Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers

Understand

We develop three new methods to implement any Linear Combination of Unitaries (LCU), a powerful quantum algorithmic tool with diverse applications.

• While the standard LCU procedure requires several ancilla qubits and sophisticated multi-qubit controlled operations, our methods consume significantly fewer quantum resources.
• The first method (Single-Ancilla LCU) estimates expectation values of observables with respect to any quantum state prepared by an LCU procedure while requiring only a single ancilla qubit, and no multi-qubit controlled operations.
• The second approach (Analog LCU) is a simple, physically motivated, continuous-time analogue of LCU, tailored to hybrid qubit-qumode systems.