Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEnergetic cost of quantum control protocols
86
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We quantitatively assess the energetic cost of several well-known control protocols that achieve a finite time adiabatic dynamics, namely counterdiabatic and local counterdiabatic driving, optimal control, and inverse engineering. By employing a cost measure based on the norm of the total driving Hamiltonian, we show that a hierarchy of costs emerges that is dependent on the protocol duration. As case studies we explore the Landau-Zener model, the quantum harmonic oscillator, and the Jaynes-Cummings model and establish that qualitatively similar results hold in all cases. For the analytically tractable Landau-Zener case, we further relate the effectiveness of a control protocol with the spectral features of the new driving Hamiltonians and show that in the case of counterdiabatic driving, it is possible to further minimize the cost by optimizing the ramp.
rate research
Read More
We discuss thermodynamic work cost of various stages of a quantum estimation protocol: probe and memory register preparation, measurement and extraction of work from post-measurement states. We consider both (i) a multi-shot scenario, where average work is calculated in terms of the standard Shannon entropy and (ii) a single-shot scenario, where deterministic work is expressed in terms of min- and max-entropies. We discuss an exemplary phase estimation protocol where estimation precision is optimized under a fixed work credit (multi-shot) or a total work cost (single-shot). In the multi-shot regime precision is determined using the concept of Fisher information, while in the single-shot case we advocate the use of confidence intervals as only they can provide a meaningful and reliable information in a single-shot experiment, combining naturally with the the concept of deterministic work.
We analyze work extraction from a qubit into a wave guide (WG) acting as a battery, where work is the coherent component of the energy radiated by the qubit. The process is stimulated by a wave packet whose mean photon number (the batterys charge) can be adjusted. We show that the extracted work is bounded by the qubits ergotropy, and that the bound is saturated for a large enough batterys charge. If this charge is small, work can still be extracted. Its amount is controlled by the quantum coherence initially injected in the qubits state, that appears as a key parameter when energetic resources are limited. This new and autonomous scenario for the study of quantum batteries can be implemented with state-of-the-art artificial qubits coupled to WGs.
We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-SNE, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiability problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {it uncertainty relation} is a generic term for various trade-off relations in nature. In this letter, we improve the Kennard-Robertson uncertainty relation, and clarify how much coherence we need to implement quantum measurement under conservation laws. Our approach systematically improves and reproduces the previous various refinements of the Kennard-Robertson inequality. As a direct consequence of our inequalities, we improve a well-known limitation of quantum measurements, the Wigner-Araki-Yanase-Ozawa theorem. This improvement gives an asymptotic equality for the necessary and sufficient amount of coherence to implement a quantum measurement with the desired accuracy under conservation laws.
In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
