Hybrid Quantum-Classical Solutions in Finance
I am all in for theoretical results!
But, is it completely useless to pursue practical quantum computing research (such as applications in finance) until a solid demonstration has been found for most algorithms with expected practical impact?
The quantum advantage of several quantum algorithms has been formally proven.
For example, we all know that Shor’s algorithm provides an exponential speedup over the best-known classical algorithms for factoring large numbers.
We also know that Grover’s algorithm offers a polynomial speedup for unstructured search problems.
However, many (if not all) of the quantum algorithms with near-term practical applications, such as portfolio optimization and quantum machine learning, have not yet been rigorously proven to outperform classical counterparts.
Does that mean, then, that research should stop until we have formal proof of their advantage?
Should we prioritize proving mathematical advantage first, or is there value in exploring applications despite the uncertainty?
There are several compelling arguments in favor of continuing research:
1. Many breakthrough technologies were developed before their theoretical foundations were fully understood.
For instance, the transistor revolutionized electronics long before the full understanding of semiconductor physics was established.
Similarly, quantum computing could benefit from exploratory research and experimental validation.
2. Insights from machine learning: In classical AI and machine learning, empirical results often precede theoretical guarantees.
Deep learning, for example, achieved remarkable success before we had a solid theoretical framework explaining why it works so well.
The same approach could apply to quantum algorithms—practical experimentation might guide theoretical breakthroughs rather than the other way around.
3. Perspectives from the quantum computing for finance community: Industries like finance are already exploring quantum algorithms for portfolio optimization, Monte Carlo simulations, and machine learning.
Financial institutions are not particularly interested in whether a practical problem can be solved faster by a classical computer.
This information is irrelevant if the computer cannot be practically built or if competitors cannot access it.
What matters is having a quantum computer that outperforms the classical or quantum systems of the competition.
In some cases, it’s sufficient to have a faster solution, even if it isn’t the most precise one.
This could be especially valuable in high-frequency trading, where speed often outweighs precision.
These are some of the arguments in favor of NISQ algorithms, in particular, in finance.
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