One way the waiter can counteract this force and walk quicker is by tilting the tray with the glass so as to keep the water from spilling, modifying the tilt as they weave around the restaurant to account for the shifting direction and magnitude of the force. The faster the waiter moves, the stronger the force, so the only way to keep the glass from spilling is to move very slowly. When the waiter starts moving they accelerate and induce a ‘force’ on the glass, making it wobble and splash around. Imagine a waiter carrying a glass of water on a tray from the bar to a customer at a table. H(t) and (C) evolving via H(t) with an added counterdiabatic drive. Its ground state at t = 0, (B) evolving via time-dependent Hamiltonian (or whatever suits your fancy), but really it's a quantum system in (A) This may LOOK like a waiter's hand carrying a tray with a glass of water The concept of CD can be made clear using a very popular analogy (see Fig. One way of achieving this is to use something called counterdiabatic driving (CD), which involves counteracting potential excitations by applying an external drive. The question then becomes how to speed up these Hamiltonian dynamics without exciting unwanted transitions. Preparing ground states in this way, or adiabatically, is difficult evolving a quantum system for very long times makes it difficult to maintain coherence, but evolving it too quickly excites it out of the required state. However, if the time T is too short, the system has a high chance of transitioning out of the ground state into an excited one. This is because of something called the Quantum Adiabatic Theorem, which tells us, simply, that functions describing states evolving slowly will adapt to the slowly-changing conditions. Importantly, the change from H(0) to H(T) has to be slow enough. If we perform this evolution slowly enough, we can keep the quantum system in the instantaneous ground state for every point in time (assuming all ground states are non-degenerate, meaning they represent unique energies throughout the evolution). However, we can then evolve this Hamiltonian for a time T to Hamiltonian H(T)-like combining snapshots into a movie-whose ground state encodes something interesting (say, the solution to the aforementioned optimization problem or some novel phase of matter). This state is easy to prepare, but isn't particularly useful-it's basically just a snapshot of the system. In order to represent the ground state, we begin with a pared-down, time-dependent version of the Hamiltonian called H(0). We think of quantum states in terms of their Hamiltonian, an operator that represents a system's potential and kinetic energy as an equation. So-how do we do it? One way is counterdiabatic driving, and it's a lot like running with a glass of water on a tray. Being able to prepare and manipulate such ground states is also incredibly important in understanding various quantum phenomena, such as high-temperature superfluidity and superconductivity as well as, say, topological quantum computing. Finding a system's ground state is often equivalent to solving a very hard optimization problem. Ground states of many-body quantum systems (especially systems made of spins) are cool – and I don’t just mean their temperature. By Ieva Čepaitė, University of Strathclyde, Glasgow
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