相关论文: Geometric Phase Based Quantum Computation Applied …
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…
Geometric phases and holonomies (their non-commuting generalizations) are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against noise and experimental…
Non-adiabatic and non-closed evolutionary paths play a significant role in the fidelity of quantum gates. We propose a high-fidelity quantum control framework based on the quasi-topological number ($\nu_{\text{qua}}$), which extends the…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
Due to its geometric nature, holonomic quantum computation is fault-tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantum computation is still an open…
The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…
Nonadiabatic holonomic quantum computation has received increasing attention due to the merits of both robustness against control errors and high-speed implementation. A crucial step in realizing nonadiabatic holonomic quantum computation…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with…
This article deals with non-adiabatic processes (i.e. processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximated formula for the probabilities of the non-adiabatic transitions is…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric…
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…
Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
High-fidelity quantum gates are an essential prerequisite for large-scale quantum computation. When manipulating practical quantum systems, environmentally and operationally induced errors are inevitable, and thus, in addition to being…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…