AQM: A Refresh of the Abstract Qubit Model for Quantum Co-design

Qubits are the fundamental building blocks of quantum information science and applications, whose concept is widely utilized in both quantum physics and quantum computation. While the significance of qubits and their implementation in physical devices have been extensively examined, we posit that now is the right time to revisit this understanding. In this paper, we introduce an abstract qubit model (AQM), offering a mathematical framework for higher-level algorithms and applications, and setting forth criteria for lower-level physical devices to enable quantum computation. We first provide a comprehensive definition of "qubits", regarded as the foundational premise for quantum algorithms (bottom-up support), and examine their requisites for devices (top-down demand). We then investigate the feasibility of moderating specific requirements, thereby broadening device support while considering techniques that tradeoff extra costs to counterbalance this moderation. Lastly, we delve into the quantum applications that only require incomplete qubits, and discuss the physical systems having restricted AQM support but are still useful in quantum applications. AQM may serve as an intermediate interface between quantum algorithms and devices, facilitating quantum algorithm-device co-design.