Industry Insights: The Quantum Advantage in Portfolio Optimisation

In this member thought-leadership piece, Ciaran Fennessy of Citi explores how quantum computing’s unique strengths align with the growing complexity of modern portfolio construction.

In a recent conversation with a colleague, he asked the thought-provoking question, ‘Why is portfolio optimisation considered the go-to use case when discussing quantum computing?’  Whilst this technology can be applied to numerous use cases across various industries, portfolio optimisation consistently ranks as a top application for financial services.  Indeed, a research paper ‘A Survey of Quantum Computing for Finance’ highlights not only portfolio optimisation, but also other use cases such as stochastic modelling and machine learning.  Further applications include Deep Hedging  and quantum security.  Citi recently published an article titled Quantum Security which focuses on the potential of future large-scale quantum computers to break many of the public-key cryptographic algorithms.  What makes portfolio optimisation particularly well-suited for quantum approaches? And as quantum computing moves from theoretical promise to practical application, what should organisations within the Irish Funds community be considering?

Quantum Computing’s Core Value Proposition

Before exploring quantum computing's applications, it's important to understand its core value proposition: the ability to rapidly process very large datasets and perform intricate calculations at speeds impossible for traditional computers. While conventional computers—powering everything from laptops to high-performance computing systems—use bits that exist as either '1' or '0', quantum computers harness the laws of quantum physics to take a fundamentally different approach. The basic unit of a quantum computer is a quantum bit, or qubit, which can be '0', '1', or, critically, any combination of both simultaneously. A phenomenon known as superposition. Superposition enables quantum computers to process intricate calculations, offering them significantly quicker and more powerful processing capability, for specific problem classes.

Portfolio optimisation was pioneered by Harry Markowitz in his ground breaking 1952 paper ‘Portfolio Selection’. This work introduced what became known as Modern Portfolio Theory (MPT).  Markowitz's insight was revolutionary: rather than selecting stocks individually based solely on expected returns, investors should consider the entire portfolio's risk-return profile by analysing the covariance of assets. He formulated this as a mathematical optimisation problem.  Minimizing portfolio variance (risk) for a given level of expected return, or maximizing return for a given level of risk.  Portfolio optimisation becomes significantly more computationally intensive as the number of assets grows — requiring analysis of all correlations between assets. With thousands of assets and various constraints (regulatory, sector limits, ESG criteria etc), traditional computers methods cannot support, often requiring simplifications or approximations. Hence, portfolio managers employ MPT frameworks, to analyse the efficient frontier and use metrics like the Sharpe Ratio, with the objective of maximising return whilst minimizing risk.

The Quantum Opportunity

This inherent computational complexity is precisely what makes portfolio optimisation an ideal candidate for quantum approaches. As the number of assets increases, the problem grows rapidly analysing a portfolio of 1,000 assets requires evaluating nearly 500,000 correlation pairs, and this explodes further when multiple constraints (risk limits, regulatory requirements, ESG criteria, sector allocations) are layered on top. Classical computers can solve these problems but often require significant time or must resort to simplifications that sacrifice accuracy.

Stephen Hawking, in his foreword to his seminal book A Brief History of Time, warned that for every mathematical equation you include, you will lose half your readers. Taking this sage advice to heart, I will spare you the complex mathematical frameworks—involving quadratic programming, covariance matrices and quantum algorithms—that underpin quantum portfolio optimisation. What's important to understand is that quantum computers, leveraging superposition and quantum annealing techniques, can explore vast solution spaces simultaneously, offering pathways to more optimal portfolio allocations in significantly less time than traditional methods.  Whilst this may sound like a futuristic view and something that is a long way down the road, that is not true. Quantum computing has moved from laboratory curiosity to commercial reality.  Indeed, a recent BBC News report focused on Googles quantum computer called Willow.  From an Irish perspective, Equal1 recently announced $60M funding “to accelerate development of scalable, silicon-based quantum computers and deployment of its datacentre-ready Bell-1 quantum server”.

Progress Today, Potential Tomorrow

Whilst there is clear momentum with quantum computing, where does quantum portfolio optimisation currently stand? The field is continually evolving. In 2020, Dwave published research demonstrating portfolio optimisation on 60 US equities using quantum algorithms, building on earlier work with 40-stock portfolios. By 2025, IBM released findings on quantum portfolio construction applied to ETF bond portfolios. Their results showed that “109 qubit noiseless simulations achieve encouraging results,” with the technology “evolving continuously towards better solutions.” While these studies focus on portfolios far smaller than the thousands of assets managed by institutional investors, they demonstrate steady progress. The trajectory is clear: as quantum systems scale and error rates decrease, the gap between experimental demonstrations and real-world applications continues to narrow.

Why is portfolio optimisation considered a go-to use case for quantum computing?  The answer lies in the elegant alignment between the problem's structure and quantum computing's strengths. Markowitz's 1952 framework, while revolutionary, created an optimisation challenge that grows increasingly complex with scale. Portfolio optimisation has well-defined mathematical properties, clear performance metrics, and immediate practical value—making it an ideal use-case as quantum systems mature. As we've seen from recent developments, quantum computing is transitioning from research labs to commercial deployment. Citi has a strong focus on this technology over the past few years.  It has established Quantum Computing research programs exploring applications across finance, including portfolio optimisation. Through partnerships with quantum computing laboratories, Citi is developing expertise at the intersection of quantum physics, mathematics, and finance.  

Implications for Asset Managers

For those working in Asset Management, understanding how quantum approaches might reshape portfolio optimisation isn’t about futuristic speculation. It’s about recognizing a fundamental shift in computational capabilities that directly addresses one of finance’s most enduring mathematical challenges. When can Asset Managers optimize across complex models more quickly and efficiently than current approaches? When the trade-off between model sophistication and computational feasibility no longer exists? These questions will soon move from theoretical to practical. The quantum computing breakthroughs we’re seeing today are not laboratory curiosities. They’re early indicators of a transformation that will reshape how we think about portfolio construction and investment optimisation itself.