Peer-reviewed Physical Review Research paper shows efficient preparation of financial distributions on quantum hardware

Haiqu, a leading developer of quantum middleware, has announced the publication of joint research with HSBC in Physical Review Research demonstrating an efficient approach to encoding real-world probability distributions into quantum circuits.

Quantum State Preparation

Quantum state preparation, the process of encoding classical data into quantum states, is widely recognised as a major bottleneck when implementing many algorithms on hardware. This challenge is particularly relevant for applications such as financial risk modelling and simulation, where complex probability distributions must be loaded onto quantum devices.

The research uses matrix product state (MPS) methods to construct shallow circuits that encode smooth functions, including probability distributions, directly into quantum states. It also introduces a sampling-based workflow that avoids storing the full discretised dataset in classical memory, enabling larger encoding circuits to be generated.

The approach was validated on finance-relevant models including heavy-tailed Lévy distributions, commonly used to capture extreme market events. 

On IBM quantum hardware, circuits up to 25 qubits produced samples that passed standard statistical tests, showing the method can accurately reproduce the probability distributions these models rely on in practice. 

Sampling-Based Workflow

Using the sampling-based workflow, the researchers also executed circuits up to 64 qubits, reproducing qualitative features of the target distributions under realistic device noise and demonstrating feasibility at larger scales. Similar behavior was observed in simulations up to 156 qubits, indicating the approach can extend to substantially larger problem sizes.

“Preparing complex probability distributions efficiently is a key step in many quantum algorithms,” said Dr. Philip Intallura, Group Head of Quantum Technologies at HSBC. “This work shows how they can be implemented with much shallower circuits, bringing practical applications such as financial risk modelling closer.” 

“One of the biggest practical barriers is getting realistic financial data onto today’s quantum hardware. This work shows a scalable path around that barrier and helps move quantum finance workflows from theory toward execution.” Mykola Maksymenko, Co-founder & CTO, Haiqu

Read the paper in Physical Review Research. 

About Haiqu   

Haiqu is an emerging leader in quantum software that supports the notion that near-term, commercially viable applications are achievable with the right software, even on current hardware. Haiqu’s hardware-agnostic software can run applications with up to 100x more operations on current devices compared to competitors. Headquartered in New York City in the United States, Haiqu’s expert team operates from US, Canada, Ukraine, UK, EU, and Singapore, contributing to the company’s mission to make quantum computing practical as soon as possible.

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Niamh Kingsley, Founder & CEO of the the post-digital consultancy firm ace, on the Quantum future for financial services

Just last week, I sat across from a head of engineering at a major city-based bank and asked about their quantum preparedness. His response? “As far as I’m concerned, that’s science fiction.”

From my perspective, this view is definitely misguided. But more concerning, it’s also really prevalent. Despite some senior leaders dismissing quantum as a distant concern, their organisations are already exposed to quantum-enabled threats, and their competitors are quietly positioning for advantage.

Breakthroughs from the likes of IBM, Google, Rigetti, and Quantinuum show the ten-year timeline is a mirage. The quantum threat is not future tense. It is present and accelerating. In the race for computational advantage, the largest institutions are already in the lab. In the race for security, the threat actors are already in your network.

The time for planning is over, and the time for migration is now.

The Security Imperative: Your Data is Already at Risk

When we talk about the quantum threat, we’re primarily talking about Shor’s Algorithm. On a sufficiently large, fault-tolerant quantum computer (CRQC), Shor would break the public-key cryptography (RSA and most ECC) that underpins many secure protocols and systems, including virtually every secure digital communication and transaction globally.

But here is the critical point: the impact doesn’t start on the day a CRQC goes live; it began years ago the with ‘Harvest/Store-Now, Decrypt-Later (HNDL/SNDL)’ attack vector, where adversaries record encrypted traffic today to decrypt it once quantum capabilities arrive. (Symmetric cryptography like AES is affected differently by Grover’s algorithm, and it is generally mitigated by larger key sizes.)

Why ‘Harvest Now, Decrypt Later’ is the Real Crisis

Think about your most sensitive, high-value data:

  • KYC and client records: Confidential information that must remain private for decades.
  • Proprietary trading strategies: Models and algorithms that define your competitive edge.
  • Intellectual property and M&A communications: Data whose confidentiality window extends well beyond the projected arrival of a CRQC.

Sophisticated adversaries, often state-sponsored, are already harvesting vast quantities of this currently encrypted data. They are storing it, bit by bit, waiting for the eventual arrival of a cryptographically relevant quantum computer, which they will then use to decrypt later.

This means that data encrypted today will be vulnerable to breach tomorrow. The shelf-life of your confidential information directly dictates the urgency of your response. Any financial institution that relies on current public-key cryptography to protect data with a retention requirement of five years or more is already compromised in principle.

Post-Quantum Cryptography Migration: Why it’s Non-Negotiable

A wholesale migration to Post-Quantum Cryptography (PQC), algorithms resistant to quantum attack, is the only defence. This isn’t a simple software patch; it’s a foundational re-architecture of your digital trust layer.

  • What institutions should prioritise: Any data requiring confidentiality beyond a ten-year horizon is at risk. The UK’s National Cyber Security Centre and G7 frameworks explicitly call out finance to begin migration planning now, with several guides targeting 2035 completion for critical sectors.
  • Inventory everything: You cannot protect what you don’t know you have. Conduct a rigorous, firm-wide audit to map every single instance of public-key cryptography, from TLS certificates and VPNs to digital signatures, PKI, and key management systems.
  • Focus on the long-lived: Prioritise the migration of systems protecting data with the longest necessary confidentiality (the HNDL targets) and those that are hardest to change (e.g., embedded systems, legacy code, or critical, highly-available infrastructure).
  • Mandate the standards: Adopt the new, standardised PQC algorithms, such as CRYSTALS-Kyber (for key establishment) and CRYSTALS-Dilithium (for digital signatures), as decreed by global bodies like the US NIST.

Capturing Computational Advantage

But here’s what the industry isn’t telling you: whilst you’re busy securing your systems, there’s a competitive dividend waiting for institutions willing to explore quantum’s computational capabilities.

I’m not talking about vague promises of exponential speedups. I’m talking about targeted, measurable advantages in specific use cases where quantum algorithms demonstrably outperform classical approaches.

Monte Carlo simulations for derivative pricing, XVA calculations, and Value-at-Risk models are obvious starting points. Amplitude Estimation provides a quadratic speedup over classical Monte Carlo, achieving the same error tolerance with exponentially fewer samples. That means shorter calculation windows, faster intraday rehedging, and material energy savings. For path-dependent options or rare-event tail scenarios, quantum approaches offer better resolution of low-probability events without exploding compute budgets.

Portfolio optimisation, collateral allocation, and limit setting are fundamentally combinatorial optimisation problems. Quantum heuristics may deliver quality and latency benefits under complex constraints, including funding requirements, capital adequacy, central counterparty margin rules.

HSBC made headlines deploying quantum algorithms for foreign exchange pricing optimisation. That wasn’t a marketing exercise; it was a proof point that the technology has crossed from research into application.

But, and this matters, we don’t yet have large-scale, fault-tolerant quantum computers. IBM’s roadmap targets approximately 200 logical qubits by 2029. We’re not there yet. Which means the smart play is running parallel tracks: migrate to PQC now for security; experiment with quantum algorithms in targeted pilots to understand future advantage.

The pilot framework should be rigorous. Choose use cases where runtime and tail-risk scenarios dominate P&L. Establish measurement frameworks comparing quantum approaches against equal-error, equal-time, and equal-energy classical baselines. Report outcomes honestly. Build institutional knowledge whilst the hardware matures.

The Competitive Landscape: The Window is Closing

The quantum era is a global, systemic shift. It is a dual-sided challenge, an existential security risk and an unprecedented performance opportunity.

We are entering a phase of hyper-competition. The market is already separating into two distinct groups:

  • The value capturers: These are the institutions that have already established quantum governance, initiated PQC pilots, and embedded crypto-agility into their DNA. They will be secure against HNDL, will meet regulatory mandates like DORA, and, crucially, will be the first to operationalise quantum speed-ups in pricing, risk, and optimisation. They will gain an insurmountable performance edge.
  • The vulnerable and disadvantaged: These are the firms facing “crypto-procrastination.” They risk massive compliance penalties, systemic data theft via HNDL, and the competitive disadvantage of relying on slower, less accurate classical models while competitors price derivatives and optimise collateral in real-time.

The quantum inflection point is not an event on a distant calendar; it is a process happening right now. The firms that act today are building an unbreakable digital fortress while simultaneously designing the algorithms that will define the next decade of finance.

Don’t wait for Q-Day. Secure your future, then innovate in it.

Learn more at aceadvantage.io

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