Theory of Quantum Information and Computation: Chunhao Wang

Efficient Quantum Algorithms for Simulating Lindblad Evolution

Chunhao Wang

The Lindblad equation is the natural generalization to open systems of the Schrödinger equation. We give a quantum algorithm for simulating the evolution of an n-qubit system under the Lindblad equation with local terms. The gate cost of the algorithm is O(mTlog^2(T/\epsilon)/loglog(T/\epsilon)), where T is the evolution time, \epsilon is the precision of the output state, and m is the number of local terms occurring in the equation. In order to accomplish this, we introduce a novel "linear combinations of unitaries" construction that pertains to channels that we believe is of independent interest.