Barclays: Quantum Algorithms for Securities Settlement Optimization

The Problem

When financial firms settle securities transactions, a settlement engine processes large batches of trades within fixed windows. The engine must decide which trades to settle in a given batch subject to legal and operational constraints: each delivery-versus-payment transaction must satisfy funding and eligibility rules, parties may collateralise assets or draw on credit facilities, and trades can form dependency chains where settling A enables B, which enables C.

Choosing the optimal subset of trades to settle is a combinatorial optimization problem with both binary decisions (settle a trade or not) and continuous variables (how much funding or collateral to allocate). This combination is what researchers call a mixed binary optimization problem.

Lee Braine of Barclays’ chief technology and innovation office described the core difficulty as “a combination of both the legal constraints that must be satisfied when settling delivery-versus-payment transactions and the additional optionality introduced by … collateralising assets and utilising credit facilities.”

A Quantum Approach to Mixed Binary Optimization

Barclays researchers worked with IBM to study whether quantum optimization could address this class of problem. The collaboration produced a published algorithm, “Quantum algorithms for mixed binary optimization,” which decomposes the settlement problem into a binary part suitable for a quantum routine and a continuous convex part handled classically, then alternates between the two until they agree.

The binary subproblem can be written as a QUBO (Quadratic Unconstrained Binary Optimization) and explored with variational quantum routines such as QAOA or VQE. The simplified snippet below is an illustration only, showing how a small settlement instance can be set up as a QUBO. It is not Barclays’ production code or a reproduction of the published results.

# Illustrative only: how a tiny settlement batch can be framed as a QUBO.
# This is a teaching example, not Barclays' code or results.
import numpy as np

n_trades = 7  # matches the seven-qubit scale of the demonstration
np.random.seed(0)

# Diagonal: reward for settling a trade (negative = preferred)
settle_value = -np.random.uniform(0.5, 2.0, n_trades)
Q = np.diag(settle_value)

# Off-diagonal: penalties where two trades cannot both settle
# (e.g. they would breach a shared funding limit)
for i in range(n_trades):
    for j in range(i + 1, n_trades):
        if np.random.rand() < 0.3:
            penalty = np.random.uniform(1.0, 3.0)
            Q[i, j] = Q[j, i] = penalty

def qubo_cost(bits):
    x = np.array([int(b) for b in bits])
    return float(x @ Q @ x)

# Brute-force the best settlement subset for this toy instance
best = min((format(k, f"0{n_trades}b") for k in range(2 ** n_trades)),
           key=qubo_cost)
print("Best toy settlement subset:", best, "cost", round(qubo_cost(best), 3))

A real settlement batch contains far more than seven trades, but the structure is the same: binary include-or-exclude decisions coupled by shared constraints.

What Was Demonstrated

The team ran the core optimization aspects of the problem on a seven-qubit IBM cloud quantum computer. They reported being able to identify settlement features that were “of sufficient complexity” to be meaningful test cases for the quantum approach. This was explicitly a proof of concept rather than a production system or a claim of advantage over classical settlement engines.

Stated Limitations

The Barclays team was candid about what stands between this demonstration and practical use:

• Scale: Any quantum advantage would only emerge at large batch sizes, on the order of tens of thousands of trades, not the small instances that current hardware can handle.
• Skills: Quantum computing expertise is scarce, which constrains how quickly banks can build and validate these methods.
• Hosting and jurisdiction: Running sensitive workloads on third-party cloud quantum hardware raises data and regulatory jurisdiction questions.
• Explainability: Regulators expect banks to explain how a decision was reached, and the explainability of quantum optimization results remains unresolved.

Why It Still Matters

Settlement optimization is a clean example of a real, constrained, combinatorial problem in banking, which makes it a useful testbed for quantum optimization methods even while the hardware is far from production scale. The value of the Barclays work is in formulating a genuine industry problem precisely, mapping it onto near-term quantum routines, and reporting honestly on both the proof of concept and the gap that remains.

For students, the case study illustrates the mixed binary optimization framing, the decomposition of a hard problem into quantum and classical parts, and the difference between demonstrating that something can be expressed on a quantum computer and showing that doing so beats classical methods.

Learn more: Qiskit Reference | QAOA Algorithm Guide

Sources

• Barclays demonstrates proof-of-concept quantum clearing algorithm (Computer Weekly)
• Quantum Algorithms for Mixed Binary Optimization applied to Transaction Settlement (arXiv:1910.05788)