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arXiv:1703.03514 · Physical review. B./Physical review. B

Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits

Xiu–Hao Deng, Edwin Barnes, Sophia E. Economou

Published Jul 27, 2017• 32 citations
arXivHTMLPDF

Abstract

Superconducting transmon qubits comprise one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we use a protocol for speeding up waveforms by inducing phases to harmful transitions (SWIPHT) [S. E. Economou and E. Barnes, Phys. Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we determine the parameter regimes in which SWIPHT is effective and demonstrate that in these regimes, it systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%--99.9% with gate times as fast as 23 ns. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing. These high fidelities persist over a wide range of system parameters that encompass many current experimental setups and are insensitive to small parameter variations and pulse imperfections.

DOI
10.1103/physrevb.96.035441

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Superconducting transmon qubits comprise one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we use a protocol for speeding up waveforms by inducing phases to harmful transitions (SWIPHT) [S. E. Economou and E. Barnes, Phys. Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we determine the parameter regimes in which SWIPHT is effective and demonstrate that in these regimes, it systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%--99.9% with gate times as fast as 23 ns. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing. These high fidelities persist over a wide range of system parameters that encompass many current experimental setups and are insensitive to small parameter variations and pulse imperfections.
Recent experimental work on superconducting transmon qubits in three-dimensional (3D) cavities shows that their coherence times are increased by an order of magnitude compared to their two-dimensional cavity counterparts. However, to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where the leakage transition of qubits is close to computational transitions in other qubits. Here, it is shown that fast pulses are possible which address single qubits using two-quadrature control of the pulse envelope, while the derivative removal by adiabatic gate method of Motzoi et al. [Phys. Rev. Lett. 103, 110501 (2009)] alone only gives marginal improvements over the conventional Gaussian pulse shape. On the other hand, a first-order result using the Magnus expansion gives a fast analytical pulse shape which gives a high-fidelity gate for a specific gate time, up to a phase factor on the second qubit. Further numerical analysis corroborates these results and yields to even faster gates, showing that leakage-state anharmonicity does not provide a fundamental quantum speed limit.
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This dissertation describes research to coherently control quantum states of superconducting devices. In the first project, the state of an 8 GHz 3D superconducting Al cavity at 20mK was manipulated to add a quantum of excitation. Preparing a harmonic resonator in a state with a well-defined number of excitations (Fock states) is not possible using one external classical drive. I generated Fock states by transferring a single excitation from a 5.5 GHz transmon qubit to a cavity using Stimulated Raman Adiabatic Passage (STIRAP). I also extended the STIRAP technique to put the cavity in higher Fock states, superpositions of Fock states, and Bell states between the qubit and the cavity. Master-equation simulations of the system’s density matrix were in good agreement with the data, and I obtained estimated fidelities of 89%, 68% and 43% for the first three Fock states, respectively. The second project involved implementing an entangling gate between two Al/AlOx/Al transmon qubits that were mounted in an Al cavity and cooled to 20mK. Pertinent system frequencies were as follows: one qubit was at 6.0 GHz, the other qubit at 6.8 GHz, the cavity at 7.7 GHz, and the qubit-qubit dispersive shift was -1MHz. By applying a specially-shaped pulse of duration tg = 907ns, I implemented a generalized CNOT gate using an all-microwave technique known as Speeding up Waveforms by Inducing Phases to Harmful Transitions (SWIPHT). Using quantum process tomography, I found that the gate fidelity was 80%–82%, close to the 87% fidelity expected from decoherence in the transmons during the gate time. Details of the device fabrication, device characterization, measurement techniques, and extensive modeling of device behavior are presented, along with chi-matrix characterization of single-qubit gates and SWIPHT gates.
Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the e f transition of a transmon qubit with an anharmonicity of − 212 MHz, we implement R X ( π / 2 ) gates achieving a leakage error below 3.0 × 10 − 5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of ( 1.56 ± 0.07 ) × 10 − 4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024
High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates still suffer from error rates that are orders of magnitude higher. One limiting factor is the residual ZZ-interaction, which originates from a coupling between computational states and higher-energy states. While this interaction is usually viewed as a nuisance, here we experimentally demonstrate that it can be exploited to produce a universal set of fast single- and two-qubit entangling gates in a coupled transmon qubit system. To implement arbitrary single-qubit rotations, we design a new protocol called the two-axis gate that is based on a three-part composite pulse. It rotates a single qubit independently of the state of the other qubit despite the strong ZZ-coupling. We achieve single-qubit gate fidelities as high as 99.1% from randomized benchmarking measurements. We then demonstrate both a CZ gate and a CNOT gate. Because the system has a strong ZZ-interaction, a CZ gate can be achieved by letting the system freely evolve for a gate time tg=53.8t_g=53.8tg​=53.8 ns. To design the CNOT gate, we utilize an analytical microwave pulse shape based on the SWIPHT protocol for realizing fast, low-leakage gates. We obtain fidelities of 94.6% and 97.8% for the CNOT and CZ gates respectively from quantum progress tomography.
We have embedded two fixed-frequency Al/AlOx{\mathrm{Al}/\mathrm{AlO}}_{x}Al/AlOx​/Al transmons, with ground-to-excited transition frequencies at 6.0714 and 6.7543 GHz, in a single three-dimensional Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a $\ensuremath{-}1$ MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (speeding up wave forms by inducing phases to harmful transitions) technique [Economou and Barnes, Phys. Rev. B 91, 161405 (2015)], we demonstrate the operation of a generalized controlled-not gate between the two qubits, with a gate time of ${\ensuremath{\tau}}_{g}=907$ ns optimized for this device. Using quantum process tomography we find that the gate fidelity is 83--84%, somewhat less than the 87% fidelity expected from relaxation and dephasing in the transmons during the gate time.