Measurement errors for phase qubits

Erik A. Lucero, M. Ansmann, Radoslaw C. Bialczak +8 more

Abraham G. Kofman, Qin Zhang, John M. Martinis +1 more

We analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase qubits. The damped oscillations of the superconducting phase after the measurement of the first qubit may significantly excite the second qubit, leading to its measurement error. The first qubit, which is highly excited after the measurement, is described classically. The second qubit is treated both classically and quantum mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the frequency of two-qubit operations) for a given tolerable value of the measurement error probability.

Jack D. Hidary

Peyman Najafi, Pedro C. S. Costa, Dominic William Berry

Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems. When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is not possible to measure the phase with a minimum mean-square error. In standard methods, there would be a logarithmic (in error) number of control qubits needed in order to achieve this minimum error. Here, we show how to perform this measurement using only two control qubits, thereby reducing the qubit requirements of the quantum algorithm. To achieve this task, we prepare the optimal control state one qubit at a time, at the same time as applying the controlled unitaries and inverse quantum Fourier transform. As each control qubit is measured, it is reset to |0⟩ then entangled with the other control qubit, so only two control qubits are needed.

Jack D. Hidary

Qin Zhang, Abraham G. Kofman, John M. Martinis +1 more

We analyze several mechanisms leading to errors in a course of measurement of a superconducting flux-biased phase qubit. Insufficiently long measurement pulse may lead to nonadiabatic transitions between qubit states \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩, before tunneling through a reduced barrier is supposed to distinguish the qubit states. Finite (though large) ratio of tunneling rates for these states leads to incomplete discrimination between \ensuremath{\mid}1⟩ and \ensuremath{\mid}0⟩. Insufficiently fast energy relaxation after the tunneling of state \ensuremath{\mid}1⟩ may cause the repopulation of the quantum well in which only the state \ensuremath{\mid}0⟩ is supposed to remain. We analyze these types of measurement errors using analytical approaches as well as a numerical solution of the time-dependent Schr\"odinger equation.