Dilution of error in digital Hamiltonian simulation

Understand

We provide analytic, numerical and experimental evidence that the amount of noise in digital quantum simulation of local observables can be independent of system size in a number of situations.

• We provide a microscopic explanation of this dilution of errors based on the "relevant string length" of operators, which is the length of Pauli strings in the operator at time $s$ that belong to the exponentially small subspace of strings that can give a non-zero expectation value at time $t$.
• We show that this explanation can predict when dilution of errors occurs and when it does not.
• We propose an error mitigation method whose efficiency relies on this mechanism.