We disclose transconductor-capacitor classical dynamical systems that emulate quantum dynamical systems and quantum-inspired systems by composing them with 1) capacitors that represent ℏ termed Planck capacitors; 2) a ‘quantum admittance’ element, which can be emulated efficiently via coupled transconductors; 3) an emulated ‘quantum transadmittance element’ that can couple emulated quantum admittances to each other; and 4) an emulated ‘quantum transadmittance mixer element’ that can couple emulated quantum admittances to each other under the control of an input. We describe a ‘Quantum Cochlea’, a biologically-inspired quantum traveling-wave system with coupled emulated quantum two-state systems for efficient spectrum analysis that uses all of these parts. We show how emulated quantum transdmittance mixers can help represent an exponential number of quantum superposition states in the spectral domain with linear classical resources, even if they are not all simultaneously accessible as in actual quantum systems.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A probability pattern-recognition circuit intended for use in quantum or quantum-inspired emulations comprised of a set of 3 paired inputs (R1, I1), (R2, I2), (R3, I3) each corresponding to the real and imaginary parts of a complex signal, from which a squared-sum probability-like measure, p1=R12+I12, p2=R22+I22, p3=R32+I32 of each of these signals, is computed inside said circuit, an output current that is proportional to (1−p1)p2(1−p3) is generated via a multiplicative transconductance circuit, and said current is filtered by a parallel RC circuit to generate an output voltage that is largest when patterns of correlated probability in the input that follow a Low-High-Low pattern are dominant with 1/RC determining the averaging bandwidth for estimating such correlations. 2. The circuit of claim 1 wherein other multiplicative patterns of correlated probability amongst the inputs such as p1p2p3 or (1−p1)p2 in a High-High-High or Low-High-Neutral pattern respectively or any other combinatorial such combination of 3 inputs is estimated by altering the multiplicative design of only the transconductance portion of the claim 65 circuit. 3. The N-input generalization of the circuits of claim 1 when N pairs with index (Ri, Ii) are input to the circuit and a desired pattern of High, Low, or Neutral probability emphasis for this pair is architected by having the transconductance output current altered to include a multiplicative term of value pi, (1−pi), or 1 respectively in its N-product-dependent output with i spanning from 1 to N for each such input pair. 4. A Quantum Cochlea circuit for spectral analysis of an input comprised of an abutting cascade of topologically identical emulated quantum two-state systems with transadmittance mixers, each configured with an exponentially decreasing taper in the difference between their high-energy and low-energy emulated-quantum-admittance transconductance values as one proceeds along the cochlear cascade, and with a sequential alternation in their orientation such that only compatibly similar high-energy admittances or only compatibly similar low-energy admittances abut each other when two cochlear stages join. 5. The quantum cochlear circuit of claim 4 wherein the forward-propagation transadmittance value of the quantum cochlear stage along the cascade is made slightly higher than that of the backward-propagation transadmittance value of the quantum cochlear stage such that reflections of traveling waves along the cascade are minimized. 6. The quantum cochlear circuit of claim 4 wherein the probability pattern recognition circuit of claim 1 is used on the outputs of the cochlear cascade to improve its spectral analysis capabilities. 7. The quantum cochlear circuit of claim 4 wherein the modulation frequency at any spectral output of the Quantum Cochlea is measured to obtain amplitude information about the cochlear input. 8. The quantum cochlear circuit of claim 4 wherein the location of maximum response at any spectral output of the Quantum Cochlea is measured to obtain frequency information about the cochlear input. 9. An implementation of the quantum cochlear circuit of claim 4 in physical quantum hardware where physical quantum two-state systems such as atoms, electrons, ions, spins, or Josephson junctions with different energy levels replace the quantum admittance emulation circuits, and correspondingly electromagnetic waves, electric, or magnetic fields, or voltages serve as the cochlear input, and said atoms, electrons, ions, spins, or Josephson junctions are coupled to each other via approximately-nearest-neighbor coupling in an exponentially tapered fashion to create the cochlear cascade. 10. A classical circuit architecture for representing and storing a superposition of 2N quantum states as the spectrum of two real and imaginary output classical signals with said architecture needing circuit hardware resources proportional to N+1 comprising N emulated quantum two-state systems, indexed by k=0, 1, 2, 3, . . . N, with each said two-state system with two emulated quantum admittance circuits with quantum admittance values of +iE02k and −iE02k whose complex outputs are summed to architect a superposition of two states within each two-state system and then mixed, in a complex mixer, with analogous superposed signals from the corresponding two-state system with index k+1 such that the resulting mixed signal creates a new signal that represents a superposition of 2k+1 states at distinguishable frequency locations, which may then be used to re-initiate this process in a recursive fashion such that if the said recursive process is initiated at k=0 and terminated at k=N−1, the final output signals will represent a superposition of 2N quantum states. 11. The circuit architecture of claim 10 wherein the probability of the two states of each of the emulated two-state quantum systems of any index k is ½ such that the superposition of all 2N quantum states in the final output signal has an equally balanced probability amongst all states. 12. The circuit architecture of claim 10 wherein the initial-condition probability amplitudes of the states of each emulated two-state quantum system with index k are transiently established with the use of emulated transadmittance mixer circuits and an emulated two-state system and configured with a control input resonant with the energy difference between the two states corresponding to k such that N+1 resonant control inputs can transiently couple all the two emulated quantum admittance circuits of claim 74 within a two-state system to establish or alter their initial conditions but then be subsequently turned off, thus enabling emulation of write capability that also scales with N+1 hardware resources. 13. The circuit architecture of claim 10 wherein any of the k=0, 1, 2, . . . N−1 output signals from successive stages of the recursive architecture are fed to the quantum cochlear circuit of any of claims 4 through 8 such that the emulated quantum states of the superposition may be spectrally analyzed and measured, without destroying the superposition as would occur in an actual quantum system. 14. The circuit architecture of claim 10 wherein any emulated quantum admittances connected to CHBAR capacitors are replaced by oscillators architected to have input-output behavior and dynamics that are functionally like in whole or in part as that exhibited by the emulated quantum-admittances and CHBAR capacitors but are not constructed by the same means. 15. The complex mixer used in the circuit architecture of claim 10 implemented with a complex transadmittance mixer circuit in a voltage-in-voltage-out mode or with the output currents of the mixer converted to voltages via classical impedance circuit elements. 16. The circuit architecture of claim 10 where a different set of exponentially spaced Ek are used, with the exponential radix not necessarily being 2. 17. The circuit architecture of claim 10 where a different set of Ek are used but with the Ek still sufficiently different from one another such that all quantum-state superposition information in the spectral domain is preserved by one or more cascaded complex mixing operations. 18. A circuit architecture comprising 2(N+1) emulated quantum-admittance circuits attached to CHBAR capacitors indexed by k=0, 1, 2, . . . N with quantum admittance energies of −iE02k and +iE02k at each k and 2(N+1) associated emulated quantum transadmittance mixer circuits, said mixer circuits all receiving a classical signal Vin at one of their real or imaginary inputs, and mixing it with complex real-and-imaginary signals output by said emulated quantum admittances to create current outputs that are averaged on a capacitor for a fixed period of time to create 4(N+1) quadrature real and imaginary output signals, said output signals representing either spectral-analysis outputs of the input signal Vin or a means for using Vin to establish initial conditions on quantum or quantum-inspired state variables that encode information about Vin in these outputs. 19. The circuit architecture of claim 18 wherein the averaging capacitors are replaced by leaky capacitors with time constant RC such than an analog continuous running average may be obtained. 20. The circuit architecture of claim 18 wherein its output signals are used to establish initial conditions for the circuit architecture. 21. The circuit architecture of claim 18 wherein the emulated quantum admittance circuits are identical to those in the circuit architecture and shared by both circuit architectures via multiplexing. 22. The emulation of quantum or quantum-inspired systems with classical transconductor-capacitor circuits wherein the final measurement circuits do not destroy the information being read out. 23. The emulation of quantum or quantum-inspired systems with classical transconductor-capacitor circuits wherein the emulation is used to emulate a quantum system and a classical system simultaneously. 24. The emulation of quantum or quantum-inspired systems with classical transconductor-capacitor circuits wherein the emulation uses linear or nonlinear current-mode processing to implement any polynomially nonlinear input-output function that is necessary for emulation. 25. The circuit architecture of claim 10 wherein the same emulated quantum two-state systems are used to both create superposition states as well as to perform quantum or quantum-inspired computing. 26. The quantum cochlear circuit of claim 4 that incorporates gain-control computations or circuits to achieve wide dynamic range via any means involving nonlinearity, parametric amplification, parametric attenuation, or controlled instability. 27. The quantum cochlear circuit of claim 26 wherein inputs that determine the gain of the gain-control circuits or computations arise from sensing the modulation frequency of the cochlear outputs.