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arXiv:1006.5084 · Physical Review B

Quantum process tomography of two-qubit controlled-Z and controlled-NOT gates using superconducting phase qubits

Tsuyoshi Yamamoto, M. Neeley, Erik A. Lucero, Radoslaw C. Bialczak, J. Kelly, M. Lenander, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, Martin P. Weides, J. Wenner, Yi Yin, Andrew N. Cleland, John M. Martinis

Published Nov 9, 2010• 105 citations
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Abstract

We experimentally demonstrate quantum process tomography of controlled-Z and controlled-NOT gates using capacitively coupled superconducting phase qubits. These gates are realized by using the $|2⟩$ state of the phase qubit. We obtain a process fidelity of 0.70 for the controlled phase and 0.56 for the controlled-NOT gate, with the loss of fidelity mostly due to single-qubit decoherence. The controlled-Z gate is also used to demonstrate a two-qubit Deutsch-Jozsa algorithm with a single function query.

DOI
10.1103/physrevb.82.184515

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We experimentally demonstrate quantum process tomography of controlled-Z and controlled-NOT gates using capacitively coupled superconducting phase qubits. These gates are realized by using the ∣2⟩|2⟩∣2⟩ state of the phase qubit. We obtain a process fidelity of 0.70 for the controlled phase and 0.56 for the controlled-NOT gate, with the loss of fidelity mostly due to single-qubit decoherence. The controlled-Z gate is also used to demonstrate a two-qubit Deutsch-Jozsa algorithm with a single function query.
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A general approach to the provision of the quality and efficiency of quantum information technologies is proposed. The approach is based on the analysis of quantum noise generated on the implementation of quantum operations. The method of precision quantum measurements of logic quantum gates based on superconducting phase qubits is developed. The universal method of quantum state and process tomography is used to carry out a comprehensive analysis of the fidelity of the tomography of two-qubit SQiSW, CNOT, and CZ gates arising from the capacitive coupling between qubits. The method of optimization of quantum process tomography is proposed to provide a substantially higher degree of adequacy and fidelity compared to those attained by previously known methods. The examples of simulation of depolarizing quantum noise and amplitude- and phase-relaxation processes on the implementation of quantum operations in registers are considered.
A major challenge in operating multiqubit quantum processors is to mitigate multiqubit coherent errors. For superconducting circuits, besides crosstalk originating from imperfect isolation of control lines, dispersive coupling between qubits is a major source of multiqubit coherent errors. We benchmark phase errors in a controlled-phase gate due to dispersive coupling of either of the qubits involved in the gate to one or more spectator qubits. We measure the associated gate infidelity using quantum-process tomography. We point out that, due to coupling of the gate qubits to a noncomputational state during the gate, two-qubit conditional-phase errors are enhanced. Our work is important for understanding limits to the fidelity of two-qubit gates with finite on-off ratio in multiqubit settings.