Related papers: Quantum brachistochrone problem for spin-1 in a ma…
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…
For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and…
We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and…
According to the Heisenberg uncertainty principle between time and energy fluctuation, a concept of the quantum speed limit (QSL) has been established to determine the minimum evolutionary time between quantum states. Considerable…
We present a number of new physical systems that may be addressed using methods of time dependent transformation. A recap of results available for two-state systems is given, with particular emphasis on the AC stark effect. We give some…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In…
It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical…
Transforming an initial quantum state into a target state through the fastest possible route---a quantum brachistochrone---is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent…
We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is…
We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity.…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By…
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%…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by…
Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some…
Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary pre-assigned…