Related papers: Topological sum rule for geometric phases of quant…
In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
Berry monopoles always cancel when summing over a complete set of energy eigenstates. We demonstrate that analogous sum rules exist for geometric phases and their underlying 2-forms in non-adiabatic evolution. Our result has implications…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We present an idealized model involving interacting quantum dots that can support both the dynamical and geometrical forms of quantum computation. We show that by employing a structure similar to the one used in the Aharonov-Bohm effect we…
Examples of non-hermitian quantum systems admitting topological insulator phase are presented in one, two and three space dimensions. All of these non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A…
We prove an entanglement sum rule for $(d-1)$-dimensional quantum lattice models with finite abelian higher-form symmetries, obtained by minimally coupling a sector on $p$-simplices carrying a $p$-form $G$ symmetry to a sector on…
We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this…
We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum…
We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…