Inteference Tomography

Processing quantum data on a quantum computer can, on certain tasks, offer significant improvement over a purely classical scenario where a classical computer is used to process classical data from conventional measurements. More specifically, recent work has shown that by interfering and measuring two copies of any target state it is possible to estimate the absolute value of all Pauli strings’ expectation values with a sample complexity that is constant with respect to the number of qubits. We propose a modified version of the same scheme that computes the sign of all expectation values. For classes of states where the magnitude of Pauli string expectation values does not decrease as the number of qubits increases, the constant sample complexity is preserved. Once the sign of all expectation values has been learned, the target state can be fully reconstructed.