Rapid readout of a register of qubits using open loop quantum control

Measurements are a primitive for characterizing quantum systems. Reducing the time taken to perform a measurement may be beneficial in many areas of quantum information processing. We show that permuting the eigenvalues of the state matrix in the logical basis, using open loop control, provides a $O(n)$ reduction in the measurement time, where $n$ is the number of qubits in the register. This reduction is of the same order as the (previously introduced) locally optimal feedback protocol. The advantage of the open loop protocol is that it is far less difficult experimentally. Because the control commutes with the measured observable at all times, our rapid measurement protocol could be used for characterizing a quantum system, by state or process tomography, or to implement measurement-based quantum error correction.