Abstract
Developments in Artificial Intelligence (AI) are helping to solve complex physical problems that otherwise may be too computationally demanding to solve using traditional approaches. Universal Approximation Theorems tell us that we can model any physical system if we can approximate the system with some continuous function (i.e., compact convergence topology and algorithmically generated sets of functions, such as the convolutional neural network), whether for an arbitrary depth or arbitrary width neural network. We consider the problem of solving a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> coupled algebraic equations as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> becomes very large and apply machine learning (ML) to solve this problem for any value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> . The physical problem we are focusing on is to model the equilibrium positions of ions in an ion trap. A storage ring quantum computer could contain well over tens of thousands of ions. Quickly determining the equilibrium positions will be important to minimize the time to target and observe each ion. As each ion serves as a single qubit, this is important for setting and measuring the individual qubit states. The phonon modes from a collection of ions acts as another qubit, useful for gate operations. Measuring the phonon modes, where ions are oscillating around their respective equilibrium positions also means understanding the equilibrium positions very well. Turning all of this into a virtual diagnostic allows real time prediction and comparison to ensure unique definition of each ion.
Highlights
Q UANTUM information systems (QIS) refers to developing technologies, such as quantum communication and quantum computing (QC) [1]
A virtual diagnostic tool can be enabled by multiple supervised Machine Learning (ML) algorithms, such as Neural Networks (NN), and the accuracy of the machine learning (ML) model depends on the quality of data used for training, i.e., there should be a good amount of data that correctly represents the expected solutions, as the number of ions becomes large
Quantum computers based on ion traps are limited by the small number of ions that can be used as qubits
Summary
Q UANTUM information systems (QIS) refers to developing technologies, such as quantum communication and quantum computing (QC) [1]. The technological leap enabled by QIS comes from harnessing the quantum properties of atomic, electronic, and photonic systems, to perform calculations that are virtually impossible even with state-of-art computational systems. The principle of superposition in quantum mechanics (QM) is conceptually different than in classical physics [3] We describe it in the context of the QM mathematical framework. In the context of QC, a quantum bit, or qubit, exists as a superposition of the normal states represented by |0 and |1. Measuring the qubit will result in either 0 or 1 Note how this situation is different from classical computing, where the state of the classical bit is either 0 or 1 at any specific time, but not both of them. This work concerns a particular QIS: the storage ring quantum computer (SRQC) [7], which uses an unprecedented long chain of ions as qubits
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