Related papers: Accuracy of the quantum adiabatic theorem in its o…
The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.
The quantum adiabatic theorem is fundamental to time dependent quantum systems, but being able to characterize quantitatively an adiabatic evolution in many-body systems can be a challenge. This work demonstrates that the use of appropriate…
The quantum superposition principle is reconsidered based on adiabatic theorem of quantum mechanics, nonadiabatic dressed states and experimental evidence. The physical mechanism and physical properties of the quantum superposition are…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its…
Since the discovery of adiabatic quantum computing, a need has arisen for rigorously proven bounds for the error in the adiabatic approximation. We present in this paper, a rigorous and elementary derivation of upper and lower bounds on the…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
Adiabatic quantum control protocols have been of wide interest to quantum computation due to their robustness and insensitivity to their actual duration of execution. As an extension of previous quantum learning algorithms, this work…
According to the quantum adiabatic theorem, we can in principle obtain a true vacuum of a quantum system starting from a trivial vacuum of a simple Hamiltonian. In actual adiabatic digital quantum simulation with finite time length and…
The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard…
We analyze the performance of adiabatic quantum computation (AQC) under the effect of decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast…
We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…
In order to understand quantum decoherence of a quantum system due to its interaction with a large system behaving classically, we introduce the concept of adiabatic quantum entanglement based on the Born-Oppenhemeir approximation. In the…
Adiabatic approximation for quantum evolution is investigated quantitatively with addressing its dependence on the Berry connections. We find that, in the adiabatic limit, the adiabatic fidelity may uniformly converge to unit or diverge…
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and…
The adiabatic theorem is an important concept in quantum mechanics, it tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In…