Correlated Computing

JR Minkel

Bülent Demirel, Weikai Weng, Christopher Thalacker +2 more

Abstract Quantum correlations are central to the foundations of quantum physics and form the basis of quantum technologies. Here, our goal is to connect quantum correlations and computation: using quantum correlations as a resource for computation—and vice versa, using computation to test quantum correlations. We derive Bell-type inequalities that test the capacity of quantum states for computing Boolean functions within a specific model of computation and experimentally investigate them using 4-photon Greenberger–Horne–Zeilinger (GHZ) states. Furthermore, we show how the resource states can be used to specifically compute Boolean functions—which can be used to test and verify the non-classicality of the underlying quantum states. The connection between quantum correlation and computability shown here has applications in quantum technologies, and is important for networked computing being performed by measurements on distributed multipartite quantum states.

André L. Oestereich

This dissertation explores some diferences between quantum mechanics and other theories from a computational perspective, in particular with respect to the kind of correlations they allow, and their computational consequences. It starts with an operational characterization of locality, no-signaling and noncontextuality. Then it proceeds to an introduction to measurement-based quantum computation, a model in which quantum correlations are used to perform computation. Such a model is then generalized in a framework, proposed by Anders and Browne [1] and studied by Raussendorf [2], that aims to make the computational power of correlations more evident. We proceed to see that noncontextual resources do not provide a computational enhancement and that quantum resources do provide it even without adaptivity. We continue by reviewing a scheme for reliable computation using faulty components, rst proposed by von Neumann and later studied by Hajek and Weller [3] and Evans and Schulman [4]. This scheme is then used to show how a range of bipartite quantum correlations su ce for reliable computation. We conclude by showing that quantum correlations that violate non-contextuality bounds by an arbitrarily small amount can be used to enable reliable computation

George A. Bekey

Peyton Schales

Abstract Quantum computing is an emerging technology that, with its exponential computational speedup, will allow us to solve a new level of hard problems. From rapid vaccine development, efficient discovery of exotic materials, and complex AI models, to quickly cracking RSA encryption, quantum computers have the potential to revolutionize science. However, for quantum computing to solve these problems, quantum error correction methods are needed to eliminate qubit errors. An underlying assumption of current quantum error correction is that qubit errors are not correlated. If correlated qubit errors are prevalent, quantum error correction will be difficult, if not impossible. In this work, I developed a method to identify correlated errors between pairs of qubits and used this method to determine if correlations exist on current small-scale quantum computers. My method uses independence of error probabilities P(qa) ⨉ P(qb) = P(qaqb) to determine correlation. After running 40 million experiments to collect error probabilities by varying the quantum gates, number of gates, and pairs of qubits on multiple quantum computers, I found that these computers have a high occurrence of correlated qubit errors when qubits are topological neighbors. For example, I found that Hadamard gate operations can cause correlated errors, supported by a p-value of 0.0160. My work shows that the assumption that qubit errors are not correlated is incorrect for current quantum computers. In the future, scientists can use these methods to test for correlated errors as they develop new quantum computers, enabling quantum computing to achieve its full potential.