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Register a new userClassical Computer, Quantum Computer, and the Godels theorem
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Biao Wu
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I show that the cloneability of information is the key difference between classical computer and quantum computer. As information stored and processed by neurons is cloneable, brain (human or non-human) is a classical computer. Penrose argued with the Godel theorem that human brain is not classical. I demonstrate with an example why his argument is flawed. At the end, I discuss how to go beyond quantum computer.
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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.
The design of new devices and experiments in science and engineering has historically relied on the intuitions of human experts. This credo, however, has changed. In many disciplines, computer-inspired design processes, also known as inverse-design, have augmented the capability of scientists. Here we visit different fields of physics in which computer-inspired designs are applied. We will meet vastly diverse computational approaches based on topological optimization, evolutionary strategies, deep learning, reinforcement learning or automated reasoning. Then we draw our attention specifically on quantum physics. In the quest for designing new quantum experiments, we face two challenges: First, quantum phenomena are unintuitive. Second, the number of possible configurations of quantum experiments explodes combinatorially. To overcome these challenges, physicists began to use algorithms for computer-designed quantum experiments. We focus on the most mature and textit{practical} approaches that scientists used to find new complex quantum experiments, which experimentalists subsequently have realized in the laboratories. The underlying idea is a highly-efficient topological search, which allows for scientific interpretability. In that way, some of the computer-designs have led to the discovery of new scientific concepts and ideas -- demonstrating how computer algorithm can genuinely contribute to science by providing unexpected inspirations. We discuss several extensions and alternatives based on optimization and machine learning techniques, with the potential of accelerating the discovery of practical computer-inspired experiments or concepts in the future. Finally, we discuss what we can learn from the different approaches in the fields of physics, and raise several fascinating possibilities for future research.
The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software package generates test plans for arbitrary quantum circuits using the very efficient simulator QuIDDPro[1]. The quantum fault table is introduced and mathematically formalized, and the test generation method explained.
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking thermal noise. By slow cooling, it freezes the system in a low-energy configuration, but the algorithm often gets stuck in local minima. In quantum annealing, the thermal noise is replaced by controllable quantum fluctuations, and the technique can be implemented in modern quantum simulators. However, quantum-adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasi-degenerate ground states.
Frequently, subroutines in quantum computers have the structure $mathcal{F}mathcal{U}mathcal{F}^{-1}$, where $mathcal{F}$ is some unitary transform and $mathcal{U}$ is performing a quantum computation. In this paper we suggest that if, in analogy to spin echoes, $mathcal{F}$ and $mathcal{F}^{-1}$ can be implemented symmetrically such that $mathcal{F}$ and $mathcal{F}^{-1}$ have the same hardware errors, a symmetry boost in the fidelity of the combined $mathcal{F}mathcal{U}mathcal{F}^{-1}$ quantum operation results. Running the complete gate--by--gate implemented Shor algorithm, we show that the fidelity boost can be as large as a factor 10. Corroborating and extending our numerical results, we present analytical scaling calculations that show that a symmetry boost persists in the practically interesting case of a large number of qubits. Our analytical calculations predict a minimum boost factor of about 3, valid for all qubit numbers, which includes the boost factor 10 observed in our low-qubit-number simulations. While we find and document this symmetry boost here in the case of Shors algorithm, we suggest that other quantum algorithms might profit from similar symmetry-based performance boosts whenever $mathcal{F}mathcal{U}mathcal{F}^{-1}$ sub-units of the corresponding quantum algorithm can be identified.
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