**Rebecca Keating, building on her talk at last year’s Annual Conference, offers a novice’s guide to some of the key concepts of quantum computing, how near we are to practical quantum computing and the implications for lawyers .**

At first glance the image on you right may appear to be something from the next instalment of a sci-fi movie or a hat that C-3PO might have sported at the premiere of the latest edition of Star Wars. The most popular suggestion is that it resembles an odd, and yet strangely beautiful, chandelier. If you are in this category you are not far off. This is what IBM call a quantum chandelier, their nickname for a quantum computer.

The quick pace of development in this area means that by the time you read this article, it is likely to have been outpaced. However, I hope it offers a starting point for quantum computing novices to the concepts underpinning the technology, together with some musings on how quantum computers may ultimately revolutionise many industries and necessitate changes in the legal world as a result.

Why do we care?

Quantum computers will revolutionise the ways in which we currently work for two principal reasons:

1. The limits on the exponential growth possible with classic computers

Quite simply, there are limits on the exponential improvement possible with conventional or “classic computers”. There are limitations on both how energy efficient classic computers can ever be and on their physical size: for example, there is a minimum size below which their capabilities cannot evolve further. Quantum computers offer the potential to surpass these physical limitations and consume less energy while doing so.

2. Solving intractable problems

Secondly, quantum computers approach problems in a different way so they can solve problems that are beyond classic computers. They are not intended to replace classic computers: quantum computers will probably continue to rely on classical computers to support their specialised abilities. However, a quantum computer’s output can be quite distinct in a number of ways.

While speed is often cited as the main benefit of quantum computer they will not be universally faster. For example, the advent of quantum computers will not necessarily assist with the frustrating moment when Bake Off is loading slowly on your laptop.

Instead, by performing calculations simultaneously, the amount of time taken to obtain an answer to a complex problem is reduced which means they can resolve very complex problems in science, maths and engineering and push huge advances in areas such as AI, machine learning, climate change, medicine and large database searching: the popular example is cracking an “uncrackable” code. Quantum computers therefore present huge potential improvements for code breaking and cyber security.

What is a quantum computer?

There are several important operational differences between classic and quantum computers. Two of the most important concepts to have on your radar are superposition and entanglement. They are important because they begin to explain the power and scale of a quantum computer.

At the outset it is important to note that there are many ways to “build” a quantum computer. I will not attempt to provide a single explanation here as it would be subjective at best. However, it is clear that these two concepts - superposition and entanglement - are at the core to understanding the basics of quantum computers.

In order to explain them I will go back to basics slightly. I would rather avoid mentioning Schrödinger’s cat, Einstein’s dice and “spooky action at a distance” within the space of a paragraph as you may feel you have stumbled into a nightmare combination of a first-year philosophy class and quantum physics. So instead I will refer to a coin.

Superposition

Quantum computers work by manipulating quantum entities such as electrons, photons or single atoms.

It can help to use classic computers as a framework when we begin to consider how a quantum computer works. Classic computers store and manipulate information consisting of binary digits known as “bits”, represented by either 1 or 0. The quantum computing equivalent is the qubit; the quantum computer’s fundamental unit of information. Qubit, unsurprisingly, is a portmanteau of “quantum bit”.

Unlike the binary bits of the classic computer, qubits can, until they are measured, be in the state 0 or 1, both 1 and 0, or in a superposition of both states.

*a bloch sphere representation of a single qubit. The north and south poles of the sphere represent the |0) and |1) state (spin up/spin down). When the qubit is in a superposition of |0) and |1), the vector will point somewhere between the two on the sphere. *

Some people like to explain this superposition of both states by using the example of a coin. A classic bit, being a 1 or 0, is like the heads or tails on a coin. However, qubits are more akin to spinning coins: an observer asked whether a coin is heads or tails while it is spinning would not be able to answer.

This concept is known as the spin state. The direction of a qubit’s magnetic moment (“spin”) can point in different directions: up (high energy) or down (low energy) with respect to a magnetic field and, in the case of superposition, balanced between these two states.

In order to understand why this matters we need to look at the power of qubits. Two classical bits can represent numbers 0, 1, 2 to 3 in any of the four combinations 00, 01, 10 and 11. That is fairly simple. To represent all four numbers at the same time you would need four pairs of numbers, in effect one byte (so 8 bits). However, just two qubits can represent these numbers simultaneously.

This means that qubits can scale exponentially. Even on a small scale the difference is evident. A two-qubit machine allows you to do four calculations at once as we have discussed. A four-qubit machine gives you 16 calculations, all simultaneously.

On a larger scale, a properly constructed quantum computer with just 300 qubits could process as much information as a classical computer containing more transistors (2³°°) than there are particles in the known universe.

Entanglement

The second key concept is entanglement which is important for a stable quantum computer and unleashes the power of superposition.

Using the coin analogy, in the quantum world both coins could be entangled so that when one coin stops spinning the other coin will instantly land the same way: so both heads or both tails for example.

Remarkably, and provably, particles can behave as a single unified system even when they’re separated by immense distances. The current record distance for measuring entangled particles is 1,200 kilometres or about 745.6 miles. Applying this concept to qubits, when a qubit is measured it collapses it into a single state (1 or 0) so if it is entangled with another qubit, this measurement instantly causes the other qubit to reflect the same state, despite being separated by potentially large distances.

So what does this mean?

The combination of superposition and entanglement, along with other factors, reduce the number of calculations needed to carry out a complex process, making the quantum computer a potential game changer.

The example of Tianhe-2, which is one of the most powerful ‘classical’ computers on the planet, provides a sense of perspective. It cost $400 million, burns about 20 megawatts of electricity (enough to power 20,000 households) and has 3.2 million Intel cores. In comparison a single chip with about 50 to 60 qubits on it would be more powerful than the entire Tianhe-2 half-football-field-sized machine.

Where we are now?

Large companies such as Google, Intel and IBM down to smaller start-ups like D-Wave Systems, IonQ and Rigetti Computing are racing for quantum supremacy. At the same time governments, particularly the military and those interested in code breaking, are also investing a lot of money and resources into the quantum computing race. As an aside, this focus on on code-breaking has a poetic resonance with Alan Turing’s activities at Bletchley Park and his conceptual Turing machine.

Take for example the European Commission Quantum Technologies Flagship, a €1bn initiative which over the next ten years will provide funding to over 5,000 of Europe’s leading quantum technologies researchers. In December last year the US Senate passed the National Quantum Initiative Act which committed $1.2 billion to quantum information science research over the next five years. This figure might be dwarfed by the reported $10 billion being spent in China.

But how close are we to a commercial quantum computer? In January IBM announced the world’s first stand-alone commercial quantum computer the IBM Q System. However, the IBM Q System only has a 20-qubit processor, short of the 50 qubits that many researchers believe will be required to obtain the quantum computing crown.

It has been said that the qubit is the ultimate diva. There are countless hurdles, from cooling to reading qubits, that must be overcome in order to build a stable and reliable quantum computer. One of the main challenges is lengthening the time qubits can maintain their quantum state: this is known as “coherence”. Quantum computers are delicate machines and the state of coherence is the timespan in which a calculation may be performed. A full explanation of coherence itself merits a separate article but using the coin analogy, when a coin is in that delicate state between heads and tails any interference may mean that it will collapse into a state of either heads or tails. Where interference occurs to a qubit its ability to stay in a superposition of states or entangled is compromised. Such interference could be caused easily by, for example, changes in heat, light or vibrations. If decoherence cannot be eliminated, the quantum environment can be destroyed, resulting in errors and a loss of information and undermining the stability of the quantum computer.

Legal implications

Like all things in the quantum world there is a degree of uncertainty and so the full legal implications of quantum computing are, at the moment, unknowable. However, there are some obvious examples that we can begin to think about while we wait for the change that quantum computers will bring: errors, quantum brute force and blockchain.

Errors

As with all new technology there will be errors. At the moment the error rate in a quantum computer ranges from just 1% to 10%.

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_{Courtesy of IBM}

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The scale and speed at which a quantum computers operate means that such a level of error is a concern.

Error correction in quantum computers poses a particular challenge because if you measure a qubit directly, following Heisenberg’s uncertainty principle, you change the outcome. And all kinds of interference can easily modify the fragile state of the qubits stored in the machine.

From a litigation perspective, as well as a practical perspective of course, it will be important that the error rate and correction improves.

Quantum brute force

This is of interest from the perspective of the internet of things, securities, encryption and cryptocurrencies. For example, decryption of an RSA ciphertext (an algorithm used by modern computers to encrypt and decrypt messages) is currently infeasible because classic computers do not have an efficient algorithm for factoring large numbers. However, in 1994 Peter Shor showed that a quantum computer could be used to factor a number n in polynomial time (the time required for a computer to solve a problem), thus effectively breaking RSA (“Shor’s Algorithm”).

Given a quantum computer’s increased power, it could factorise codes at a rate that make cracking RSA cryptography possible in a matter of minutes. In theory the increased computing power of a quantum computer would render RSA obsolete, thus leaving vulnerable, for example, security systems of companies and cryptocurrency. In addition to security concerns, this would of course also raise privacy concerns.

However, the converse may also be true and quantum computers could promise great improvements in the world of cryptography. For example, a concept called quantum key distribution (“QKD”) might be more secure and so may lattice-based cryptography.

Blockchain

Bitcoin and blockchain technology rely on public key cryptography to maintain the security of the ledger. Moreover, bitcoin relies on the work of “miners” to use computing power resources to solve certain complex mathematical problems to verify transactions, a task that could be upended by entities with quantum computing platforms. This once again poses a security concern and threatens the integrity of blockchain. The need for quantum resistant algorithms, as referred to above, will therefore be of the utmost importance.

TEOTWAWKI?

So does quantum computing mean the end of the world as we know it? (I have been asked that exact question many times)

The answer is the same as we would have given for any huge advance in technology in history: yes and no. It depends what we do with it, who controls it and how we plan for it.

Quantum computers pose a challenge to our current systems but offer huge possibilities for developing and improving new systems.

The government has acknowledged both “the huge potential offered by quantum technology” whilst also acknowledging “the potential to break currently secure computer and telecommunications systems. It could also transform military power by giving vehicles and weapons systems substantial additional abilities” (see paragraph 3.36 of the Enterprise Act 2002 Changes to the Turnover and Share of Supply Tests for Mergers: Guidance 2018). In terms of developments at a government level:

- The Blackett review (November 2016), highlights the significant potential for quantum technologies, including quantum computers.
- In terms of national security and investment, proposed legislative reforms have raised the issue of quantum computing such as the government's powers for scrutinising investment for the purposes of protecting national security (which includes quantum technology as an area of advanced technology - see paragraph 30 of the government response to the first consultation).
- A memorandum of understanding on science, technology, and innovation between Canada and the UK aimed to accelerate the commercialisation of emerging technologies, grow domestic firms which will initially focus on a number of areas including quantum technologies.
- Reform last year to the Enterprise Act 2002 enables the government to intervene in mergers in relation to the “development and production of quantum technology” (see section 23A) where certain requirements are met.

There are therefore already some small steps being taken to make the UK quantum safe and quantum ready.

Conclusion

John Gribben said that if "the business of physics is ever finished, the world will be a much less interesting place in which to live.” In terms of the development of quantum computers this is certainly true. All this talk of coins, Schrödinger’s cat and Einstein’s dice really does herald huge potential for the future of computers. The real question will be how we respond and what can we achieve in the age of the quantum chandelier.

Published: 2019-04-10T10:00:00

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