Related papers: Discrete phase-space structure of $n$-qubit mutual…
We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The…
Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary…
We investigate the fate of dissipative phase transitions in quantum many-body systems when the individual constituents are qudits ($d$-level systems) instead of qubits. As an example system, we employ a permutation-invariant $XY$ model of…
A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, $d$, of the considered Hilbert space is a power of…
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic geometric phase shift is extensively investigated. In this paper, we demonstrate the nonadiabatic scheme for the geometric phase shift and conditional geometric…
The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…
We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation,…
We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…
We discuss a general physical mechanism for arbitrary control of the quantum states of multiple qubits in the symmetric Dicke subspace. The qubit-qubit coupling leads to unequal energy spacing in the symmetric Dicke subspace. This allows…
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the moduli space of stable algebraic curves and,…
Complex mesoscopic systems play increasingly important roles in modern science -- from understanding biological functions at the molecular level, to designing solid-state information processing devices. The operation of these systems…
We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction. We use a numerical method combing the cluster mean-field theory and the matrix product state(MPS) to obtain the…
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
Finite coherent quantum systems exhibit a nontrivial response to local sources of phase curvature, which cannot be reduced to conventional forces, disorder-induced localization, or simple gap opening. Here we show that, in finite fermionic…
We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of…
We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…