Related papers: Quantum Computation and the localization of Modula…
This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired…
We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang-Baxter operators in monoidal categories. The essential problem is to determine when a…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit…
A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…
Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown…
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…
We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces…