High-fidelity quantum driving (1111.1579v1)

Abstract: The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize these quantum manipulations in the shortest possible time in order to minimize decoherence, and with a large stability against fluctuations of the control parameters. While optimizing a protocol for speed leads to a natural lower bound in the form of the quantum speed limit rooted in the Heisenberg uncertainty principle, stability against parameter variations typically requires adiabatic following of the system. The ultimate goal in quantum control is to prepare a desired state with 100% fidelity. Here we experimentally implement optimal control schemes that achieve nearly perfect fidelity for a two-level quantum system realized with Bose-Einstein condensates in optical lattices. By suitably tailoring the time-dependence of the system's parameters, we transform an initial quantum state into a desired final state through a short-cut protocol reaching the maximum speed compatible with the laws of quantum mechanics. In the opposite limit we implement the recently proposed transitionless superadiabatic protocols, in which the system perfectly follows the instantaneous adiabatic ground state. We demonstrate that superadiabatic protocols are extremely robust against parameter variations, making them useful for practical applications.

• The paper achieves near-100% fidelity and minimal transition times by applying composite pulse techniques in Bose-Einstein condensate systems.
• It introduces transitionless superadiabatic protocols that enable robust adiabatic state tracking even under parameter fluctuations.
• Experimental results underscore the potential to advance quantum information processing with precise and rapid state preparation.

High-Fidelity Quantum Driving: An Analysis

The paper "High-fidelity quantum driving" addresses the fundamental challenge of achieving precise control over the dynamics of quantum systems, a necessity in fields such as quantum information processing and molecular system manipulation. The authors present experimental implementations of optimal quantum control schemes aiming for high-fidelity transformations within two-level systems realized using Bose-Einstein condensates (BECs) in optical lattices.

Quantum Control Schemes

The paper explores two primary control schemes called "short-cut" protocols for achieving high fidelity in quantum transitions:

1. Quantum Brachistochrone Protocol: This protocol minimizes transition time to the quantum speed limit, akin to the classical brachistochrone problem. By employing composite pulse techniques, derived from Nuclear Magnetic Resonance (NMR), the protocol achieves near-100% fidelity in the shortest possible time. The experimental results indicate that the time required to reach the target state approaches the theoretical Fleming-Bhattacharyya quantum speed limit.
2. Transitionless Superadiabatic Protocols: These ensure transitionless tracking of the system's adiabatic ground state with high robustness against parameter fluctuations. Theoretical underpinnings follow from Berry's superadiabatic formalism, with practical implementation achieved by modifying the Hamiltonian to account for transitionless evolution.

Experimental Implementation and Results

Experiments utilized BECs in accelerated optical lattices to model two-level quantum systems. The dynamics guided by the Hamiltonian, expressed via Pauli matrices, were manipulated to transform an initial state into a desired target state with maximum fidelity. The composite pulse protocol allowed for a quantum speed limit approach, while the superadiabatic protocols ensured stable adiabatic following even under parameter variance, as demonstrated by high fidelities persisting across a wide range of conditions.

The comparison of protocols—composite pulse, Landau-Zener, and Roland-Cerf protocols—revealed distinctions in speed and fidelity: composite pulses provide rapid transitions; Roland-Cerf, while slower, guarantees a predefined adiabatic following within acceptable error bounds. The superadiabatic tangent protocol, analyzed for robustness and speed, achieved stability without speed penalties, getting remarkably close to the quantum speed limit.

Theoretical and Practical Implications

These findings hold significant implications for quantum computation and state preparation reliant on minimizing decoherence effects during quantum evolution. The experimental demonstrations and theoretical calculations elucidate strategies to achieve near-perfect state preparation with minimal time or error overhead, a critical requirement for reliable quantum information systems.

Future developments might involve extending these protocols to more complex, multi-level systems, further optimizing quantum computational processes and enhancing the capacity for quantum error correction through precise state manipulation.

In summary, the advancements presented in high-fidelity quantum driving delineate strategies for overcoming key challenges inherent in quantum control, making notable progress toward practical and robust quantum technology applications.