History of Quantum Mechanics
Theories of quantum mechanics were only first introduced into the field of Physics towards the end of the 19th century and at the start of the 20th. Renowned physicists such as Max Plank (pictured below) and Albert Einstein paved the way of this quantum revolution, which completely changed the lens through which our understanding of Physics is viewed. This so-called ‘paradigm shift’ offered many explanations to previously confusing problems and introduced many new ideas to be explored. It took some time for the understanding of quantum mechanics to develop and become integrated into the general scientific understanding and as such, its ideas had not quickly branched out into other fields of research, such as economics and finance.
Evolution of Quantum Theories in Finance
It was not for around three quarters of a century, when in 1978 Pakistani mathematician Asghar Qadir published a paper titled ‘Quantum Economics’, that these quantum theories made the leap over into the financial world. Qadir argued that the formalism of quantum mechanics was the best approach for modelling the ‘vagaries’ of economics behaviour, such as consumer patterns.
In fact, in the 1990s, a group of researchers in the field of quantum cognition confirmed aspects of Qadir’s thesis, pointing out that parts of the human decision-making process, specifically relating to economic decisions, could be effectively mapped to quantum logic.
Stock Market:
Refers to the collection and other venues where the buying, selling and issuance of shares of publicly listed companies take place
Financial Option:
Refers to a contract that is based on the value of an underlying security such as stocks. The contract specifies a price which the security can be bought or sold at (depending on the type of contract) by the end of the specified contract time.
At a similar time in the 1990s, the first work was being done on modelling stock markets and their uncertainty using quantum theories. This was the first example of quantum theories being applied directly to the real financial markets, effectively marking the shift of physics in finance from a theoretical standpoint to more of a practical one.
In 2007 the book ‘Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates’ by Belal E. Baaquie first introduced the idea of using quantum physics to aid with the pricing of financial options, which at this point in time is the primary area in which quantum physics is applied within finance.
Throughout the decade of the 2010s, there was an increase in the number of papers published concerning quantum finance, as people were quick to realise the potential benefits of conducting research in the area. This was mostly seen in the field of quantum computing, as there have been a large influx of investments into research into the field from financial institutions.
As will be discussed, these quantum computers are able to theoretically operate a very high speed when compared to normal computers. As a result, these are highly desirable within the financial world where probabilities of market movements need to be calculated extremely quickly, and considering large data sets.
On the left is an image of IBM’s 53-qubit quantum computer. The processor is located within the silver cylinder in the centre.
Timeline of Evolution
Quantum Models of the Stock Market
Modelling the stock market is an endeavour tried by many in the financial world for an obvious reason – successful models can and do make a lot of money for institutions.
In quantum mechanics, the Schrödinger equation can be used to model the evolution of a quantum particle throughout space and time. This equation can be seen below:
The Schrödinger Equation:
In this equation, the only variables we need to be concerned about is r, which is the position of the particle at time t, which is the other variable. As this equation gives information as to how a particle will evolve over time, it was thought that this equation could be applied to a financial setting to model the evolution of a stock over time. As previously mentioned, this would be extremely useful for investors as determining the future price of a stock could lend insight into when to buy or sell a particular stock.
As a result, the Schrödinger equation has been applied to stocks to try and model their price fluctuations. This was done by making a couple relatively simple changes to the above equation:
In place of the variable r which represents the position of the particle, there is instead the price, p, of the stock
The addition, the variable of trend, T, has been added to the equation. This variable allows the factors that affect the levels of investment to be taken into consideration such as the economic climate at the time.
The variable, H, is known as the ‘Hamiltonian’ and represents the variables in the square brackets in the Schrödinger equation above.
This type of equation is known as a partial differential equation. Consequently, when the initial value for the price of the stock is known, this equation can be solved to find the distribution of the price of the stock at any point in time in the future.
Limitations
Very difficult to produce the T, or Trend, to accurately quantify the human decisions that go into the buying and selling of stocks. Many of the factors that go into this variable are essentially intangible, such as the level of confidence of investors and the general economic climate. Therefore, the accuracy of this approach will be largely dependent on how accurately this variable can be produced which currently cannot be done effectively.
Like most models attempting to model the stock market, it fails to be able to predict the possibility of a market crash that could greatly affect stock prices. Although the Trend variable can be altered to try and fit the economics climate, as the name suggests, this assumes that the market will follow a trend. Therefore, if a trend breaking event were to occur, this would not have been predicted by the model, and an investor following the stock price prediction could then potentially incur significant financial losses.
As a consequence of these limitations, this model of the stock market is not used in practice. There are simply too many variables and events that could occur that cannot be accurately predicted by using the Schrödinger equation. Although it does give some interesting insight into how some economic behaviour resembled quantum behaviour, it is not accurate at predicting the changing price of stocks in the market and as such, is not relied upon.
Pricing of Financial Options
As we have just seen, many of the applications of quantum theories within finance concern the pricing of financial instruments, such as stocks. Another similar example is that of financial options.
The method of pricing these options however, has an even higher degree of complexity when compared to the pricing of other financial instruments. This is largely due to the necessity to keep up with the market patterns in real-time when formulating the solutions to the pricing of equations.
Due to this, classical computers have been found to not have the computational power that is necessary to find the solutions of these equations in real-time, and much as classical mechanics evolved into quantum mechanics, computational research in the financial world is slowly progressing into the quantum field.
Quantum computing is an area of active research and has already showed potential to cause massive waves in the financial world. It is discussed below.
Quantum Computing
The benefits of using quantum computers in the financial world are clear - they allow for a much higher processing power than classical computers, allowing for much larger datasets to be analysed more quickly than is currently possible. This has been shown: in 2019 the Sycamore Quantum Processor at Google performed a task in a little under three minutes that would have taken some of the world’s best supercomputers thousands of years to do. The reasons for this lie in the capabilities of qubits, in the place of classical bits.
How it works:
Classical computers use the function of qubits to process the data that they intake. These are entities that can take a value of either 0 or 1, meaning that they contain dualistic processing systems
Quantum computers is based on the principle of ‘superposition’, which states that some of the properties that quantum particles exhibit can be in two different states at one time, or any combination of these two states.
Superposition enables a massive amount of information to be accessed – a quantity of ‘N qubits can express the same amount of information as 2^N classical bits.’
This allows for very fast calculations and high amount of information storage
Superposition:
As mentioned on the left-hand side, superposition is the property of a quantum system to be in multiple states at one point in time.
At first, it may seem confusing as to how this property benefits quantum computing, but an analogy of a maze can be used to help this:
Many computational problems can be compared to that of a maze, containing lots of dead ends and only one correct solution. To solve this puzzle, a classical computer would try each route until it found a correct solution, turning back at each dead end. This is a very time consuming process.
However, the property of superposition allows the quantum computer to test out all of the routes simultaneously, through the quantum particles occupying many states at one time. As such, the correct path is found immediately, much more quickly than the classical computer.
Calculations using quantum computers are determined on a probabilistic basis rather than a deterministic basis in classical computers - Calculations are run many times so that the results converge towards a mean.
However, as we would be dealing with probabilities, there would be a small error on the result.
Another interesting property of quantum systems that can be exploited is what is known as ‘entanglement’ – this is the property of quantum particles whereby the action of one qubit will affect the action of another, even if they are completely separated in space.
By harnessing the properties of both entanglement and superposition, the increase in computational speed and processing power bring massive benefits to the financial sector.
The video on the right-hand-side gives an in-depth explanation into the workings of quantum computers
(Current) Limitations of Quantum Computing
The results of quantum computing are probabilisitic instead of deterministic. This means there will be an uncertainty associated with the result.
There is a lot of difficulty assembling large amount of qubits into one machine - the most qubits assembled into one machine is 127. Many of the calculations needed for the financial industry would require hundreds if not thousands of qubits to complete them.
The environment which qubits need to operate is very difficult to maintain. Slightly fluctuations in temperature or a stray radio wave can force them back into their classical states and out of their quantum ones.
Examples of the Use of Quantum Mechanics in Finance
As of 2022, the use of quantum theories in finance is still very much in its infancy. Many of the models that have been created to price financial instruments do indeed have their faults and are not widely used in practice. There has been a lot of research into the topic, but much like many of the financial models created, they have not been widely implemented by very risk-averse financial institutions.
At this point in time, most of the work done on quantum computers has been independent from finance as the technology is still being improved upon. As a result, most of the examples are purely research based, but in the near future there will be an increasing number of examples as we better understand the subject. It is projected that within the next five to ten years the technology on quantum computers will be sufficient to be used in calculations in the financial industry.
On the right is an image of researchers working on the quantum computer at IBM
Learn More: Interesting Articles for Additional Examples
Below is a list of interesting examples of current uses of quantum theories within the world of finance. Articles can be accessed via the hyperlinks.
‘Dharma Capital and Toshiba have joined forces in exploring the potential of quantum computers in accessing the effectiveness of high-frequency trading strategies for listed stocks in Japanese markets’. Click here
Multiverse Computing - ‘Chicago Quantum’s proprietary algorithm identifies efficient stock portfolios and, according to the company, “is currently beating the S&P 500 and the NASDAQ Composite 100 indices”’. Click here
‘In 2019, Google claimed ‘quantum supremacy after demonstrating that its quantum computer (named Sycamore with 53 qubits) could perform a computation in minutes that would take the world’s most powerful classical supercomputer thousands of years’ Click here
Summary
In all, the evolution of quantum physics within finance is still very much underway. Having stemmed from the discoveries of famous physicists in the early 20th century such as Einstein and Planck, it was not until the 1970s until papers began to be published on the topic. From here, there was steady development in the field for a few decades as people began to realise that some economic and financial behaviour is well reflected by the properties of quantum particles. Models of the stock market were created using Schrödinger’s equation, but most importantly, the utility of using quantum computers within finance was realised. The processing capabilities were clearly suited to the pricing of financial options and as a result, a lot of research and progress has been made on quantum computers and their implementation into the finance sector. This progress is far from complete, and will certainly continue in the years to come. As discussed in the ‘Future of Finance’ section, quantum mechanics will become more prevalent in finance, through the increased use of quantum computers.
Quick Quiz
Below is the link to a quick quiz to help consolidate your understanding of the above information about the use of quantum mechanics in finance!
References
‘Quantum Economics’, Wikipedia, accessed 18/02/22, https://en.wikipedia.org/wiki/Quantum_economics
‘Quantum Economics’, David Orrell, July 2018
‘A Quantum Theory of Money and Value’, David Orrell, 2016
‘How Quantum Computing could change financial services’, McKinsey & Company, https://www.mckinsey.com/industries/financial-services/our-insights/how-quantum-computing-could-change-financial-services
‘Quantum Computing in Banking and Finance - Threat or Opportunity’, Supertrends, https://www.supertrends.com/quantum-computing-in-banking-and-finance-threat-or-opportunity/
‘Quantum Computing and the Financial System: Spooky action at a Distance?’, IMF eLibrary, https://www.elibrary.imf.org/view/journals/001/2021/071/article-A001-en.xml
The Evolution of Physics in Finance
Completed by: Jake Wilkes, James Penston, Sam Jones and James Lundie.
© 2022 Physics in society project
