US 10,769,338 B2 · Emulation of quantum and quantum-inspired dynamical systems with classical transconductor-capacitor circuits

Abstract

We disclose transconductor-capacitor classical dynamical systems that emulate quantum dynamical systems and quantum-inspired systems by composing them with 1) a real capacitor, whose value exactly emulates the value of the quantum constant ℏ termed a Planck capacitor; 2) a ‘quantum admittance’ element, which has no classical equivalent, but which can be emulated by approximately 18 transistors of a coupled transconductor system; 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 quantum admittances to each other under the control of an input. These four parts can be composed together to create arbitrary discrete-state, traveling-wave, spectral, or other quantum systems.

Claims36

Dependent claims

A system comprising a classical analog circuit to perform an emulation of a quantum or quantum-inspired dynamical system

wherein a complex probability amplitude of a component of a vector state of a quantum wave function is represented by, first and second voltages, VR and VI on identical first and second capacitors CR and CI respectively, corresponding to real and imaginary parts of the complex probability amplitude of said component respectively,
wherein a value of the identical capacitance of the first and second capacitors CR and CI is given by an adjustable capacitance value CHBAR with the adjustable capacitance value CHBAR being directly proportional to a value of a universal quantum Planck constant, h, divided by a mathematical constant, 2π, and
wherein current flows onto the first and second capacitors CR and CI correspond to Hamiltonian energy flows in the quantum or quantum-inspired dynamical system corresponding to said component.

A classical circuit element used to emulate a quantum admittance in a quantum or quantum-inspired dynamical system comprising

two input voltages VI and VR at its I and R terminals respectively that generates output currents of −GE0RVR at the I terminal and +GE0IVI at the R terminal respectively via two transconductors with their transconductances GE0I and GE0R both equal to a transconductance GE0;
both GE0R and GE0I having the same algebraic positive or negative sign respectively, and with GE0 being proportional to E0, a term in an energy Hamiltonian of the quantum dynamical system being emulated, which describes dynamics of a component of a vector quantum state under an influence of just its own probability amplitude component that is represented by real and imaginary voltages VR and VI respectively.

A classical circuit element used to emulate a quantum transadmittances in a quantum or quantum-inspired dynamical system comprising

two input voltages VI1 and VR1 referenced to ground or another reference at its I1 and R1 terminals respectively that generates output currents of −GARVR1 at an another I2 terminal and +GAIVI1 at another R2 terminal respectively via two transconductors with their transconductances GAR and GAI both equal to a transconductance GA2
both GAR and GAI having the same algebraic positive or negative sign respectively with GA being proportional to A, a term in the energy Hamiltonian of the quantum dynamical system being emulated, which describes the dynamics of a component of a vector quantum state represented by real and imaginary voltages VR2 and VI2 under the control of another probability amplitude component that is represented by real and imaginary voltages VR1 and VI1 respectively.

A classical circuit element used to emulate a quantum transadmittance mixer in a quantum or quantum-inspired dynamical system, comprising

four input voltages, VI1 and VR1 and VI2 and VR2 at its I1 and R1 and I2 and R2 terminals respectively, with all voltages referenced to a d.c. reference voltage or being differential voltages, that generates output currents proportional to −GAI(VR1VI2+VR2VI1) at an another I3 terminal and +GAR(VR1VR2−VI1VI2) at another R3 terminal respectively with GAR and GAI both equal to a transconductance GA
with G4 being proportional to ε, a term in an energy Hamiltonian of the quantum dynamical system being emulated, which describes dynamics of a component of a vector quantum state represented by real and imaginary voltages VR3 and VI3 under control of a product of two probability amplitude components that are represented by real and imaginary voltages VR1 and VI1 and VR2 and VI2 respectively.

Dependencies are inferred from the claim text.

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

Life of this patent

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

Life of this patent

Abstract

Claims36