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Running quantum programs is fraught with challenges on on today’s noisy intermediate scale quantum (NISQ) devices. Many of these challenges originate from the error characteristics that stem from rapid decoherence and noise during measurement, qubit connections, crosstalk, the qubits themselves, and transformations of qubit state via gates. Not only are qubits not “created equal”, but their noise level also changes over time. IBM is said to calibrate their quantum systems once per day and reports noise levels (errors) at the time of such calibration. This information is subsequently used to map circuits to higher quality qubits and connections up to the next calibration point. This work provides evidence that there is room for improvement over this daily calibration cycle. It contributes a technique to measure noise levels (errors) related to qubits immediately before executing one or more sensitive circuits and shows that just-in-time noise measurements can benefit late physical qubit mappings. With this just-in-time recalibrated transpilation, the fidelity of results is improved over IBM’s default mappings, which only uses their daily calibrations. The framework assess two major sources of noise, namely readout errors (measurement errors) and two-qubit gate/connection errors. Experiments indicate that the accuracy of circuit results improves by 3-304% on average and up to 400% with on-the-fly circuit mappings based on error measurements just prior to application execution. 

This work contributes a generalized model for quantum computation called NChooseK. NChooseK is based on a single parametrized primitive suitable to express a variety of problems that cannot be solved efficiently using classical computers but may admit an efficient quantum solution. We implement a code generator that, given arbitrary parameters for N and K, generates code suitable for execution on IBM Q quantum hardware. We assess the performance of the code generator, limitations in the size of circuit depth and number of gates, and propose optimizations. We identify future work to improve efficiency and applicability of the NChooseK model. 

Adiabatic computing with two degrees of freedom of 2-local Hamiltonians has been theoretically shown to be equivalent to the gate model of universal quantum computing. But today’s quantum annealers, namely D-Wave’s 2000Q platform, only provide a 2-local Ising Hamiltonian abstraction with a single degree of freedom. This raises the question what subset of gate programs can be expressed as quadratic unconstrained binary problems (QUBOs) on the D-Wave. The problem is of interest because gate-based quantum platforms are currently limited to 20 qubits while D-Wave provides 2,000 qubits. However, when transforming entire gate circuits into QUBOs, additional qubits will be required. The objective of this work is to determine a subset of quantum gates suitable for transformation into single-degree 2-local Ising Hamiltonians under a common qubit base representation such that they comprise a compound circuit suitable for pure quantum computation, i.e., without having to switch between classical and quantum computing for different bases. To this end, this work contributes, for the first time, a fully automated method to translate quantum gate circuits comprised of a subset of common gates expressed as an IBM Qiskit program to single-degree 2-local Ising Hamiltonians, which are subsequently embedded in the D-Wave 2000Q chimera graph. These gate elements are placed in the chimera graph and augmented by constraints that enforce inter-gate logical relationships, resulting in an annealer embedding that completely characterizes the overall gate circuit. Annealer embeddings for several example quantum gate circuits are then evaluated on D-Wave 2000Q hardware.