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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum control of superconducting phase qubits

Philip R. Johnson, Frederick W. Strauch, Alex J. Dragt, J. R. Anderson, Christopher J. Lobb, F. C. Wellstood

Published Aug 24, 2004• 0 citations
Publisher

Abstract

We describe quantum control for implementing fast universal quantum gates using Josephson junction-based phase qubits. We have determined the effects of quantum tunneling and leakage on the gate fidelity by performing nonperturbative simulations of the Schrodinger equation. Phase qubits are seen to have many attractive features, and an experimental demonstration of a simple phase-qubit quantum gate should be possible in the near future.

DOI
10.1117/12.542524

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We describe quantum control for implementing fast universal quantum gates using Josephson junction-based phase qubits. We have determined the effects of quantum tunneling and leakage on the gate fidelity by performing nonperturbative simulations of the Schrodinger equation. Phase qubits are seen to have many attractive features, and an experimental demonstration of a simple phase-qubit quantum gate should be possible in the near future.
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.
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
The technologies of Josephson-junction-based qubits have been progressing rapidly, ever since its first demonstration by a superconducting charge qubit1. A variety of systems have been implemented with remarkable progress in coherence time and read-out schemes. Although the current level of this solid-state device is still not as advanced as that of the most advanced microscopic-system-based qubits, these developments, together with the potential scalability, have renewed its position as a strong candidate as a building block for the quantum computer. Recently, coherent oscillation and microwave spectroscopy in capacitively-coupled superconducting qubits have been reported. The next challenging step toward quantum computation is a realization of logic gates. Here we demonstrate a conditional gate operation using a pair of coupled superconducting charge qubits. Using a pulse technique, we prepare different input states and show that they can be transformed by controlled-NOT (C-NOT) gate operation in the amplitude of the states. Although the phase evolution during the gate operation is still to be clarified, the present results are a major step toward the realization of a universal solid-state quantum gate.
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
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.