Simulating non-unitary dynamics using quantum signal processing with unitary block encoding

Understand

We adapt a recent advance in resource-frugal quantum signal processing - the Quantum Eigenvalue Transform with Unitary matrices (QET-U) - to explore non-unitary imaginary time evolution on early fault-tolerant quantum computers using exactly emulated quantum circuits.

• We test strategies for optimising the circuit depth and the probability of successfully preparing the desired imaginary-time evolved states.
• For the task of ground state preparation, we confirm that the probability of successful post-selection is quadratic in the initial reference state overlap $\gamma$ as $O(\gamma^2)$.
• When applied instead to thermal state preparation, we show QET-U can directly estimate partition functions at exponential cost.