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.
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.
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operations on a finite-dimensional Hilbert space, are not unique to quantum systems but may be found in certain classical systems as well. Previously, it has been shown that one can represent an arbitrary multi-qubit quantum state in terms of classical analog signals using nested quadrature amplitude modulated signals. Furthermore, using digitally controlled analog electronics one may manipulate these signals to perform quantum gate operations and thereby execute quantum algorithms. The computational capacity of a single signal is, however, limited by the required bandwidth, which scales exponentially with the number of qubits when represented using frequency-based encoding. To overcome this limitation, we introduce a method to extend this approach to multiple parallel signals. Doing so allows a larger quantum state to be emulated with the same gate time required for processing frequency-encoded signals. In the proposed representation, each doubling of the number of signals corresponds to an additional qubit in the spatial domain. Single quit gate operations are similarly extended so as to operate on qubits represented using either frequency-based or spatial encoding schemes. Furthermore, we describe a method to perform gate operations between pairs of qubits represented using frequency or spatial encoding or between frequency-based and spatially encoded qubits. Finally, we describe how this approach may be extended to represent qubits in the time domain as well.
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g. acoustic, electromagnetic, etc.) but this paper will focus on electronic signals. Individual qubits are represented by in-phase and quadrature sinusoidal signals, while unitary gate operations are performed using simple analog electronic circuit devices. In this manner, the Hilbert space structure of a multi-qubit quantum state, as well as a universal set of gate operations, may be fully emulated classically. Results from a programmable prototype system are presented and discussed.
In this paper we present a novel approach to emulating a universal quantum computer with a classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g., acoustic, electromagnetic, etc), but we focus our discussion here on electronic signals. Unitary gate operations are performed using analog electronic circuit devices, such as four-quadrant multipliers, operational amplifiers, and analog filters, although non-unitary operations may be performed as well. In this manner, the Hilbert space structure of the quantum state, as well as a universal set of gate operations, may be fully emulated classically. The required bandwidth scales exponentially with the number of qubits, however, thereby limiting the scalability of the approach, but the intrinsic parallelism, ease of construction, and classical robustness to decoherence may nevertheless lead to capabilities and efficiencies rivaling that of current high performance computers.
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.
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.
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.