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We demonstrate how quantum field theory problems can be embedded on quantum annealers. The general method we use is a discretisation of the field theory problem into a general Ising model, with the continuous field values being encoded into…
The procedure proposed recently by J.Bougie, A.Gangopadhyaya and J.V.Mallow to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order…
Quantum computing is a promising paradigm to solve computationally intractable problems. Various companies such as, IBM, Rigetti and D-Wave offer quantum computers using a cloud-based platform that possess several interesting features.…
Quantum Computers, one fully realized, can represent an exponential boost in computing power. However, the computational power of the current quantum computers, referred to as Noisy Internediate Scale Quantum, or NISQ, is severely limited…
The 1+1D Ising model is an ideal benchmark for quantum algorithms, as it is very well understood theoretically. This is true even when expanding the model to include complex coupling constants. In this work, we implement quantum algorithms…
Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
Four decades after Richard Feynman's famous remark, we have reached a stage at which nature can be simulated quantum mechanically. Quantum simulation is among the most promising applications of quantum computing. However, like many quantum…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
We show how a universal gate set for topological quantum computation in the Ising TQFT, the non-Abelian sector of the putative effective field theory of the $\nu=5/2$ fractional quantum Hall state, can be implemented. This implementation…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…