We extend variational quantum optimization algorithms for Quadratic Unconstrained Binary Optimization problems to the class of Mixed Binary Optimization problems. This allows us to combine binary decision variables with continuous decision variables, which, for instance, enables the modeling of inequality constraints via slack variables. We propose two heuristics and introduce the Transaction Settlement problem to demonstrate them. Transaction Settlement is defined as the exchange of securities and cash between parties and is crucial to financial market infrastructure. We test our algorithms using classical simulation as well as real quantum devices provided by IBM Quantum.

In this position paper, we consider some foundational topics regarding smart contracts (such as terminology, automation, enforceability, and semantics) and define a smart contract as an automatable and enforceable agreement. We explore a simple semantic framework for smart contracts, covering both operational and non-operational aspects, and describe templates and agreements for legally-enforceable smart contracts, based on legal documents. Building upon the Ricardian Contract, we identify operational parameters in the legal documents and use these to connect legal agreements to standardised code. We also explore the design landscape, including increasing sophistication of parameters, increasing use of common standardised code, and long-term research.

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