Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and $O(\epsilon^{-2})$ queries in achieving learning error $\epsilon$ due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error $\epsilon$ through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM Quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves up to a $99.8\%$ reduction in queries required, and a $99.1\%$ reduction over the comparable non-adaptive learning algorithm. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.
翻译:汉密尔顿学习的标准技术要求仔细设计查询和美元(Epsilon ⁇ ⁇ -2})查询,以达到标准的量限。为了在学习错误范围内有效和准确地估计汉密尔顿参数的目标,通过最低限度查询,我们引入了一位活跃的学习者,该学习者将获得一套初步培训范例,并有能力交互查询量量子系统以生成新的培训数据。我们正式确定并实验评估了汉密尔顿学习中积极学习(HAL)算法的性能,用于在四种不同的超导IBM 量子装置上学习双重交叉共振动汉密尔密尔顿仪的6项参数。与同一问题的标准技术以及特定学习错误相比,高水平AL达到9.8美元,在必要查询中减少查询,并能够交互质质质质询系统生成新的培训数据。我们正式确定和实验性地评估这一汉密尔顿积极学习(HAL)算法的6项参数,用于在4种不同的IBM Q Qalimalnial Exeral 期间学习标准比级算法,可以比Healnial-Cal-deal-dealexex