Patrick Coles

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). In this work, we prove the first out-of-distribution generalization guarantees in QML, where we require a trained model to perform well even on testing data drawn from a distribution different from the training data distribution. Namely, we establish out-of-distribution generalization for the task of learning an unknown unitary using a quantum neural network and for a broad class of training and testing distributions. In particular, we show that one can learn the action of a unitary on entangled states using only product state training data. Since product states can be prepared using only single-qubit gates, this advances the near-term prospects of QML for learning quantum dynamics, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Based on these insights, we propose a QML-based algorithm for simulating quantum dynamics on near-term quantum hardware and rigorously prove its resource-efficiency in terms of qubit and training data requirements. We also demonstrate the viability of this algorithm through numerical experiments, both in classical simulations and on quantum hardware. Finally, we embed this algorithm in a broader framework for using QML methods for quantum dynamical simulation on NISQ devices.

Abstract Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data $\{X_i^{noisy},X_i^{exact}\}$ via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where $X_i^{noisy}$ and $X_i^{exact}$ are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.