### Executive Summary

On Oct 2019, researchers from Barclays and IBM published __a research article__ on quantum algorithms for transaction settlement. Specifically, the authors extend the well-known Quantum Approximate Optimization Algorithms (QAOA) to solve the transaction settlement problem which is mapped onto a Mixed Binary Optimisation (MBO) problems. The authors demonstrate a proof-of-concept experiment on IBM’s 5-qubit machine obtaining results for three delivery-versus-payment transactions.

### Our opinions

As mentioned in the paper, the transaction settlement problem, in the real-world situation, requires complex optimisation algorithm to settle as many transactions as possible or to maximise the total value of the settled transactions, while meeting both the legal constraints and optionality introduced by collateralising assets and utilising credit facilities.

A full-fledged quantum computer can solve several optimisation problems exponentially faster than a classical computer using the standard Grover’s algorithm. However, current quantum devices, also known as noisy intermediate-scale quantum (NISQ) hardware, are small and very noisy. __QAOA____,__ used in the paper, is one of the standard quantum algorithms specifically designed for NISQ devices. It makes use of a classical feedback to passively correct noise in the quantum hardware. However, quantum advantage of QAOA, when applied to the real-world problems such as transaction settlement, is much less clear compared to Grover’s algorithm.

In our opinion, the paper presented by IBM and Barclays provides an interesting mathematical foundation for using NISQ devices to tackle the transaction settlement problem. However, similar to other state-of-the-art works, both quantum software and hardware have to be improved before obtaining quantum advantage on real-world use cases.