The unitary dependence theory for characterizing quantum circuits and states

Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms. Using mathematical structures to characterize quantum circuits and states may lead to systematic development of quantum algorithms. Here, the authors propose a unitary dependence theory to characterize the behaviours of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities.

Automated summary

Most existing quantum algorithms are accidental discoveries or adaptations from classical algorithms. There is a need for a systematic theory to understand and design quantum circuits. The authors propose a unitary dependence theory that characterizes the behaviors of quantum circuits and states, offering practical information on measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon system partitioning.