Machine Learning Enhances Quantum Control, Boosts Quantum Computation and Simulation

Preparing quantum many-body states, crucial for quantum computation and simulation, is a complex process requiring careful control field design. This article discusses using a dynamic control neural network to optimize control fields, which can suppress defect density and enhance cat-state fidelity in the quantum Ising model. The method’s robustness against random noise and spin number fluctuations suggests it could be a reliable approach for quantum control in many-body dynamics. This could have significant implications for practically implementing quantum computation and simulation.

What is the Importance of Precise Preparation of Quantum Many-Body States?

Quantum many-body states are crucial for the practical implementation of quantum computation and quantum simulation. The preparation of these states is a complex process that requires careful design of control fields. The inherent challenges posed by unavoidable excitations at critical points during quench processes necessitate this careful design. The preparation of quantum many-body states is also important for applications in various fields including quantum computation and quantum simulation.

Quantum metrology, a rapidly advancing field of quantum information science, is currently experiencing a surge of theoretical developments and experimental breakthroughs. A pivotal focus of a quantum metrology scheme involves the preparation of optimal non-classical states. Through the utilization of inherent quantum properties such as entanglement, coherence, and discord, quantum metrology can achieve the sensitivity for estimating unknown parameters that surpasses the constraints imposed by the standard quantum limit of classical strategies.

However, a comprehensive understanding of the relationship between quantum features and ultimate scaling sensitivity beyond the standard quantum limit remains elusive. Various forms of entangled states have been generated in engineered many-body systems to increase the phase sensitivity. But the relationship between these quantum features and the ultimate scaling sensitivity that goes beyond the standard quantum limit is still not fully understood.

How is the Preparation of Quantum Many-Body States Achieved?

The preparation of quantum many-body states involves utilizing unitary evolution. This process transforms the initial state, typically the ground state of some simple Hamiltonian, into the ground state of the target Hamiltonian. According to the adiabatic theorem, the unitary transformation can be implemented with arbitrary accuracy by changing the Hamiltonian sufficiently slowly.

However, the strict requirement of the adiabatic limit dictates infinitely long evolution time, inevitably resulting in system decoherence and the disappearance of entanglement. In particular, crossing a quantum critical point (QCP) in finite time challenges the adiabatic condition due to the closing of the energy gap, which ultimately results in the formation of excitations. Consequently, a trade-off must be considered between the evolution time and the excitations generated by the system.

Efforts have recently been dedicated to achieving an optimal passage through the non-adiabatic evolution, particularly across the QCP, aiming to minimize unwanted excitations or to maximize fidelity. Shortcut to adiabaticity (STA) provides a way of finding fast trajectories that connect the initial and final states by manipulating the system’s parameters in a non-adiabatic fashion while still obtaining results akin to those of an adiabatic process.

What is Quantum Optimal Control?

Quantum optimal control is a prevalent approach where time-dependent control parameters of a system are fine-tuned using optimal control theory. Governed by time-energy uncertainty relations, the characteristic time scales during non-adiabatic evolution are encapsulated by the quantum speed limit, which delves into the minimum time required for quantum states to achieve specific predetermined objectives.

This is particularly crucial in the field of quantum information where rapid dynamics are often advantageous. While the quantum optimal control finds widespread applications in various systems, it is of fundamental interest to formulate the control theory in a general framework.

Over the past few years, machine learning technology has become an integral part of the optimization theory and has been proved to be applicable to optimizing the parameters of variational states in a variety of interacting quantum many-body systems.

How Does Machine Learning Aid Quantum Control?

In this work, a promising and versatile dynamic control neural network is introduced, tailored to optimize control fields. This method addresses the problem of suppressing defect density and enhancing cat-state fidelity during the passage across the critical point in the quantum Ising model.

The method facilitates seamless transitions between different objective functions by adjusting the optimization strategy. In comparison to gradient-based power-law quench methods, this approach demonstrates significant advantages for both small system sizes and long-term evolutions.

Numerical simulations demonstrate the robustness of this proposal against random noise and spin number fluctuations. The optimized defect density and cat-state fidelity exhibit a transition at a critical ratio of the quench duration to the system size, coinciding with the quantum speed limit for quantum evolution.

What are the Implications of this Research?

This research provides a detailed analysis of the specific forms of control fields and summarizes common features for experimental implementation. Using a dynamic control neural network to optimize control fields presents a promising and versatile approach to quantum control.

The method’s ability to suppress defect density and enhance cat-state fidelity during the passage across the critical point in the quantum Ising model could have significant implications for the practical implementation of quantum computation and simulation.

Furthermore, the robustness of this proposal against random noise and spin number fluctuations, as demonstrated by numerical simulations, suggests that this approach could be a reliable method for quantum control in many-body dynamics.