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README.md

IBM Q 5 Tenerife V1.x.x

display_name: IBM Q 5 Tenerife
backend_name: ibmqx4
backend_version: 1.x.x
sample_name: raven

This document contains information about the IBM Q experience ibmqx4 backend for version 1.x.x.

Contributors (alphabetical)

Baleegh Adbo, Lev Bishop, Markus Brink, Jerry Chow, Antonio Córcoles, Andrew Cross, Jay M. Gambetta, Oblesh Jinka, Abhinav Kandala, Sami Rosenblatt, Jim Rozen, Maika Takita

Device Specifications

The connectivity is provided by two coplanar waveguide (CPW) resonators with resonances around 6.6 GHz (coupling Q2, Q3 and Q4) and 7.0 GHz (coupling Q0, Q1 and Q2). Each qubit has a dedicated CPW for control and readout. The following picture shows the chip layout.

The following tables shows some of the main experimental parameters for this device:

Qubit ωRi/2π (GHz) ωi/2π (GHz) δi/2π (MHz) χ/2π (kHz) κ/2π (kHz)
Q0 6.52396 5.2461 -330.1 410 -
Q1 6.48078 5.3025 -329.7 512 -
Q2 6.43875 5.3562 -323.0 408 -
Q3 6.58036 5.4317 -327.9 434 -
Q4 6.52698 5.1824 -332.5 458 -

where ωRi is the resonance frequency of the readout resonator, ωi = (Ei - E0)/ℏ is the qubit frequency with i={00001,00010,00100,01000,10000}. The anharmonicity (δi) is the difference between the frequency of the 1-2 transition and the 0-1 transition. That is, it is given by δi = (E2i - 2Ei+ E0 )/ℏ. χ is the qubit-cavity coupling strength, and κ is the cavity coupling to the environment (κ).

Crosstalk, which we parameterize by ζij = (Ei+j - Ei - Ej + E0)/ℏ is measured using a Joint Amplification of ZZ (JAZZ) experiment, which is a modified BIlinear Rotational Decoupling (BIRD) [^fn1]. The standard BIRD sequence used in nuclear magnetic resonance (NMR) is a Ramsey experiment on one qubit, with echo pulses on both the measured qubit (Qi) and the coupled qubit (Qj). In the JAZZ experiment, this sequence is performed twice, for each initial state of the coupled qubit. Additionally, the phase of the final π/2-rotation is varied in order to detect an oscillating signal. ζij is equal to the frequency difference found between the two experiments. The JAZZ experiment is shown in the figure below, and the measurements of all ζij are in the following table. The GD pulse notation is defined below in the Gate Specification section.

[^fn1]: J.R. Garbow, D.P. Weitekamp, A. Pines, Bilinear rotation decoupling of homonuclear scalar interactions, Chemical Physics Letters, Volume 93, Issue 5, 1982, Pages 504-509.

In the crosstalk matrix, the error bar is less than 1 kHz for all ζij and a dash indicates an interaction strength for that pair < 25 kHz. This crosstalk matrix was taken for V1.0.0 (see version log for specific changes).

ζij/2π (kHz) Q0 Q1 Q2 Q3 Q4
Q0 X -43 -72 - -
Q1 -41 X -16 - -
Q2 -73 -18 X -52 -90
Q3 - - -51 X -175
Q4 - - -89 -176 X

Experimental Setup

The following cartoon shows a depiction of the device I/O microwave setup:

Gate Specification

A frame change (FC) is equivalent to applying a virtual Z-gate in software, where Z(θ)=FC(-θ). Gaussian derivative (GD) and Gaussian flattop (GF) pulses are defined with amplitude and angle parameters.

Two-Qubit Gates

Generally, two-qubit gates are possible between neighboring qubits that are connected by a superconducting bus resonator (see picture below). The IBM Q experience uses the cross-resonance interaction as the basis for the CX-gate. This interaction is stronger when choosing the qubit with higher frequency to be the control qubit, and the lower frequency qubit to be the target, so the frequencies of the qubits determines the direction of the gate. There are some exceptions to the rule of high frequency control/low frequency target: the gate direction must be reversed if the higher levels of the control qubit are degenerate with the target qubit, or if either qubit is coupled to a third (spectator) qubit that has the same frequency or a higher level with the same frequency as the target. Directions of the two-qubit gates are defined in the version_log.

Reported gate errors are measured using simultaneous randomized benchmarking (RB)[^fn2]. RB gives the average error per Clifford gate, which we convert to error per gate according to the set of primitive gates used on QX2.

[^fn2]: Jay M. Gambetta, A. D. Córcoles, S. T. Merkel, B. R. Johnson, John A. Smolin, Jerry M. Chow, Colm A. Ryan, Chad Rigetti, S. Poletto, Thomas A. Ohki, Mark B. Ketchen, and M. Steffen, Characterization of Addressability by Simultaneous Randomized Benchmarking, Phys. Rev. Lett. 109, 240504.