Decision Diagrams for Quantum Measurements with Shallow Circuits

• Published in: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) pp. 24 - 34
• Main Authors: Hillmich, Stefan, Hadfield, Charles, Raymond, Rudy, Mezzacapo, Antonio, Wille, Robert
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2021
• Subjects: classical shadows; decision diagrams; Merging; Probabilistic logic; Probability distribution; Protocols; Quantum chemistry; quantum measurements; Qubit; shallow circuits; Tensors
• DOI: 10.1109/QCE52317.2021.00018

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases. This approach generalises previously known uniform and locally-biased randomised estimators. The decision diagrams are constructed given target quantum operators and can be optimised considering different strategies. We show numerically that the estimators introduced here can produce more precise estimates on some quantum chemistry Hamiltonians, compared to previously known randomised protocols and Pauli grouping methods.