Quantum computers can outperform classical computers in certain tasks. However, there are still many challenges to the current quantum computers such as decoherence and fault tolerance, and other drawbacks such as portability and accessibility. In this study, we circumvent these issues by realizing an analog quantum emulation device (AQED) where each qubit state is represented by a unique analog signal. It is possible to do this because previously it was shown that Hermitian operations on a Hilbert space are not unique to quantum systems and can also be applied to a basis of complex signals that form a Hilbert space. Orthogonality of the complex signal basis can be maintained by separating the signals into the frequency domain or the spatial domain. We study both these approaches and present a comparison. We finally realize the entire device on a UMC 180nm processing node and demonstrate the computational advantage of an AQED by emulating Grover's search algorithm (GSA) and Quantum Fourier Transform (QFT). We also present the equivalent quantum volume achieved by this device.
Quantum computers can outperform classical computers in certain tasks. However, there are still many challenges to the current quantum computers such as decoherence and fault tolerance, and other drawbacks such as portability and accessibility. In this study, we circumvent these issues by realizing an analog quantum emulation device (AQED) where each qubit state is represented by a unique analog signal. It is possible to do this because previously it was shown that Hermitian operations on a Hilbert space are not unique to quantum systems and can also be applied to a basis of complex signals that form a Hilbert space. Orthogonality of the complex signal basis can be maintained by separating the signals into the frequency domain or the spatial domain. We study both these approaches and present a comparison. We finally realize the entire device on a UMC 180nm processing node and demonstrate the computational advantage of an AQED by emulating Grover's search algorithm (GSA) and Quantum Fourier Transform (QFT). We also present the equivalent quantum volume achieved by this device.
Quantum computers are regarded as the future of computing, as they are believed to be capable of solving extremely complex problems that are intractable on conventional digital computers. However, near-term quantum computers are prone to a plethora of noise sources that are difficult to mitigate, possibly limiting their scalability and precluding us from running any useful algorithms. Quantum emulation is an alternative approach that uses classical analog hardware to emulate the properties of superposition and entanglement, thereby mimicking quantum parallelism to attain similar speeds. By contrast, the use of classical digital hardware, such as field programmable gate arrays (FPGA), is less inefficient at emulating a quantum computer, as it does not take advantage of the fundamentally analog nature of quantum states. Consequently, this approach adds an inherent hardware overhead that also prevents scaling. In this work, an energy-efficient quantum emulator based on analog circuits realized in UMC 180-nm CMOS technology is proposed along with the design methodologies for a scalable computing architecture. A six-fold improvement in power consumption was observed over the FPGA-based approach for a ten-qubit emulation of Grover's search algorithm. The proposed emulator is also about 400 times faster than a Ryzen 5600x six-core processor performing a simulation of six-qubit Grover's search algorithm
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.
Existing approaches to emulating quantum computing algorithms using classical electronic hardware are limited by exponential scaling limitations in space, such as circuit size, or time, such as runtime or bandwidth. We introduce a scheme for representing quantum information using analog signals that lessens the bandwidth limitation problem (in certain regimes) seen in existing approaches by taking full advantage of the ability of analog signals to encode information using RMS voltage as well as frequency and phase. We introduce the mathematical framework for this representation, which separates the information relevant for measurement in the computational basis from information that is not relevant to it. We introduce circuits that take advantage of this separation of concerns to achieve simplifications, for working with quantum information in this representation. We argue that it is comparatively very inexpensive (as low as ~$5.00 / qubit) to outmatch the computing capabilities of existing FPGA based emulators, though scaling beyond tens of qubits is still impractical due to constraints of analog hardware module precision. However, our approach opens the door to a new avenue by which classical emulators can hope to improve: by improving on analog electronic circuit performance.
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 2n lines are required to represent n 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.
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.
Abstract In this paper, a novel method for the emulation of qutrit and ququart based quantum computers is proposed. The Hilbert space and Bloch sphere representations of qutrits are initially discussed, preceding the emulation of a single qutrit using a classical system. The signal representing the state of the quantum system is defined as the sum of quadrature and in-phase 2-dimensional space-varying signals, which represent the basis states of the quantum system. Focus is mainly conferred on the frequency-domain representation of the signal, due to an innate bijective mapping found between the dimensions in the Hilbert space and the frequencies of the signal. An m -qutrit addressing scheme is then proposed which is used in the application of quantum ternary gates and measurement operations. The proposed theory is then used to simulate a ternary version of the Deutsch-Jozsa algorithm on MATLAB. This paper also includes a section on the extension of the theory to the case of ququarts. It concludes with a brief introduction to a potential system for emulation, and lists algorithms that can be implemented on the proposed system.