[论文解读] The power and limitations of learning quantum dynamics incoherently

Sofiène Jerbi, Joe Gibbs+5 more|arXiv (Cornell University)|Mar 22, 2023

Quantum Computing Algorithms and Architecture被引用 8

一句话总结

本文分析在不相干设置下学习幺正动力学，证明在可以进行任意深度测量时可以高效学习可高效表示的幺正；但仅使用浅层测量时只能高效学习低纠缠的幺正，存在基本的不可行性界限。

ABSTRACT

Quantum process learning is emerging as an important tool to study quantum systems. While studied extensively in coherent frameworks, where the target and model system can share quantum information, less attention has been paid to whether the dynamics of quantum systems can be learned without the system and target directly interacting. Such incoherent frameworks are practically appealing since they open up methods of transpiling quantum processes between the different physical platforms without the need for technically challenging hybrid entanglement schemes. Here we provide bounds on the sample complexity of learning unitary processes incoherently by analyzing the number of measurements that are required to emulate well-established coherent learning strategies. We prove that if arbitrary measurements are allowed, then any efficiently representable unitary can be efficiently learned within the incoherent framework; however, when restricted to shallow-depth measurements only low-entangling unitaries can be learned. We demonstrate our incoherent learning algorithm for low entangling unitaries by successfully learning a 16-qubit unitary on exttt{ibmq\_kolkata}, and further demonstrate the scalabilty of our proposed algorithm through extensive numerical experiments.

研究动机与目标

• Motivate learning quantum processes without direct interaction between target and model systems.
• Establish sampling and computational limits for incoherent learning of unitaries.
• Compare deep (arbitrary measurements) versus shallow (Pauli) measurement regimes.
• Demonstrate practical implementation on near-term hardware for low-entangling dynamics.

提出的方法

• Define Hilbert-Schmidt Test cost to quantify learning accuracy of V(θ) to approximate U (Eq. 1).
• Use training data from input-output state pairs and local training losses to enable learning (Eq. 4, Eq. 5).
• Prove that with deep measurements (Clifford shadows) one can incoherently emulate coherent learning for any efficiently representable unitary (Theorem III.1, informal).
• Show that with shallow measurements (Pauli shadows) only low-entangling unitaries can be efficiently learned (Theorem III.2, informal).
• Prove a no-go result: there exist efficiently representable unitaries requiring exponential samples with only shallow measurements (Theorem III.3, informal).
• Provide experimental demonstrations: learning a 16-qubit low-entangling unitary on ibmq_kolkata and numerical scalability studies.

实验结果

研究问题

• RQ1 Can coherent-unitary learning be emulated in an incoherent setting under arbitrary measurements?
• RQ2 What are the sample complexity and computational implications of incoherent learning with deep versus shallow measurements?
• RQ3 Are there fundamental limits to incoherent learning when restricted to simple (Pauli) measurements?
• RQ4 How does the entangling rate of the target unitary affect learnability and resource requirements?
• RQ5 Can the proposed incoherent learning approach be demonstrated on real quantum hardware for practical problem sizes?

主要发现

• With arbitrary measurements, any efficiently representable unitary can be learned incoherently with polynomial sample complexity (Theorem III.1, informal).
• With shallow (local) measurements, one can efficiently learn only low-entangling unitaries (Theorem III.2, informal).
• There exists a fundamental no-go: some efficiently representable unitaries require exponential samples under shallow measurements (Theorem III.3, informal).
• Clifford-shadow based deep-measurement approach can emulate coherent learning but suffers from barren plateaus and computational inefficiency for deep circuits.
• Demonstrated learning of a 16-qubit low-entangling unitary on ibmq_kolkata and scalability studies show practical viability for near-term hardware.