Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state preparation, dynamics, and measurement) are a priori unknown. We prove that, without any prior knowledge, if one can explore the full quantum state space by composing the operations, then every operation can be learned. When one cannot explore the full state space but all operations are approximately known and noise in Clifford gates is gate-independent, we find an efficient algorithm for learning all operations up to a single unlearnable parameter characterizing the fidelity of the initial state. For learning a noise channel on Clifford gates to a fixed accuracy, our algorithm uses quadratically fewer experiments than previously known protocols. Under more general conditions, the true description of the noise can be unlearnable; for example, we prove that no benchmarking protocol can learn gate-dependent Pauli noise on Clifford+T gates even under perfect state preparation and measurement. Despite not being able to learn the noise, we show that a noisy quantum computer that performs entangled measurements on multiple copies of an unknown state can yield a large advantage in learning properties of the state compared to a noiseless device that measures individual copies and then processes the measurement data using a classical computer. Concretely, we prove that noisy quantum computers with two-qubit gate error rate $\epsilon$ can achieve a learning task using $N$ copies of the state, while $N^{\Omega(1/\epsilon)}$ copies are required classically.
翻译:了解从实验中可以学到什么是科学进步的核心。 在这项工作中, 当所有操作( 状态准备、 动态和测量) 都事先未知时, 我们用学习理论视角来研究在量子机器中学习物理操作的任务。 我们证明, 在没有任何事先知识的情况下, 如果一个人可以通过执行操作来探索完整的量子状态空间, 那么每个操作都可以学习。 当一个人无法探索完整的状态空间, 但所有操作都是已知的, 而在克里福尔门的所有操作都离门不开门, 我们找到一种有效的算法, 学习所有操作, 直至一个单一的不可忽略的参数, 来描述初始状态的忠实性。 为了在克里福尔门上学习一个噪音频道, 我们的算法比以前已知的规程少了二次实验。 在更一般的条件下, 噪音的真实描述是不可忽视的; 比如, 我们证明基准协议无法在克里福尔特+T门门的大门上学习离门的保利的噪音, 即使无法了解噪音, 我们也可以用一个冷的量量的硬度计算机, 来获取一个不固定的硬质的硬度, 。