Quantum dynamical systems are capable of powerful computation but are hard to emulate on digital computers. We show that four novel analog circuit parts can emulate the phase-coherent unitary dynamics of such systems. These four parts are: a Planck capacitance analogous to a neuronal membrane capacitance; a quantum admittance element, together with the Planck capacitance, analogous to a neuronal quadrature oscillator; a quantum transadmittance element analogous to a complex neuronal synapse; and a quantum transadmittance mixer element analogous to a complex neuronal synapse with resonant modulation. These parts may be emulated classically, with paired real-value voltages on paired Planck capacitances corresponding to the real and imaginary portions of a probability amplitude; and appropriate paired real-value currents onto these Planck capacitances corresponding to diagonal (admittance), off-diagonal (transadmittance), or controlled off-diagonal (transadmittance mixer) Hamiltonian energy terms. The superposition of 2n simultaneously phase-coherent and symmetric probability-voltage amplitudes with O(n) of these parts, in a tensor-product architecture enables analog emulation of the quantum Fourier transform (QFT). Implementation of our circuits on an analog integrated circuit in a 0.18 μm process yield experimental results consistent with mathematical theory and computer simulations for emulations of NMR, Josephson junction, and QFT dynamics. Our results suggest that linear oscillatory neuronal networks with pairs of complex subthreshold/nonspiking sine and cosine neurons that are coupled together via complex synapses to other such complex neurons can architect quantum-inspired computation with classical analog circuits. Thus, an analog-circuit mapping between quantum and neural computation, both of which exploit analog computation for powerful operation, can enable future synergies between these fields.
Quantum dynamical systems are capable of powerful computation but are hard to emulate on digital computers. We show that four novel analog circuit parts can emulate the phase-coherent unitary dynamics of such systems. These four parts are: a Planck capacitance analogous to a neuronal membrane capacitance; a quantum admittance element, together with the Planck capacitance, analogous to a neuronal quadrature oscillator; a quantum transadmittance element analogous to a complex neuronal synapse; and a quantum transadmittance mixer element analogous to a complex neuronal synapse with resonant modulation. These parts may be emulated classically, with paired real-value voltages on paired Planck capacitances corresponding to the real and imaginary portions of a probability amplitude; and appropriate paired real-value currents onto these Planck capacitances corresponding to diagonal (admittance), off-diagonal (transadmittance), or controlled off-diagonal (transadmittance mixer) Hamiltonian energy terms. The superposition of 2n simultaneously phase-coherent and symmetric probability-voltage amplitudes with O(n) of these parts, in a tensor-product architecture enables analog emulation of the quantum Fourier transform (QFT). Implementation of our circuits on an analog integrated circuit in a 0.18 μm process yield experimental results consistent with mathematical theory and computer simulations for emulations of NMR, Josephson junction, and QFT dynamics. Our results suggest that linear oscillatory neuronal networks with pairs of complex subthreshold/nonspiking sine and cosine neurons that are coupled together via complex synapses to other such complex neurons can architect quantum-inspired computation with classical analog circuits. Thus, an analog-circuit mapping between quantum and neural computation, both of which exploit analog computation for powerful operation, can enable future synergies between these fields.
Analog circuits have emerged as a valuable quantum emulation and simulation platform. Specifically, they have been experimentally shown to excel in emulating coherent state vector dynamics and motifs of quantum circuits, such as the quantum Fourier transform, tensor product superpositions, two-level systems such as Josephson junctions, and nuclear magnetic resonance state dynamics, all on a very large scale integration chip at room temperature (Cressman et al., 2022; Sarpeshkar, 2019a, 2019b, 2019c; Sarpeshkar, 2020). However, the ability to model simple state vectors is insufficient for modeling open quantum systems, i.e., systems with environmental noise. Noisy quantum systems are essential in practical implementations and applications that exploit noise. The density matrix formalism enables us to model such states, including finite reservoir state systems, and all states that can be represented as state vectors. To our knowledge, no one has yet demonstrated the mapping of a density matrix system to classical analog circuit components. We review the procedure for emulating the dynamics of a finite state vector with four essential analog circuit components and extend this procedure to emulate density matrix dynamics. We then simulate these systems as analog circuits in the presence of noise. This protocol opens up exciting possibilities for further research and development in noisy quantum emulation and simulation using analog circuits for arbitrarily large or small systems.
Between the digital and quantum paradigms lies the emerging field of quantum-inspired analog computing, in which classical waves emulate quantum circuits. We introduce wavebits -- classical wave analogs of qubits whose amplitudes are carried by physical oscillatory signals -- and show that any nonseparable N-qubit state can be encoded in 2N narrowband signals that remain locally separable at every instant; the nonseparable correlations are recovered at readout by time-averaged demodulation over auxiliary carrier frequencies, the nonseparability channels. We prove that any two-qubit gate unravels into the time-averaged tensor product of two local time-varying operators, and that arbitrary circuits are emulated with a base-frequency count scaling linearly in the number of entangling two-qubit gates, independent of qubit number for a fixed gate count. The exponential cost of the 2^N-dimensional state reappears at readout and in the averaging time of circuits with many two-qubit gates, not in circuit execution, as quantified by an analytic error bound that doubles as a hardware design rule. A mixed-signal prototype emulates Bell state generation, controlled-NOT gates, phase kickback, and Bloch-sphere rotations at fidelities above 0.99, and numerical benchmarks against exact statevectors validate the scheme for up to six qubits. The architecture is directly implementable in acoustic, photonic, and mixed-signal platforms.
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schrödinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a complex state vector can be encoded in the continuous physical variables of an analog computer. Our algorithm reveals the full dynamics of complex probability amplitudes. Such real-time simulation is impossible in quantum simulation approaches without collapsing the state vector, and it is relatively computationally expensive for digital classical computers. For a real symmetric time-independent Hamiltonian, the ODEs may be solved by a simple analog mechanical device such as a one-dimensional spring-mass system. Since the underlying dynamics of quantum computers is governed by the Schrödinger equation, our findings imply that analog computers can also perform quantum algorithms. We illustrate how to simulate the Schrödinger equation in such a paradigm, with an application to quantum approximate optimization algorithm. This may pave the way to emulate quantum algorithms with physical computing devices, including analog, continuous-time circuits.
Quantum neuromorphic computing physically implements neural networks in brain-inspired quantum hardware to speed up their computation. In this perspective article, we show that this emerging paradigm could make the best use of the existing and near future intermediate size quantum computers. Some approaches are based on parametrized quantum circuits and use neural network-inspired algorithms to train them. Other approaches, closer to classical neuromorphic computing, take advantage of the physical properties of quantum oscillator assemblies to mimic neurons and synapses to compute. We discuss the different implementations of quantum neuromorphic networks with digital and analog circuits, highlight their respective advantages, and review exciting recent experimental results.
ABSTRACT Universal quantum computation that consists of producing arbitrary input states and executing universal unitary gates is an important goal for the future information field. However, realizing a device that performs practical universal quantum computation is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, we provide a novel scheme to emulate the universal quantum computer by designing a classical circuit network. In the circuit network, we encode information using correlated electrical signals. The information processing elements that correspond to the universal quantum gate set are designed and embedded into the circuit network, which gives the classical circuit networks processing functions similar to that of universal quantum computation. Taking the analogy of two‐qubit processor as an example, we experimentally verify that our proposal works well. Because classical circuit networks possess good scalability and stability, the present scheme is expected to avoid some problems faced by the quantum schemes. Thus, our findings are advantageous for information processing in the era of big data.
This paper proposes a novel quantum computing model that leverages the dynamics of neuronal behavior as its foundational building blocks. Unlike conventional quantum computing approaches reliant on purely classical qubits, this model utilizes quantum systems designed to mimic the dynamic changes observed in biological neural networks, specifically at the level of synaptic connections. The core principle involves employing quantum superposition and interference to construct quantum bits (qubits) representing the state of these simulated synapses. Algorithm execution is achieved through precise manipulation, or "quantum tuning," of these qubits. The proposed architecture represents a biologically-inspired paradigm shift in quantum computation, potentially offering advantages in terms of computational efficiency and resilience, particularly for problems exhibiting inherent biological complexity. This work outlines the theoretical framework, key equations, and the fundamental principles driving this new approach to quantum information processing.