Related papers: Aspects of Complexity in Quantum Evolutions on the…
We study the complexity of both time-optimal and time sub-optimal quantum Hamiltonian evolutions connecting arbitrary source and a target states on the Bloch sphere equipped with the Fubini-Study metric. This investigation is performed in a…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
In optimal quantum-mechanical evolutions, motion can occur along non-predetermined paths of shortest length in an optimal time. Alternatively, optimal evolutions can happen along predefined paths with no waste of energy resources and 100%…
It is known that mixed quantum states are highly entropic states of imperfect knowledge (i.e., incomplete information) about a quantum system, while pure quantum states are states of perfect knowledge (i.e., complete information) with…
We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh's approach), the evolution is specified by a traceless stationary…
The concept of quantum acceleration limit has been recently introduced for any unitary time evolution of quantum systems under arbitrary nonstationary Hamiltonians. While Alsing and Cafaro [Int. J. Geom. Methods Mod. Phys. 21, 2440009…
We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and…
In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we…
We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is…
We examine the pertinent geometric characteristics of entanglement that arise from stationary Hamiltonian evolutions transitioning from separable to maximally entangled two-qubit quantum states. From a geometric perspective, each evolution…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis,…
It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the…
For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time…
We present a novel inequality on the purity of a bipartite state depending solely on the difference of the local Bloch vector lengths. For two qubits this inequality is tight for all marginal states and so extends the previously known…