Transconductor-Capacitor Circuits Emulating Quantum Systems
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Solution Overview
Problem
Existing approaches to emulate quantum dynamical systems using analog circuits are impractical due to the inability to represent the Planck constant, probability conservation, energy conservation, and stochastic noise over an infinite frequency range, requiring large numbers of devices and lacking efficient means for probability measurement and pattern recognition, which limits their application in quantum computing and quantum-inspired systems.
Innovation Solution
The development of transconductor-capacitor classical dynamical systems that emulate quantum behavior using real capacitors to represent the Planck constant, coupled transconductor systems for quantum admittance, and transadmittance elements, enabling efficient emulation of quantum operations with a reduced number of transistors and leveraging stochastic noise in transistors for realistic quantum behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If analog circuits with 90°-phase shifters are used to represent imaginary numbers in quantum mechanics, then quantum dynamical systems can be emulated, but the system becomes impractical because 90°-phase shifters cannot be created over an infinite frequency range
Solution Approach 1:
The patent replaces the fixed 90°-phase shifter with a frequency-independent representation using capacitor values that directly encode the Planck constant h. By changing the parameter representation from phase-shift-based to capacitance-value-based, the system achieves infinite frequency range adaptability without requiring impractical 90°-phase shifters at all frequencies.
2Adaptability or versatility
If ideal mathematical signal-processing elements are used to emulate quantum features, then quantum behavior can be represented, but the device complexity increases requiring large numbers of devices
Solution Approach 1:
The patent creates universal quantum-admittance and quantum-transadmittance elements that can represent multiple quantum features (Planck constant, probability conservation, energy conservation, stochastic noise) through a single integrated circuit configuration. This multi-functional element replaces numerous ideal mathematical components, reducing device complexity while maintaining comprehensive quantum feature representation.
Solution Approach 2:
The patent uses physical transistor-based circuits that replicate the mathematical behavior of quantum operators. By creating physical copies of quantum admittance and transadmittance elements using standard transistor components, the system efficiently represents quantum features without requiring large numbers of discrete ideal mathematical elements.
3Adaptability or versatility
If classical circuits are used to emulate quantum systems, then quantum behavior can be simulated, but the ability to compensate for loss and achieve ideal lossless quantum behavior is limited
Solution Approach 1:
The patent incorporates feedback mechanisms in the transistor-based quantum-admittance and quantum-transadmittance elements that actively compensate for loss. The feedback loops monitor and correct energy dissipation, enabling the classical circuits to maintain ideal lossless quantum behavior despite inherent losses in physical components, thereby improving reliability of the emulation.
4Volume of moving object
If transistors are used to create compact quantum circuit emulations, then device size is reduced, but the ability to represent the Planck constant over an infinite frequency range becomes challenging
Solution Approach 1:
The patent represents the Planck constant h as a fixed capacitor value parameter in the transistor circuit rather than attempting to vary it with frequency. This parameter transformation allows the compact transistor-based circuit to maintain frequency independence, achieving both small size and infinite frequency range adaptability simultaneously.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
These systems allow for the efficient emulation of quantum circuits with linear scaling, enabling the representation of exponential numbers of quantum states, improved probability measurement, and noise handling, facilitating quantum computing and quantum-inspired applications with compact transistor implementations.
Implementation Method 1
coupled transconductor system; these transconductors effectively create an exact emulation of quantum behavior with two classical h capacitors that couple to each other via a symmetric negative-feedback loop, creating the oscillatory behavior and energy-current flows seen in an isolated quantum admittance
Implementation Method 2
a real capacitor, whose value exactly emulates the value of h=h/(2π) with h being Planck's constant, and being adjustable; such 'Planck capacitors', as we shall term them, are ubiquitous in our emulations
Data Source
AI summary
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.