Quantum analogues of dissipative circuit elements.

The article focuses on the theoretical possibility and implications of quantum analogues of dissipative circuit elements, specifically resistors and memristors, which can exist in superpositions of states with different resistances or conductances. Building on established quantum circuit elements like superconducting qubits that exhibit quantum inductance and capacitance, the discussion extends to dissipative elements by applying the Landauer transport theory, showing that quantum superpositions of conductance states can persist within certain timescales before decoherence occurs. The analysis includes a model where a qubit controls the scattering amplitude in a quantum point contact, leading to a conductance operator with quantum superpositions analogous to those in inductance and capacitance. The article concludes that despite their dissipative nature, quantum resistors can exhibit coherent superpositions of conductance states, with potential experimental observation through qubit dynamics such as quantum beats or Rabi oscillations.