  Experimentalists seeking to improve the coherent lifetimes of quantum bits
have generally focused on mitigating decoherence mechanisms through, for
example, improvements to qubit designs and materials, and system isolation from
environmental perturbations. In the case of the phase degree of freedom in a
quantum superposition, however, the coherence that must be preserved is not
solely internal to the qubit, but rather necessarily includes that of the qubit
relative to the "master clock" (e.g. a local oscillator) that governs its
control system. In this manuscript we articulate the impact of instabilities in
the master clock on qubit phase coherence, and provide tools to calculate the
contributions to qubit error arising from these processes. We first connect
standard oscillator phase-noise metrics to their corresponding qubit dephasing
spectral densities. We then use representative lab-grade and performance-grade
oscillator specifications to calculate operational fidelity bounds on
trapped-ion and superconducting qubits with relatively slow and fast operation
times. We discuss the relevance of these bounds for quantum error correction in
contemporary experiments and future large-scale quantum information systems,
and discuss potential means to improve master clock stability.
