Maxwell's demon in dynamic quantum circuits

Sammanfattning

Dynamic quantum circuits use intermediate measurements and classical feed-forwardto change later operations during a computation. This makes them similar in spiritto Maxwell’s demon, since measurement information is used to guide the evolution ofthe 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 preparationprotocols are compared: a non-adaptive protocol, a semi-adaptive protocol, and afully 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 andcompared using the final GHZ fidelity as the performance measure.The simulations isolate four different error sources: CX gate errors, measurementerrors, relaxation, and pure dephasing. This makes it possible to study notonly which protocol performs best, but also which physical effects limit the performanceof each protocol. In the CX gate-error regime, the results are determined bythe number of CX gates. In the measurement-error regime, the adaptive protocolsare limited by their reliance on intermediate measurements. For idle-time errors,the comparison is more subtle, since adaptive protocols reduce quantum depth butalso introduce ancilla overhead and measurement and feed-forward delays.For the noise models and timing assumptions used in this work, the non-adaptiveprotocol gives the highest fidelities in all isolated error regimes. The adaptive protocolstherefore do not gain an advantage from their reduced depth under theseconditions. The main bottleneck is found to be the measurement and feed-forwardtime, which exposes the data qubits to additional idle-time noise. This suggeststhat adaptive GHZ preparation could become more competitive on hardware withfaster measurements, faster feed-forward, or lower-overhead adaptive constructions.The results show that reduced circuit depth alone is not sufficient to guarantee anadvantage for dynamic circuits. Instead, the usefulness of adaptivity depends on thebalance between gate count, circuit depth, measurement overhead, ancilla overhead,and hardware timing.