Related papers: Geometrical perspective on quantum states and quan…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. In this theory, fundamental processes are described in terms of pairwise interactions between quantum degrees of freedom. The geometry of…
We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
We present a new model of quantum computation rooted in the representation theory of the mass less sector of unitary irreducible representations of the extended Poincare group developed in [1].
The one-way quantum computer (QCc) is a universal scheme of quantum computation consisting only of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. The computational model underlying the QCc is…
A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups…