Related papers: Intrinsic geometry of quantum adiabatic evolution …
The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this…
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of…
We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the…
In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this…
We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground…
In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is…
The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we consider quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a…
Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on…
Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the…
The codespace of a quantum error-correcting code can often be identified with the degenerate ground-space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error…
Quantum adiabatic algorithms are commonly analyzed through local spectral properties of an interpolating Hamiltonian, most notably the minimum energy gap. While this perspective captures an important constraint on adiabatic runtimes, it…
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware has raised challenging questions about how to evaluate adiabatic quantum…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
An adiabatic change of parameters along a closed path may interchange the (quasi-)eigenenergies and eigenspaces of a closed quantum system. Such discrepancies induced by adiabatic cycles are refereed to as the exotic quantum holonomy, which…
The ground-state quantum geometry is at the root of several static and adiabatic properties, while genuinely dynamic properties are routinely addressed via Kubo formulae, whose essential entries are the excited states. It is shown here that…
We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this…
Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to…
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required…
Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable…
Nonadiabatic geometric quantum computation (NGQC) has emerged as an excellent proposal for achieving fast and robust quantum control against control errors. However, previous NGQC protocols could not be strongly resilient against the noise…