Emulation of quantum and quantum-inspired discrete-state systems with classical transconductor-capacitor circuits

A classical circuit for computing signal variables that are monotonic functions of either the peak, absolute, or squared-signal amplitude deviation from a reference of either or both of the real or imaginary probability-amplitude voltage variables of an emulated quantum-admittance circuit, both of whose outputs are connected to CHBAR capacitors.

A classical circuit that emulates the quantum fluctuation-dissipation relations wherein the relationships between damping and noise between two quantum states of low and high energy is emulated by introducing one floating forward transadmittance-mixer classical circuit from low-to-high energy and one floating backward transmittance-mixer circuit from high-to-low energy, each state being emulated by two CHBAR capacitors connected to a classical quantum-admittance circuit with a transconductance proportional to the state energy, and wherein the mixer inputs are driven by environmental fluctuation noise inputs configured such that higher environmental forcing noise at high frequencies or equivalently higher energies, leads to a lower probability of occupation of the high-energy state w.r.t. the low-energy state and a detailed balance between the forward and reverse currents in the transadmittance mixers is then automatically reached to establish the correct relations between the low damped probability of the high-energy state w.r.t. the low-energy state that balances the higher probability of transition from the high-energy state due to the higher environmental driving noise to the backward transadmittance mixer than the forward transadmittance mixer.

A classical circuit that compensates for loss in an emulated quantum admittance connected to two CHBAR capacitors by compensating the loss in the circuit with an intentionally introduced small-signal instability that is stabilized by large-signal saturating nonlinearities in the transconductors to reach an equilibrium oscillation voltage amplitude at which there is no effective loss.

Quantum-inspired two-state systems comprised of a means for one emulated quantum admittance circuit to affect another emulated quantum-admittance circuit and vice versa in a feedback loop, one or both of which may incorporate additional slow or fast sensing dynamics on their probability amplitudes that is used to control additional slow or fast actuating dynamics on parameters that affect the operation of the other, and one or both of which may be unstable or lossy in isolation, and one or both of which may incorporate a means to affect the state of the other via parametric amplification, parametric attenuation, instability increase, or instability decrease.

A multi-state N×N quantum-inspired network of emulated quantum admittances wherein the circuits by which one emulated quantum admittance affects the operation of another are utilized, if desired, to create interactions between any two quantum admittances in the N×N network, and thus build an N×N network of emulated quantum admittances.

A multi-state N×N network of emulated quantum admittances wherein the circuits by which one quantum admittance affects the operation of another, if desired, comprise emulated quantum transadmittances or emulated transadmittance mixer circuits.

The emulation of quantum or quantum-inspired systems with classical transconductor-capacitor circuits wherein the emulation is used as a model for an actual quantum system, effectively creating a Kalman filter that helps control it.