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Abstract Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto’s automatic generation of circuit identities includes single-qubit and two-qubit gates, which leads to a new database of circuit identities, some of which are novel to the best of our knowledge. In addition to the generation of new circuit identities, Quanto’s optimizer applies such circuit identities to quantum circuits and finds optimized quantum circuits that have not been discovered by other quantum compilers, including IBM Qiskit and Cambridge Quantum Computing Tket. Quanto’s database of circuit identities could be applied to improve existing quantum compilers and Quanto can be used to generate identity databases for new gate sets. 

Abstract Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to reason about the behavior of these classifiers using symbolic techniques. This includes explaining decisions, measuring robustness, and proving formal properties of machine learning classifiers by reasoning about the corresponding symbolic classifiers. In this work, we present a theory for unveiling thereasonsbehind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. At the core of our theory is the notion of acomplete reason,which can be viewed as a necessary and sufficient condition for why a decision was made. We show how the complete reason can be used for computing notions such as sufficient reasons (also known as PI-explanations and abductive explanations), how it can be used for determining decision and classifier bias and how it can be used for evaluating counterfactual statements such as “a decision will stick even if ...because ... .” We present a linear-time algorithm for computing the complete reasoning behind a decision, assuming the classifier is represented by a Boolean circuit of appropriate form. We then show how the computed complete reason can be used to answer many queries about a decision in linear or polynomial time. We finally conclude with a case study that illustrates the various notions and techniques we introduced.