Procedure for systematically tuning up cross-talk in the cross-resonance gate

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Procedure for systematically tuning up cross-talk in the cross-resonance gate

Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta

Phys. Rev. A 93, 060302(R) – Published 24 June 2016

Abstract

We present improvements in both theoretical understanding and experimental implementation of the cross resonance (CR) gate that have led to shorter two-qubit gate times and interleaved randomized benchmarking fidelities exceeding 99%. The CR gate is an all-microwave two-qubit gate that does not require tunability and is therefore well suited to quantum computing architectures based on two-dimensional superconducting qubits. The performance of the gate has previously been hindered by long gate times and fidelities averaging 94–96%. We have developed a calibration procedure that accurately measures the full CR Hamiltonian. The resulting measurements agree with theoretical analysis of the gate and also elucidate the error terms that have previously limited gate fidelity. The increase in fidelity that we have achieved was accomplished by introducing a second microwave drive tone on the target qubit to cancel unwanted components of the CR Hamiltonian.

Received 23 March 2016

DOI:https://doi.org/10.1103/PhysRevA.93.060302

Physics Subject Headings (PhySH)

Entanglement production Quantum computation Quantum control Quantum optics Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Sarah Sheldon, Easwar Magesan, Jerry M. Chow, and Jay M. Gambetta

IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA

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Issue

Vol. 93, Iss. 6 — June 2016

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Images

Figure 1
(a) Schematic for the echoed cross-resonance gate with active cancellation on the target qubit. The $π$ pulse on the control is a 20-ns derivative removal via adiabatic gate (DRAG) pulse, and is buffered by two 10-ns delays. The CR pulses are flat-topped Gaussian pulses, with $3 σ$ rise time where $σ = 5$ ns. (b) The error per gate found by randomized benchmarking (blue circles) and interleaved randomized benchmarking (red squares) as a function of gate time. The benchmarking decay curves for both the control and target qubit at the point with highest fidelity are highlighted in the inset. The error-per-gate data in the main figure correspond to measurements on the target qubit. We have performed checks on both qubits to confirm that the decay rates are the same on both qubits.
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Figure 2
The device consists of two transmon qubits coupled by a superconducting resonator. Each qubit has its own readout resonator. Single-qubit gates are applied directly to each qubit at its resonance frequency. The cross-resonance gate pulses are applied to the control qubit ( $Q_{1}$ ) at the frequency of the target qubit ( $Q_{2}$ ), while the active cancellation tone is applied on the same line as the target's single-qubit drive at $ω_{2}$ .
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Figure 3
(a) CR Rabi oscillations on the target qubit projected onto $x, y$ , and $z$ for the control in $|0〉$ and the control in $|1〉$ . The Bloch vector $R$ for the target indicates gate times of maximal entanglement at points when $R = 0$ . (b) CR Hamiltonian as a function of the two-qubit drive amplitude including $IX, IY, IZ, ZX, ZY$ , and $ZZ$ . Theory predictions for $ZX$ and $ZZ$ are given as a function of the CR drive power on the upper $x$ axis. The grey shaded region corresponds to the data from (a) and later in Fig. 4.
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Figure 4
(a) CR Hamiltonian parameters as a function of the drive phase: $Z Z, Z Y, Z X, I Z, I Y$ , and $I X$ . $ϕ_{0}$ and $ϕ_{1}$ are the phases at which $Z Y$ and $I Y$ are zero. The $Z X_{90}$ gate is calibrated by first setting the two-qubit drive phase to $ϕ_{0}$ and the cancellation tone phase to $ϕ_{0} - ϕ_{1}$ . The second step is to find the correct amplitude of the cancellation tone. (b) The same Hamiltonian parameters plotted versus the active cancellation pulse amplitude ( $x$ , as shown in the pulse schematic in the inset). The correct amplitude for the cancellation pulse is the point at which $I X$ and $I Y$ both cross zero. The CR amplitude for these data corresponds to that of the shaded region in Fig. 3.
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Figure 5
CR Rabi experiments as a function of the CR pulse width after calibrating the active cancellation amplitude and phase. Shown are the expectation values $〈X〉, 〈Y〉$ , and $〈Z〉$ , and the Bloch vectors of the target qubit, $R$ . Rabi experiments were performed with the control qubit in $|0〉$ and in $|1〉$ .
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Figure 6
Target qubit states plotted on the Bloch sphere during evolution during the echoed cross-resonance gate, when the control is in $|0〉$ , and the control is in $|1〉$ . Top row: echoed CR gate with no active cancellation. Middle: echoed CR gate with active cancellation on the target qubit. Bottom: simulations of the echoed cross resonance with small $I Z$ and $I X$ errors on the two-qubit drive.
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