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arXiv:0712.3581 · Physical Review B

Suppressing charge noise decoherence in superconducting charge qubits

J. A. Schreier, Andrew Houck, Jens Koch, David Schuster, Blake Johnson, Jerry M. Chow, Jay Gambetta, Johannes Majer, Luigi Frunzio, Michel Devoret, S. M. Girvin, R. J. Schoelkopf

Published May 12, 2008• 552 citations
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Abstract

We present an experimental realization of the transmon qubit, which is an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to $1∕f$ charge noise. This removes the leading source of dephasing in charge qubits which results in homogeneously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory.

DOI
10.1103/physrevb.77.180502

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We present an experimental realization of the transmon qubit, which is an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to 1∕f1∕f1∕f charge noise. This removes the leading source of dephasing in charge qubits which results in homogeneously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called ``sweet spots.'' This latter approach led to significant improvement of T2{T}_{2}T2​ times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the ``transmon.'' Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy EJ∕EC{E}_{J}∕{E}_{C}EJ​∕EC​. The transmon benefits from the fact that its charge dispersion decreases exponentially with EJ∕EC{E}_{J}∕{E}_{C}EJ​∕EC​, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called sweet spots. This latter approach led to significant improvement of T2T_2T2​ times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the transmon. Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy EJ/ECE_J/E_CEJ​/EC​. The transmon benefits from the fact that its charge dispersion decreases exponentially with EJ/ECE_J/E_CEJ​/EC​, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.
The tunnelling of quasiparticles across Josephson junctions in superconducting quantum circuits is an intrinsic decoherence mechanism for qubit degrees of freedom. Understanding the limits imposed by quasiparticle tunnelling on qubit relaxation and dephasing is of theoretical and experimental interest, particularly as improved understanding of extrinsic mechanisms has allowed crossing the 100 microsecond mark in transmon-type charge qubits. Here, by integrating recent developments in high-fidelity qubit readout and feedback control in circuit quantum electrodynamics, we transform a state-of-the-art transmon into its own real-time charge-parity detector. We directly measure the tunnelling of quasiparticles across the single junction and isolate the contribution of this tunnelling to qubit relaxation and dephasing, without reliance on theory. The millisecond timescales measured demonstrate that quasiparticle tunnelling does not presently bottleneck transmon qubit coherence, leaving room for yet another order of magnitude increase. Superconducting circuits are promising for quantum computing, but quasiparticle tunnelling across Josephson junctions introduces qubit decoherence. Ristè et al. convert a transmon qubit into its own real-time quasiparticle tunnelling detector and accurately measure induced decoherence in the millisecond range.
Quantum computing provides significantly more efficient methods than classical computers for doing rigorous calculations such as encryption, search algorithms, and physical simulations. This is accomplished through the use of qubits which exist in a superposition of multiple states at once allowing for both complex and fast calculations. Environmental fluctuations interfere with these states and resulting in decoherence and dephasing and the break down of the algorithm. One type of qubit is the fluxonium: a superconducting artificial atom derived from the Cooper pair box. The purpose of this project was to analyze the effect of charge noise on the fluxonium qubit which, in the past, has never systematically been done before. Charge noise enters the qubit in the form of 1/f noise resulting in interference with the Cooper pairs, two loosely bound electrons, hopping between the superconducting island and reservoir. A program was developed to simulate the qubit's state over time by solving a stochastic differential Schrodinger equation numerically. The program simulated the noise by using its 1/f power spectrum. Looking into the both its wavefunction and density matrix, its dephasing and decoherence rates were determined for different inductive, capacitive, and Josephson energies. Results will be presented.
Coherence limitations of a Fourier-engineered cos⁡(2φ)\cos(2\varphi)cos(2φ) transmon qubit
Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The cos⁡(2φ)\cos(2\varphi)cos(2φ) qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a cos⁡(2φ)\cos(2\varphi)cos(2φ) qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by 1/f1/f1/f flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.