Maxwell's demon in dynamic quantum circuits

Abstract

Dynamic quantum circuits use intermediate measurements and classical feed-forward to change later operations during a computation. This makes them similar in spirit to Maxwell’s demon, since measurement information is used to guide the evolution of the system. In this thesis, this idea is studied in the context of Greenberger–Horne– Zeilinger (GHZ) states, that is, entangled states of the form (|0⟩⊗𝑁 + |1⟩⊗𝑁 )/√2, on noisy quantum devices. on noisy quantum devices. Three GHZ preparation protocols are compared: a non-adaptive protocol, a semi-adaptive protocol, and a fully adaptive protocol. The non-adaptive protocol uses only fixed unitary gates, while the adaptive protocols use ancilla measurements and conditional corrections. The protocols are implemented in a classical stabilizer simulation framework and compared using the final GHZ fidelity as the performance measure. The simulations isolate four different error sources: CX gate errors, measurement errors, relaxation, and pure dephasing. This makes it possible to study not only which protocol performs best, but also which physical effects limit the performance of each protocol. In the CX gate-error regime, the results are determined by the number of CX gates. In the measurement-error regime, the adaptive protocols are limited by their reliance on intermediate measurements. For idle-time errors, the comparison is more subtle, since adaptive protocols reduce quantum depth but also introduce ancilla overhead and measurement and feed-forward delays. For the noise models and timing assumptions used in this work, the non-adaptive protocol gives the highest fidelities in all isolated error regimes. The adaptive protocols therefore do not gain an advantage from their reduced depth under these conditions. The main bottleneck is found to be the measurement and feed-forward time, which exposes the data qubits to additional idle-time noise. This suggests that adaptive GHZ preparation could become more competitive on hardware with faster measurements, faster feed-forward, or lower-overhead adaptive constructions. The results show that reduced circuit depth alone is not sufficient to guarantee an advantage for dynamic circuits. Instead, the usefulness of adaptivity depends on the balance between gate count, circuit depth, measurement overhead, ancilla overhead, and hardware timing.