Quantum Algorithms Database
Linear Combination of Unitaries (LCU)
A general technique for implementing operations that aren't directly unitary by expressing them as a weighted combination of simpler unitary operations.
Year
2012 (Childs & Wiebe)
Inventor(s)
Childs & Wiebe
Speedup Type
Exponential Speedup
Difficulty
★★★★★
The Problem
Many useful mathematical operations in quantum simulation and algorithms aren't directly realizable as quantum gates (which must be unitary) — LCU provides a way around this.
How It Works
Decomposes a desired (possibly non-unitary) operation into a weighted sum of unitary operations, implementing it probabilistically using extra ancilla qubits and post-selection.
Real-World Impact
An important theoretical tool underlying modern quantum simulation algorithms, including advanced techniques for simulating quantum chemistry and physics beyond basic Trotterization.