extremely low temperatures. This increases costs and introduces potential complications. Even the slightest disturbance or impurity can disrupt the coherence of the circuits. One solution is to use multiple qubits to create redundancy and reduce errors, but this comes at the expense of significantly higher costs.
- Ion Trap Quantum Computer. When an electrically neutral atom loses electrons, it becomes a positively charged ion. Ions can be trapped using electric and magnetic fields, and multiple ions can vibrate coherently as qubits. The spin of the electron determines the qubit state (0 or 1), allowing for superposition. However, scaling up the number of qubits is challenging, as maintaining coherence requires constant readjustment of electric and magnetic fields, making it a complex process.
- Photonic Quantum Computers. Photonic quantum computers use light’s polarisation to represent 0 and 1. While they offer advantages like speed and the ability to operate at room temperature, their complex setup and difficulty in interacting photons limit their scalability and practicality.
- D-Wave Computers. D-Wave, a Canadian company, is developing quantum annealing, a specialised type of quantum computing. D-Wave has built machines with up to 5,600 qubits and plans to increase this to 7,000 in the near future, surpassing other current designs.[14] Though they are not general purpose quantum computers, they can solve certain problems very quickly.
The inner workings of these methods are beyond the scope of this book save to note that the relevance for lawyers is that there is not a universal method for building a quantum computer. There are advantages and disadvantages to each of these methods and therefore the risks and benefits regarding each needs to be evaluated depending on the technology used.
Quantum algorithms
With a classical computer the hardware is often considered first. However, with quantum computing, quantum algorithms have existed well before quantum computers were able to, or indeed can, run these algorithms. It has proved possible to devise algorithms for quantum computers which, should a reliably functioning quantum computer be built, could revolutionise the world of computing. The patentability of quantum algorithms is discussed in the chapter dealing with quantum computers and intellectual property below.
A few examples are explored in this book to give a flavour of the type of use cases that will arise in practice. For example, an algorithm known as Grover’s quantum search algorithm makes it possible to carry out “fuzzy” searching (a genuine technical term).[15] In terms of the practical application, while search engines operate at generally impressive speeds, they rely on inputting relatively precise search terms in order to reach the desired result. However, this is different to the usual pattern making that most humans use day to day.
Taking an example, if the authors wanted to locate the address of a “red brick building in London with flower boxes, black boards with barristers’ names to the right and left of a white framed door. The building itself is located in a courtyard which is adjacent to the lane where Mary Poppins Returns was filmed” this would not yield the result 4 Pump Court in a Google search. However, this is the kind of pattern matching our brains are used to. It is also the kind of fuzzy searching which Grover’s algorithm handles well. It completes a search using just the square root of the number of operations of a classical search, thus speeding up the ability to provide a useful result exponentially faster than a conventional computer. This would have practical applications not just for search engines but also quantum machine learning.
Shor’s algorithm is another example of a quantum algorithm which is discussed in more detail in the chapter on the practical significance of quantum computing and in the chapter on security breaches and data protection.
Challenges of building a stable quantum computer
Building a stable quantum computer is one of the greatest practical challenges facing those designing quantum computer systems. There are two core issues [1] ensuring qubits stay in a stable state and [2] transferring information in and out of the computer.
One of the major issues in building a stable, and therefore useful, quantum computer is reducing the risk of errors or incorrect information. If you take expressing the probability of weather with a classical computer, weather forecasting is difficult because the underling system being studied (weather) is chaotic in terms of the calculations that take place due to shifting variable terms. Quantum computers are vulnerable to errors given the components are so sensitive and thus qubits can lose their quantum state. As a result, quantum computers can store or manipulate information incorrectly. The errors then accumulate over time. This in turn prevents them from executing algorithms (which are based on the premise of stable qubits unaffected by their environment) that are long enough to be of use. A system of error elimination or correction is therefore needed.
In order for a quantum computer to function reliably, the qubits need to remain in phase with each other but isolated from their surroundings (called coherence). Decoherence is used to refer to the effect where quantum particles, through their interaction with their environment (such as vibrations or temperature) lose their superposed state. Qubits are very sensitive and so even a minor disturbance can cause them to fall out of coherence and so render the calculation unreliable. For superconducting qubits the ‘coherence time’ is typically only around a millisecond.
The computing industry is familiar with the need for specialist environments. Think for example of a traditional server farm. Therefore, similar consideration needs to be given to rectifying errors in quantum computers.
Google Quantum AI, along with its academic collaborators, have conducted research which was released in August 2024 which shows that adding components can reduce errors. The experiments were conducted using qubits based on superconducting circuits.[16] As noted above, previously adding more components tended to introduce more errors. However, this research indicates that error correction, as opposed to elimination, is viable method of building a reliable, and therefore useful, quantum computer.
In short, many methods of designing quantum computers have focussed on each unit of information being stored in a single physical qubit. However, Google’s research has focused on encoding each unit of information in multiple physical qubits. This group of multiple qubits is referred to as a single “logical” qubit. The benefit is that this logical qubit can hold information in a more robust form than a single physical qubit. Google’s research team then used an algorithm known as a surface code to correct errors. However, the number of qubits is large. Google demonstrated that a logical qubit composed of 105 physical qubits suppressed errors more effectively than a logical qubit composed of 72 qubits. However, Google and its researchers are yet to demonstrate they can scale up to a larger machine.
By way of another example, IBM (also using qubits made of superconducting circuits) is taking a different approach to error correction known as low-density parity-check code. It believes this will be easier to scale (as each qubit requires fewer physical qubits). By 2026, IBM plans on proving that it can create a system that uses 12 logical qubits out of 244 physical qubits.[17]
The key point to appreciate regarding error correction, from the vantage point of a lawyer, is that [1] quantum computers are, at least in their current form, susceptible to errors and [2] there needs to be a system for eliminating or correcting errors which is relevant to assessing the reliability of a quantum computer. For example, as explored in greater detail below, if two parties are contracting for the use of a quantum computer it will be relevant to consider what level of errors is acceptable and what degree of reliability one can expect from the quantum computer system.
Race for quantum supremacy or quantum advantage
The race for quantum supremacy and quantum advantage brings out some of the achievements, but also the limitations, of quantum computing, both at present and perhaps into the future.[18]
In September 2019 Google announced that its quantum computer, Sycamore, had achieved “quantum supremacy”.[19] In short, quantum supremacy is the short-hand term used to describe a quantum computer outperforming a classical computer. While a significant development, other technology companies competing in this area did note, somewhat fairly, the introspective nature of the task assigned to Sycamore. In simplified terms, Sycamore was tasked in proving whether the numbers it had generated as random were in fact random. Google stated this task would have taken the world’s fastest supercomputer 10,000 years. In 2020, the Quantum Innovation Institute at the Chinese Academy of Sciences stated that their quantum computer was 100 trillion times faster than an ordinary supercomputer.[20]
One way to view these announcements is that they do mark exciting developments in quantum computing. Other technology companies state they are aiming for quantum advantage whereby quantum computers outperform in respect of useful, rather than theoretical tasks. Setting aside the terminology, estimates vary between five and thirty years for when we may see quantum advantage being attained.[21]
It is not just private companies that are investing time and money in reaching quantum advantage. In December 2018, the US Congress passed the National Quantum Initiative Act.[22] Part of that initiative was to provide seed money to assist in research. In the UK, in July 2024 five hubs for the National Quantum Computing Centre (“NQCC”) were announced.[23] The NQCC focuses on research and innovation. They also engage with industry and researchers in drafting documents and surveys relating to quantum readiness. At a European level, the EU has invested heavily in quantum technology, launching initiatives like the Quantum Flagship and developing the European Quantum Communication Infrastructure.[24] These programs aim to advance quantum research and create a secure quantum communication network across all EU Member States.
Ethical considerations
There are a variety of important and engaging debates regarding ethical concerns surrounding quantum computers. These range from privacy concerns (stemming from, for example, the potential security risk posed by quantum computers), to concerns regarding national security (linked with the security risk) and environmental concerns (given certain designs for quantum computers require, for example, energy intensive cooling systems).
These issues are addressed throughout this book to the degree they are relevant to considering legal issues which practitioners may face in practice. However, this book does not purport to opine on the veracity or otherwise of these concerns or the balance to be struck between these competing concerns. Should readers be interested in exploring these issues further the various sources cited in the footnotes of this book explore those issues in greater detail.
Summary
In the preceding paragraphs we have discussed what a quantum computer is through the lens of history, the ways these machines work (or may work) in practice and the race for quantum advantage. As noted in the introduction, this is an area subject to significant change and development. However, the basic principles set out above should serve as both a useful guide to readers in the present, and in the future in exploring the legal issues that arise in respect of quantum computing. Before embarking on that discussion, we explore in a little more detail the practical significance of quantum computing as a way of providing a useful framework for considering the impact these computers will have on individuals and various industries.
MORE INFORMATION / PURCHASE THE BOOK ONLINE
[1] ISO/International Electrotechnical Commission C 4879:2024 (the “ISO/IEC 2024 Standard”) has developed a standard specifically for terminology and vocabulary for quantum computing. Edition 1 was published in 2024. The document defines terms commonly used in the field of quantum computing. The objective of the document is that it can be applicable to all types of organisations (e.g. commercial enterprises, government agencies, not-for-profit organisations) to exchange quantum computing concepts. Readers may find this a useful resource if drafting agreements relating to quantum computers. We return to this point later in the section dealing with risks to commercial parties and organisations.
[2] The IEEE have a working group which is developing standard terminology for quantum technologies more generally (IEEE P7130).
[3] Save in respect of arguably the use of quantum tunnelling in flash memory storage.
[4] Feynman, R.P. Simulating physics with computers. Intern. J. Theoretical Physics 21, 6/7 (1981).
[5] See ‘Google has performed the biggest quantum chemistry simulation ever’ published in New Scientist on 12 December 2019 available at https://www.newscientist.com/article/2227244-google-has-performed-the-biggest-quantum-chemistry-simulation-ever/.
[6] Page 7 of Jeffery Atik and Valentin Jeutner (2021): “Quantum computing and computational law, Law, Innovation and Technology” available at https://doi.org/10.1080/17579961.2021.1977216.
[7] See ‘11 Global Banks Probing The Wonderful World of Quantum Technologies’ in Quantum Insider (23 June 2021) available at https://thequantuminsider.com/2021/06/23/11-global-banks-probing-the-wonderful-world-of-quantum-technologies/.
[8] The IBM Quantum Platform is available at https://quantum.ibm.com/.
[9] John Preskill, ‘Quantum Computing: Pro and Con’ (1998) 454 Proceedings of the Royal Society of London A 469, 469.
[10] A portmanteau of quantum and bit.
[11] See https://www.physicsforums.com/threads/mars-landing-how-instantaneous-communication-was-possible.999911/#:~:text=The%20
time%20it%20takes%20for,travel%20from%20Earth%20to%20Mars.
[12] See IonQ’s website for further details https://ionq.com/technology.
[13] For a more detailed discussion of the various methods of building a quantum computer “Quantum Supremacy” by Michio Kaku (2023).
[14] See https://www.hpcwire.com/2024/06/18/qubits-2024-d-waves-steady-march-to-quantum-success/.
[15] Acampora, Giovanni & Luongo, Federico & Vitiello, Autilia. (2018). Quantum Implementation of Fuzzy Systems through Grover’s Algorithm. 1-8. 10.1109/FUZZ-IEEE.2018.8491579. For further reading on Grover’s underlying work see Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. “Physical Review Letters79”, 2 (1997) and Grover, L. K. A fast quantum mechanical algorithm for database search. In “Proceedings of the 28 Annual ACM Symp.” Theory of Computing, 1996. ACM, New York, NY, 212–219.
[16] MIT Technology Review, “The Download: quantum breakthrough, and the Internet Archive ruling” (September 2024).
[17] See “Google enhances quantum error correction technology” by Adam Campbell featured in Baseline (September 2024).
[18] The term ‘quantum practicality’ is also used. For a wider discussion on the terms used and the search to realise quantum advantage “Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantage” by Hoefler, Häner and Troyer (available at https://cacm.acm.org/research/disentangling-hype-from-practicality-on-realistically-achieving-quantum-advantage/) is a useful resource.
[19] See https://www.nasa.gov/technology/computing/google-and-nasa-achieve-quantum-supremacy/. The project was run in partnership with NASA and Oak Ridge National Laboratory.
[20] See https://www.tbsnews.net/tech/chinese-scientists-claim-have-built-quantam-computer-100-trillion-times-faster-japans-fugaku.
[21] See https://www.insidequantumtechnology.com/news-archive/quantum-cryptographic-threat-timeline. In 2023 the UK Government published its long-term quantum missions following the commitments made in its national quantum strategy policy paper, which it published in March 2023. There are five missions relating to quantum computing. While not necessarily an accurate reflection of what progress will be achieved, it is useful to note that the missions list 2030 and 2035 as the year by which the UK aims to have achieved its stated missions relating to quantum computing including by 2035 there will be accessible, UK-based quantum computers capable of running 1 trillion operations and supporting applications that provide benefits well in excess of classical supercomputers across key sectors of the economy and the UK will have deployed the world’s most advanced quantum network at scale, pioneering the future quantum internet.
[22] Public Law No: 115-368 (12/21/2018) available at https://www.congress.gov/bill/115th-congress/house-bill/6227#:~:text=
Shown%20Here%3A-,Public%20Law%20No%3A%20115%2D368,
(12%2F21%2F2018)&text=(Sec.,information%20science%20and%20
technology%20applications..
[23] See https://www.ukri.org/news/five-hubs-launched-to-ensure-the-uk-benefits-from-quantum-future/.
[24] See https://digital-strategy.ec.europa.eu/en/policies/european-quantum-communication-infrastructure-euroqci. In 2018, the EU also created the EuroHPC Joint Undertaking to enable the EU to become a world leader in supercomputing and quantum computing, by pooling the resources of participating EU countries and private partners. On 13 July 2021, the Council Regulation (EU) 2021/1173 established the European High Performance Computing Joint Undertaking and repealed Regulation (EU) 2018/1488.