Learning to predict arbitrary quantum processes
- URL: http://arxiv.org/abs/2210.14894v3
- Date: Sat, 15 Apr 2023 01:15:40 GMT
- Title: Learning to predict arbitrary quantum processes
- Authors: Hsin-Yuan Huang, Sitan Chen, John Preskill
- Abstract summary: We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process over $n$ qubits.
Our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.
- Score: 7.69390398476646
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present an efficient machine learning (ML) algorithm for predicting any
unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of
distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML
algorithm can learn to predict any local property of the output from the
unknown process~$\mathcal{E}$, with a small average error over input states
drawn from $\mathcal{D}$. The ML algorithm is computationally efficient even
when the unknown process is a quantum circuit with exponentially many gates.
Our algorithm combines efficient procedures for learning properties of an
unknown state and for learning a low-degree approximation to an unknown
observable. The analysis hinges on proving new norm inequalities, including a
quantum analogue of the classical Bohnenblust-Hille inequality, which we derive
by giving an improved algorithm for optimizing local Hamiltonians. Numerical
experiments on predicting quantum dynamics with evolution time up to $10^6$ and
system size up to $50$ qubits corroborate our proof. Overall, our results
highlight the potential for ML models to predict the output of complex quantum
dynamics much faster than the time needed to run the process itself.
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