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International Symposium on Quality Electronic Design (ISQED)

A SPICE-based Framework to Emulate Quantum Circuits with classical LC Resonators

Md Mazharul Islam, Shafayat Hossain, Ahmedullah Aziz

Published Apr 5, 2023• 3 citations
Publisher

Abstract

A circuit system consisting of LC-oscillators is mathematically shown to emulate quantum circuits. Here we develop a SPICE-based framework for emulating universal quantum gates (the phase-shift, the Hadamard, and the CNOT gates). To reconstruct each gate behavior, the inductors and capacitors are chosen and tuned precisely. Each quantum state is perfectly described by the phase and amplitude of each oscillator. In principle, our framework can simulate a quantum system with any arbitrary number of qubits since each gate process is perfectly achieved. Finally, we have simulated a quantum circuit with 3 qubits as input that consists of all the universal quantum gates. Our simulation result shows that our framework can classically emulate the result of any quantum circuit with an arbitrary number of qubits and quantum logic components.

DOI
10.1109/isqed57927.2023.10129351

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A circuit system consisting of LC-oscillators is mathematically shown to emulate quantum circuits. Here we develop a SPICE-based framework for emulating universal quantum gates (the phase-shift, the Hadamard, and the CNOT gates). To reconstruct each gate behavior, the inductors and capacitors are chosen and tuned precisely. Each quantum state is perfectly described by the phase and amplitude of each oscillator. In principle, our framework can simulate a quantum system with any arbitrary number of qubits since each gate process is perfectly achieved. Finally, we have simulated a quantum circuit with 3 qubits as input that consists of all the universal quantum gates. Our simulation result shows that our framework can classically emulate the result of any quantum circuit with an arbitrary number of qubits and quantum logic components.
Quantum error correction (QEC) is vital for protecting quantum information against errors induced by quantum noise and decoherence, enabling fault-tolerant quantum computation. Here, we construct a SPICE-based classical emulator framework to simulate gate-based quantum error correction circuits, specifically designed to correct both bitflip and phase flip errors. In our framework, a collection of LC-oscillators emulates the process behavior quantum gates. Each quantum state is perfectly described by the phase and amplitude of each oscillator. Our framework is scalable to any quantum error correction system with any arbitrary number of qubits since each gate process is perfectly achieved. Here, we have successfully conducted simulations for an individual bit-flip correction circuit and Shor’s nine-bit error correcting quantum circuit, demonstrating the capability of our framework to effectively address and repair random bit-flip and phase flip errors in gate-based quantum computing circuits.
We construct a completely analog framework that emulates universal quantum gates and quantum algorithms. It is based on electronic circuits made of operational amplifiers, resistors and capacitors. In these circuits, input and output lines represent the computational basis states (CBSs) and thus 2n2^n2n lines are required to represent nnn qubits. An operation of the circuits is based on classical evolution and interference of complex amplitudes associated with each CBS. The framework can emulate entangled states and is free from decoherence, measurements are classical and do not collapse states. Similar to physical quantum computers, emulated quantum algorithms can be constructed as a sequence of the gates belonging to a universal set (phase shift, Hadamard, controlled-NOT), as a unitary matrix and as combinations of the two. Circuits representing the universal gates have been made and tested. We also have made a matrix-based emulator of a 3-qubit Grover search algorithm. We tested it by searching for one and two particular states with one and two iterations and found that its outputs accurately match predicted values. We anticipate that the emulators can work as sub-components of physical quantum computers. On their own, the emulators can be used for operations that require a few qubits or operations that can be split into independent (and perhaps weakly entangled) blocks of qubits.
We propose to simulate quantum gates by LC resonators, where the amplitude and the phase of the voltage describe the quantum state.By controlling the capacitance or inductance of resonators, it is possible to control the phase of the voltage arbitrarily.A set of resonators acts as the phase-shift, the Hadamard, and the CNOT gates.They constitute a set of universal quantum gates.We also discuss an application to an artificial neuron.As an example, we study pattern recognition of numbers and alphabets by evaluating the similarity between an input and the reference pattern.We also study colored pattern recognition by using a complex neural network.
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.
Quantum computing emulation using neuromorphic artificial spiking neurons designed with CMOS electronics is introduced in this paper. By extending the Axon-Hillock neuron model, the proposed circuit can emulate a universal set of quantum gates-Phase Shift, Hadamard, and CNOT-at room temperature, with ultra-low power consumption. Simulations and layout using 180 nm CMOS technology demonstrate successful emulation of quantum logic operations and entanglement, including GHZ states, with small area and significant reduction in power compared to previous oscillator-based approaches. This work paves the way for scalable, energy-efficient quantuminspired computation on standard CMOS hardware, suitable for mobile and edge applications.