相关论文: Geometric quantum computation with NMR
Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
While Nuclear Magnetic Resonance (NMR) techniques are unlikely to lead to a large scale quantum computer they are well suited to investigating basic phenomena and developing new techniques. Indeed it is likely that many existing NMR…
Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates.…
The geometry of the parameter space is encoded by the quantum geometric tensor, which captures fundamental information about quantum states and contains both the quantum metric tensor and the curvature of the Berry connection. We present a…
The phase relation between quantum states represents an essential resource for the storage and processing of quantum information. While quantum phases are commonly controlled dynamically by tuning energetic interactions, utilizing geometric…
Quantum manipulation based on geometric phases provides a promising way towards robust quantum gates. However, in the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions…
We elaborate on the distinction between geometric and dynamical phase in quantum theory and show that the former is intrinsically linked to the quantum mechanical probabilistic structure. In particular, we examine the appearance of the…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors.…
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…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior…
Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate…
We study the geometric phase for the ground state of a generalized one-dimensional non-Hermitian quantum XY model, which has transverse-field-dependent intrinsic rotation-time reversal symmetry. Based on the exact solution, this model is…
The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is…
Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources…
While quantum information processing by nuclear magnetic resonance (NMR) with small number of qubits is well established, implementation of lengthy computations have proved to be difficult due to decoherence/relaxation. In such…
Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…
We calculate Berry's phase when the driving field, to which a spin-1/2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g., the angular…