Quantum Finance: Paving the way to
sustainable computing

The field of Quantum Computing is filled with potential and is evolving rapidly.

The introduction of Quantum Computers will revolutionize the way in which we think about algorithms and calculations. One of the earlier applications of Quantum Computers might be the replacement of large supercomputers in data centers. These supercomputers consume enormous amounts of energy each day. Could Quantum Computers reduce these energy costs? And if so, how soon will the necessary quantum technology be ready?

At the heart of Quantum Computing lies the field of Quantum Physics, which deals with the laws of physics on the scale of electrons and protons. It turns out that the laws of physics that govern our everyday experiences don’t apply to the smallest scales. Instead, Quantum Theory challenges our intuition with its striking phenomena: particles can be waves, the position of an election is inherently uncertain, and particles can be in two places at once?

A Quantum Computer leverages these weird quantum properties to do calculations. The Quantum Computer consists of “quantum bits” (called qubits), which are not restricted to only ‘0’ or ‘1’ (like classical bits). Rather, they can be both ‘0’ and ‘1’ at the same time! The peculiar properties of qubits allow Quantum Computers to execute certain algorithms exponentially faster than their classical counterparts.

However, this potential does come at a cost (quite literally): the energy bill. Firstly, you need to cool qubits to extremely low temperatures, approaching absolute zero to exploit their quantum properties effectively. Secondly, a Quantum Computer requires intricate control electronics, which consume considerable amounts of energy. This leaves you to wonder, how could these energy sucking machines ever contribute to sustainability?

We believe that the sustainability aspect of the Quantum Revolution is thus far underrepresented. Since sustainability and energy consumption are becoming increasingly important factors in the playing field of technological development, we argue that it is imperative to explore the energy saving potential of Quantum Technology more extensively!

An area where Quantum Computers could impact sustainability by replacing classical supercomputers is in financial institutions. Financial institutions use giant supercomputers to perform calculations, with which they can predict option prices. The iterative algorithm which is generally used is very computationally expensive. More concretely, this means that a lot of runs of the algorithm are required to ensure that the final prediction is sufficiently accurate.

Luckily though, there exists a “quantum version” of the option pricing algorithm, which takes far fewer runs to reach the same accuracy as the classical algorithm. So, Quantum Computers do consume energy at a rapid rate, but they might drastically improve the amount of required runs for certain algorithms. That leaves us to wonder:

Even if Quantum Computers revolutionize computing, can they reduce the energy consumption of certain algorithms?

To find out, let’s just implement the quantum algorithm! Well… it does come with a catch. The Quantum Computer that is necessary for this algorithm needs to be able to run quantum circuits with a depth of about 10000 gates! Current state-of-the-art Quantum Computers are in the Noisy Intermediate-Scale Quantum (NISQ) era, where their behavior is still flawed with errors and decoherence. Running the algorithm is therefore currently borderline impossible on these systems.

To bridge this gap, researchers have found a way to combine the strengths of classical and quantum computers in a “hybrid algorithm”. This hybrid algorithm does not improve the computational costs as much as the pure quantum algorithm, but it does still have a significant improvement over the classical algorithm. Crucially, this algorithm is based on circuits that could be run on Quantum Computers in the near future.

To estimate the impact of this hybrid algorithm on the sustainability of option pricing algorithms, we simulated a range of scenarios of different quantum computers with different hardware specifications. From these simulations, we found 4 different types of scenarios. The properties of each of these scenarios are summarized in the table below.

A prediction about the quantum energy advantage in the future and the runtime that it is paired with. The prediction is based on the trend in the development of quantum hardware systems over the past 5 years. The horizontal time axis contains an indicator for current state-of-the-art systems by Google and IBM and for IBM’s prediction about their system in 2025-2027. The grey area (I) contains scenarios where the hybrid algorithm is infeasible due to insufficient quantum hardware quality. The green area (III) contains scenarios where the hybrid algorithm uses less energy than the classical algorithm but does take longer. Finally, the blue area (IV) encapsulates scenarios in which the hybrid algorithm is both faster and more energy efficient. The figure does not show scenario II, because the development in the state-of-the-art shows that this scenario will be avoided in the future.

The existence of scenarios op type III is truly remarkable. Following the trend in the development of quantum hardware over the past 5 years clearly shows that state-of-the-art systems are still in scenario I. This trend is however clearly headed towards scenarios of type III before scenarios of type IV can be reached. The figure below shows a visual proof of this.

The figure above nicely shows the development of the quantum energy advantage in the future. The figure shows how the first few years of quantum energy advantage will be in scenario III (the green area) before the more ideal scenario of type IV is reached. It is good to note that this figure is based on assumptions and an extrapolation of developments in the past 5 years. Still, scenario III seems likely to be reached before scenario IV. This is an important conclusion, with high-stakes consequences.

The prediction that hybrid algorithms for option pricing will at first be much more energy-efficient, but slower than classical supercomputers is crucial for financial institutions that are considering quantum solutions. This result can spark interesting conversations at these financial institutions about their priorities: Do they value their carbon footprint more or less than the time efficiency of their calculations? It is crucial to proactively discuss these topics before the relevant quantum technology is available, to optimally align the quantum solutions with strategies of financial institutions.

Concretely, we propose an implementation of hybrid finance algorithms in which “Cloud Quantum Computing” is used. This approach allows multiple financial institutions to leverage a single quantum computer, operating continuously. This way, the Quantum Computer is constantly in an “active” state, which prevents huge energy wastes of Quantum computers in “idle” states.

In summary, the results from this investigation encourage financial institutions to explore quantum solutions to enhance the sustainability of their algorithms. While these quantum solutions may initially introduce a slowdown in computational speed, they offer the potential for significant reductions in carbon footprint. As such, financial institutions face a pivotal decision: Do they prioritize environmental sustainability over algorithmic runtime? If they do, then it seems that the time has come to investigate specifics concerning possible quantum solutions for option pricing algorithms!