Formulation and Emulation of Quantum-Inspired Dynamical Systems With Classical Analog Circuits

Area of Science:

• Quantum computing
• Analog circuit design
• Computational neuroscience

Background:

• Quantum dynamical systems offer powerful computation but are difficult to emulate on digital computers.
• Classical analog circuits can potentially emulate complex quantum dynamics.

Purpose of the Study:

• To introduce four novel analog circuit parts capable of emulating phase-coherent unitary dynamics of quantum systems.
• To demonstrate the analog emulation of quantum Fourier transform (QFT) dynamics using these circuit parts.
• To explore the potential for quantum-inspired computation using classical analog circuits.

Main Methods:

• Development of four novel analog circuit parts: Planck capacitance, quantum admittance, quantum transadmittance, and quantum transadmittance mixer.
• Classical emulation using paired real-value voltages and currents on Planck capacitances to represent probability amplitudes and Hamiltonian terms.
• Implementation of circuits on an analog integrated circuit and experimental validation against theory and simulations.

Main Results:

• Successful emulation of phase-coherent unitary dynamics of quantum systems.
• Analog emulation of Nuclear Magnetic Resonance (NMR), Josephson junction, and Quantum Fourier Transform (QFT) dynamics.
• Experimental results consistent with mathematical theory and computer simulations.

Conclusions:

• Linear oscillatory neuronal networks with complex neurons and synapses can architect quantum-inspired computation using classical analog circuits.
• An analog-circuit mapping between quantum and neural computation is established, enabling potential future synergies.
• Analog computation offers a powerful approach for emulating complex quantum dynamics and advancing computational capabilities.