| dc.description.abstract | Towards realizing practically useful quantum devices, the sizes of quantum devices are being scaled up. An imminent challenge to scalability is ensuring resource requirements of learning tasks that occur as part of device characterization and execution of quantum algorithms also scale favorably. Resource requirements in general grow exponentially with the system size or the number of qubits and at the standard quantum limit (SQL) with respect to the learning error. On the other hand, much is known about the quantum system, which is of known construction with prior experience. A natural question is then, can we accelerate learning of quantum systems using prior information? In this thesis, we describe how prior information can be exploited to reduce resources over current baseline methods.
In the first part, we consider the problem of quantum state tomography and identify a class of quantum states that are hard to simulate classically, to be learnable in sample complexity growing polynomially in the number of qubits. Our learning algorithm can be used to verify circuits commonly used in quantum advantage experiments. In the second part, we consider the problem of discriminating quantum channels on a physical system under experimental constraints of limited control and lack of direct readout. After introducing an ancillary measurement system that weakly interacts with the physical system, we show sequential protocols adapted to this setting outperform multi-shot and parallel protocols, achieving learning rates faster than SQL. In the third part, we consider the common recurring task of Hamiltonian learning during calibration. We introduce a batch-mode Hamiltonian active learner (HAL) that proposes informative queries adaptively during learning. In our experiments on an IBM quantum device, HAL reduced resources by 95% compared to standard methods and by 33% compared to a sequential active learner. In the fourth part, we consider the problem of estimating the expectation value of a Hamiltonian with respect to a quantum state, which features in many hybrid quantum-classical algorithms for ground state energy estimation in quantum chemistry. To guide the selection of of measurement methods designed for this problem, we propose a benchmark that assesses their performance against a set of common molecular Hamiltonians and common states. Benchmarking on IBM quantum devices reveal that decision diagrams are preferred for near-term quantum hardware. Finally in the fifth part, we propose a quantum algorithm based on molecular bootstrap embedding for ground state estimation of large molecular Hamiltonians that could potentially take advantage of access to multiple smaller quantum computers. | |
