Abstract resource cost derivation for logical quantum circuit descriptions

Resources that are necessary to operate a quantum computer (such as qubits) have significant costs. Thus, there is interest in finding ways to determine these costs for both existing and novel quantum algorithms. Information about these costs (and how they might vary under multiple parameters and circumstances) can then be used to navigate trade-offs and make optimizations within an algorithm implementation. We present a domain-specific language called QuIGL for describing logical quantum circuits; the QuIGL language has specialized features supporting the explicit annotation and automatic derivation of descriptions of the resource costs associated with each logical quantum circuit description (as well as any of its component procedures). We also present a formal framework for defining abstract transformations from QuIGL circuit descriptions into labelled, parameterized quantity expressions that can be used to compute exact counts or estimates of the cost of the circuit along chosen cost dimensions and for given input sizes. We demonstrate how this framework can be instantiated for calculating costs along specific dimensions (such as the number of qubits or the T-depth of a logical quantum circuit).