## Where Quantum Computers Are Now and Where They Are Going Next

Professor Belal Ehsan Baaquie is a theoretical physicist now resident at the International Center for Education in Islamic Finance (INCEIF) in Kuala Lumpur, which he joined in 2016. He was for the previous 32 years at the National University of Singapore, where he specialized in applying quantum mechanics to financial markets. He spoke to Future of Finance co-founder Dominic Hobson about the near and long-term prospects for quantum computers.

**Hobson: **How long must we wait for quantum computers to be adopted and applied?

**Professor Baaquie:** 30 years have passed since the beginning of quantum computers in 1982, without, even now, any practical application. A linear progression would place applications in the distant future. However, progress in science happens through sudden discontinuous advances and hence a breakthrough can be expected. It is difficult to put a time scale on it.

**Hobson:** What engineering problems remain to be solved in quantum computing?

**Professor Baaquie:** The fundamental problem is that quantum qubits are very fragile, with the smallest disturbance breaking what is the called quantum superposition that is the basis of quantum parallelism – and which is responsible for the exponential speeding up of a quantum algorithm. The breaking of quantum superposition is also called decoherence. This is a hardware problem that needs basic understanding of quantum physics to obtain a solution.

**Hobson: **Do we have enough engineers with that basic understanding of quantum physics?

**Professor Baaquie: **The semiconductor industry (which had US$430 billion sales in 2019) requires quantum mechanics. The design of all semiconductor devices is based on quantum effects in materials. Semiconductor engineers could foreseeably master the physics of quantum computers if such an undertaking becomes sufficiently rewarding.

**Hobson: **Who – governments, venture capitalists, technology vendors and corporates – do you see investing in quantum computing at the moment and why?

**Professor Baaquie:** The United States has invested US$1.2 billion in 2019 over five years, and China is not far behind. The Singapore government has invested US$70 million in 2020 on a one-year horizon. Venture capital has invested US$300 million in 2020 compared to US$4 million in 2005: PsiQuantum has received US$215 million in investments and Rigetti has received US$190 million. Why? Governments are probably driven by geo-strategic considerations, whereas venture capital investments show that the market thinks a breakthrough in quantum computing applications is close.

**Hobson:** Quantum computers do not always give the right answer. Is that a fundamental problem or an engineering problem?

**Professor Baaquie:** The error in a quantum algorithm is a fundamental engineering problem that is linked to noise. For example, error correction can be achieved for a classical computer by sending three bits of 0 and 1 instead of a single bit; on receiving three bits, the average of the three bits is taken to correct for possible errors. There is also a phase (sign) that is carried by qubits when they are superposed and could flip its sign, and needs to be corrected. So a quantum qubit would need 3×3=9 qubits for error correction. If one adds the quantum decoherence of the fragile quantum-superposed state, it is estimated that one needs 50 qubits to obtain a single error free qubit. This is the formidable problem – posed by errors in transmission and by quantum decoherence – for a quantum computer.

**Hobson:** What does quantum computing cost at the moment – measured by, say, an hour of computing time – and will that cost fall over time?

**Professor Baaquie:** Rigetti apparently charges US$1,000 per hour for a 36-qubit system. One expects the cost of quantum computing to fall, but again predictions are difficult to make as to when breakthrough technologies will occur that lower the cost.

**Hobson:** Is a hybrid of quantum and digital computing the immediate solution or the long-term path forward?

**Professor Baaquie: **Hybrid computing is currently one of the favoured approaches, with parameters provided by a classical algorithm and the simulation being carried out on a quantum computer. In the long run, there is no need for hybrid computing since classical computers are a special case of the quantum computer and its algorithms can be factored into the quantum algorithm. Since qubits are much more expensive than classical bits, hybrid algorithms are a matter of cost efficiency.

**Hobson:** Are quantum computers indifferent to the physical substrate or device they run on?

**Professor Baaquie:** Most quantum computers are devices that can support qubit states. Currently, the preferred device for a qubit is the Josephson junction. This is a two-state system based on a superconductor and hence requires low temperature. Other devices can run on photons and with the advantage of functioning at room temperature. Photonic quantum computers are based on chip-integrated silicon photonic devices and claim to be scalable and error-resistant. The most efficient device for a quantum computer at present is difficult to discern.

**Hobson:** What can quantum computers do now that digital computers cannot?

**Professor Baaquie: **There are two famous quantum algorithms. The first is the Grover algorithm that searches for a particular entry in a database of size N – and takes square root (N) steps compared to N steps of a classical computer. For example, to find an entry in a ledger of 1 million entries, Grover’s algorithm would take only 1,000 instead of a million steps. The second is the Shor algorithm, which can factorize a number into its primes (used in all encryption and secure communications) exponentially faster than a classical computer. The problem is that, for any practical problem, Grover can only efficiently search databases with N=7 and Shor, as of now, can only factorize 21=3×7. This is because of the currently limited number of qubits and the noise problem.

**Hobson:** How do you write code on a quantum computer?

**Professor Baaquie: **A classical computer’s code is written according to one’s day-to-day thinking. For instance, if one wants to add two numbers, one takes the first number and then adds to it the second number. A quantum computer code is counter-intuitive, being based on the laws of quantum mechanics. To add two numbers one has first to write the numbers in terms of the qubits. All operations (or gates, to use the classical computing term) in a quantum algorithm are special matrices called unitary transformations and so one has to decide how the operation of addition is represented by unitary matrices. Quantum algorithms are at the rudimentary level of machine language with codes written in terms of gates; it is hoped that high-level languages will be developed for quantum computers that are independent of how the quantum computer realizes the algorithms, with the high level language being task-oriented and not being tied to the hardware. When a high-level language for quantum computers is developed, it will make quantum algorithms easily accessible to professionals working in finance and other fields as well.

**Hobson: **What impact will quantum computing have on the current state of artificial intelligence (AI) and machine learning (ML)?

**Professor Baaquie:** An application of machine learning is, for example, taking the present day value of stocks and applying an algorithm to generate a prediction for tomorrow’s prices. Quantum algorithms are being developed to address machine learning. Similarly for AI and deep learning.

**Hobson:** How can firms actually access quantum computing services? For example, are they accessible from the Cloud?

**Professor Baaquie:** IBM’s Qiskit and Amazon’s Braket provide a few qubits free of charge to the public.

**Hobson: **What practical applications of quantum computing are taking place in financial services today?

**Professor Baaquie:** It is the view of many experts that the breakthrough for quantum algorithms is going to take place in finance. Unlike in devices such as solar panels where the algorithmic content is negligible compared to the hardware component, in finance efficient algorithms can have a far greater impact. The reason is that a slight improvement in the performance of a quantum algorithm over the classical algorithm will lead to substantial gains in finance, given the massive volume of the debt and capital markets. Furthermore, due to the market constantly providing up-to-date data, the algorithms can be calibrated and tested far more efficiently that in hardware-oriented devices.

**Hobson: **In what areas of financial services will quantum computing have an effect and why?

**Professor Baaquie:** There is an almost universal consensus amongst experts that two areas of finance hold the best promise for applying quantum algorithms. The first is portfolio optimization. A large hedge fund usually has a collection of 10,000 to 20,000 instruments in its investment universe from which to form its portfolio. Typically, the fund managers would like to run their models over a 30-year period. The optimization is to maximize returns, subtracting the dispersion of the portfolio as well as transaction costs, and with a budget constraint. Classical computers are quite inadequate to exhaustively study all the different possibilities, including generating the outliers that are so important to fund managers. A quantum computer can simulate outliers since its powerful algorithms can scan all possibilities, even those events that for a portfolio are highly unlikely. The quantum computer can compute the probability of the occurrence of these outliers – a computation that is beyond the computing power of classical computers. Outliers are not important for arbitrage but rather for risk management. Outliers can be useful for detecting financial fraud as well, since the occurrence of a fraud would most likely violate the computed likelihood of outliers. The second is arbitrage opportunities, based on the development of advanced pricing models that can spot arbitrage opportunities. The options market has a notional value of over US$650 trillion (with actual value of US$12 trillion) and to scan this market in real-time needs the computing power of a quantum computer. There are many other fields of finance where quantum algorithms can make a difference, such as the credit rating of customers, risk management and so on.

**Hobson: **Why is business so slow to invest in quantum computing?

Professor Baaquie: The horizon of when one can get returns is not clear. Once there is a winning application, it will open the floodgates for benefits to end-users and businesses – and will lead to massive investment in this game-changing technology.

**Hobson:** Quantum computers can complete calculations that would otherwise be impossible. What are the implications of that for current cryptographic methods?

**Professor Baaquie: **The Sycamore (IBM 54 qubits) performed a calculation in 200 seconds that would have taken the best super-computers 10,000 years. So, clearly, the quantum computer can perform computations that no classical computer can ever perform. A quantum computer would need about 20 million qubits and eight hours (rather than requiring 1 billion qubits as previously theorized) to break the 2048 RSA code, so it is still quite a distant possibility. Shor’s algorithm has the potential to completely overpower all classical encryption, but maybe not in the immediate future.

**Hobson: **Quantum computing has a flavour of the Manhattan Project about it. What geopolitical concerns does it foster?

**Professor Baaquie:** Quantum computers will impact all military technology, cyber-security, secure communications and so on. So leading nations in the world probably consider quantum computers to be a strategic asset that needs to be mastered at any economic cost.

**Hobson:** Does quantum computing create a risk that humanity is overwhelmed by a Superintelligence?

**Professor Baaquie:** Yes, quantum computers do pose a serious risk to humanity for the following reason. Artificial intelligence (AI) is premised on analysing patterns in big data and then making predictions and taking decisions. Technologies such as autonomous vehicles, cyber-warfare and so on will be greatly enhanced by combining AI with quantum computers. There are two kinds of AI algorithms. The first is Artificial Narrow Intelligence (ANI), which can carry out a task assigned to it such as driving an autonomous vehicle. The second is Artificial General Intelligence (AGI), which can do a wide range of tasks and can also decide by itself what task it will carry out. For example, consider an AGI-empowered robotic soldier. This machine will decide on who lives and who dies on the battlefield and maybe even off the battlefield. At present, AGI is comparable to human intelligence, so human beings can create devices to manage and control an autonomous AGI. But if AGI is enhanced and empowered by a quantum computer, it will have algorithms and computing power that no human being can match or fathom, and can give rise to Superintelligence. The quantum computer will give AGI access to unknown algorithms, patterns and predictions that no human being can understand, let alone control. The danger is that we may (inadvertently) mishandle a quantum computer-empowered AGI, since we have no clue about what it is doing. An out-of-control quantum computer-empowered AGI can wreak havoc on human society and on the environment. It is Superintelligence, a quantum computer-empowered AGI, that carries the greatest threat to humanity. The development of AGI should definitely be watched closely, especially in combining it with a quantum computer.

**Hobson:** What are quantum computers teaching us about our quantum mechanical universe?

**Professor Baaquie:** Quantum computers bring the paradoxes and conundrums of quantum mechanics – that have been encased in a thick shell of formalism – to the forefront. To illustrate these paradoxes, note that to store the information carried by a quantum computer with 300 qubits requires 2^(300) classical bits. The number of atoms in the known Universe are less than the number of bits required. One can easily imagine a 1,000-qubit quantum computer being made within a year, and for which no possible physical device can store all the information that it is processing. So the question arises: where is the information of the quantum computer being stored and where does the process of quantum computation take place? To answer this, one needs to start with the quantum nature of a qubit: the qubit is intrinsically indeterminate, simultaneously existing in many (actually infinitely many) mutually exclusive determinate states. Such an entity cannot exist in physical spacetime, as is evidenced by the fact that every time a qubit is observed, it is found to be in a determinate state, for example either 0 or 1. The Copenhagen interpretation of quantum mechanics – pioneered by Niels Bohr and Werner Heisenberg, and which is the one used in quantum computers – provides the following explanation: the indeterminate quantum state (of the qubits) “exists” in Hilbert space, an abstract space that is a superstructure of quantum mechanics. Hilbert space, amazingly enough, exists outside of space and time. Both of the non-trivial phenomena of quantum superposition and quantum entanglement – essential resources for a quantum computer – are properties of elements of Hilbert space. As the quantum device – that is to say, the hardware – evolves in the laboratory, all the qubits simultaneously and coherently evolve in Hilbert space. On the completion of the computation, a measurement is performed on the quantum device that “collapses” – with different likelihoods – the indeterminate quantum state of the qubits to a determinate state. In other words, the process of measurement (metaphorically) “moves” the solution from Hilbert space to a range of definite and determinate classical bits (with different likelihoods) that are part of the hardware. Hilbert space is a fundamental ingredient of quantum mechanics, and quantum computers bring out this aspect of quantum mechanics with full force: it is as if Hilbert space is staring us in the face while the process of the quantum algorithm is being carried out.

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