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Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…
Making use of an universal quantum network or QCPU proposed by me [6], some special quantum networks for simulating some quantum systems are given out. Specially, it is obtained that the quantum network for the time evolution operator which…
The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in…
Quantum computing and the workings of the brain have many aspects in common and have been attracting increasing attention in academia and industry. The computation in both is parallel and non-discrete. Though the underlying physical…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multi-configurational methods, face computational hurdles in solving the electronic Schr\"odinger…
High-energy particle collisions can convert energy into matter through the inelastic production of new particles. Quantum computers are an ideal platform for simulating the out-of-equilibrium dynamics of collisions and the formation of…
Using the subdynamical kinetic equation for an open quantum system, a formulation is presented for performing decoherence-free (DF) quantum computing in Rigged Liouville Space (RLS). Three types of interactions were considered, and in each…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not…
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still…
Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…
We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and…
There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer.…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…