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Bulletin of the American Physical Society

High-fidelity gates in Josephson phase qubits

Erik A. Lucero, M. Ansmann, Radoslaw C. Bialczak, M. Hofheinz, Nadav Y. Katz, M. Neeley, A. D. O’Connell, Haohua Wang, Andrew N. Cleland, John M. Martinis

Published Mar 11, 2008• 0 citations
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arXiv:0811.2174•Physical Review B•Feb 25, 2009•37 citations
We propose a method to achieve strong coupling between a spin ensemble and a large Josephson junctions (LJJ). Then, the strong coupling between two spin ensembles can be induced by a LJJ. A non-adiabatic holonomic single-qubit quantum gates is realized. Moreover, with the dispersive interaction between the spin ensembles and the LJJ, the high-fidelity two-qubit phase gate can be implemented with two spin ensembles within an operation time 0.41 ns and πππ phase-swap gate can be realized within an operation time 103.11 ns with a high fidelity greater than 99%.
We present theoretical schemes for performing high-fidelity one- and two-qubit pulsed gates for a superconducting flux qubit. The 'IBM qubit' consists of three Josephson junctions, three loops and a superconducting transmission line. Assuming a fixed inductive qubit–qubit coupling, we show that the effective qubit–qubit interaction is tunable by changing the applied fluxes, and can be made negligible, allowing one to perform high-fidelity single qubit gates. Our schemes are tailored to alleviate errors due to 1/ f noise; we find gates with only 1% loss of fidelity due to this source, for pulse times in the range of 20–30 ns for one-qubit gates ( Z rotations, Hadamard) and 60 ns for a two-qubit gate (controlled- Z ). Our relaxation and dephasing time estimates indicate a comparable loss of fidelity from this source. The control of leakage plays an important role in the design of our shaped pulses, preventing shorter pulse times. However, we have found that imprecision in the control of the quantum phase plays a major role in the limitation of the fidelity of our gates.
In a Josephson phase qubit, the coherent manipulations of the computational states are achieved by modulating an applied ac current, typically in the microwave range. In this work, we show that it is possible to find optimal modulations of the bias current to achieve high-fidelity gates. We apply quantum optimal control theory to determine the form of the pulses and study in details the case of a NOT gate. To test the efficiency of the optimized pulses in an experimental setup, we also address the effect of possible imperfections in the pulses shapes, the role of off-resonance elements in the Hamiltonian, and the effect of capacitive interaction with a second qubit.