In recent years, quantum computing has promised a revolution in computing performance, based on massive parallelism enabled by many entangled qubits. Josephson junction integrated circuits have emerged as the key technology to implement such a universal digital quantum computer. Indeed, prior experiments have demonstrated simple Josephson qubit configurations with quantized energy levels and long coherence times, which are a necessary prerequisite for a practical quantum computer. However, these quantized states do not directly prove the presence of entanglement or macroscopic superposition, which are essential for the superior speed of such a digital quantum computer. On the contrary, an alternative realistic foundation for quantum mechanics has recently been proposed, with coherent transitions between quantized states, but without entanglement. A new experiment is proposed that may test whether superconducting quantum circuits can exhibit quantized states without macroscopic entanglement or superposition. Specifically, a flux qubit (a bi-stable SQUID) may be configured with a resonant input line for excitation and a single-flux quantum output line for simultaneous direct measurement of quantized energy and flux states, which are incompatible measurements in standard quantum theory. Such an observation could undermine the assumptions of superposition and entanglement, bringing into question the foundation and the ultimate performance of a universal digital quantum computer.