Efficient Quantum Algorithms for Quantum Optimal Control

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.Comment: 17 pages, 2 figure

Simulating Markovian open quantum systems using higher-order series expansion

We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel's principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series.Comment: 28 pages, various minor changes. To appear in the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023

Artificial Intelligence in Radiotherapy Treatment Planning: Present and Future.

Treatment planning is an essential step of the radiotherapy workflow. It has become more sophisticated over the past couple of decades with the help of computer science, enabling planners to design highly complex radiotherapy plans to minimize the normal tissue damage while persevering sufficient tumor control. As a result, treatment planning has become more labor intensive, requiring hours or even days of planner effort to optimize an individual patient case in a trial-and-error fashion. More recently, artificial intelligence has been utilized to automate and improve various aspects of medical science. For radiotherapy treatment planning, many algorithms have been developed to better support planners. These algorithms focus on automating the planning process and/or optimizing dosimetric trade-offs, and they have already made great impact on improving treatment planning efficiency and plan quality consistency. In this review, the smart planning tools in current clinical use are summarized in 3 main categories: automated rule implementation and reasoning, modeling of prior knowledge in clinical practice, and multicriteria optimization. Novel artificial intelligence-based treatment planning applications, such as deep learning-based algorithms and emerging research directions, are also reviewed. Finally, the challenges of artificial intelligence-based treatment planning are discussed for future works

Efficient Quantum Algorithms for Simulating Lindblad Evolution

We consider the natural generalization of the Schrodinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an n-qubit system for time t within precision epsilon. If the Lindbladian consists of poly(n) operators that can each be expressed as a linear combination of poly(n) tensor products of Pauli operators then the gate cost of our algorithm is O(t polylog(t/epsilon) poly(n)). We also obtain similar bounds for the cases where the Lindbladian consists of local operators, and where the Lindbladian consists of sparse operators. This is remarkable in light of evidence that we provide indicating that the above efficiency is impossible to attain by first expressing Lindblad evolution as Schrodinger evolution on a larger system and tracing out the ancillary system: the cost of such a reduction incurs an efficiency overhead of O(t^2/epsilon) even before the Hamiltonian evolution simulation begins. Instead, the approach of our algorithm is to use a novel variation of the "linear combinations of unitaries" construction that pertains to channels