Cross Resonance Gate Superconducting

Short answer: The cross-resonance (CR) gate is an all-microwave two-qubit entangling gate for superconducting qubits, used with fixed-frequency transmons. Papers report interleaved randomized benchmarking fidelities above 99 percent in one set of experiments, 97.0 percent in a calibration study at another lab, and simulations suggesting an intrinsic infidelity below 10^-3 with a simple pulse. These are lab results and simulations, not specifications for any commercial system.

What the gate is

A 2016 Physical Review A paper describes the CR gate as an entangling gate for superconducting qubits that uses only microwave control and has been the standard for multiqubit experiments in superconducting architectures using fixed-frequency transmon qubits. It requires a small static coupling of the qubit pair that slightly hybridizes the combined system, plus one additional microwave drive. The paper contrasts it with gates that use magnetic flux drives to tune qubits into resonance or to tune a coupler directly. It says the low overhead, since the additional control line is combined with a single-qubit drive at room temperature, makes the gate attractive for planar superconducting architectures, and that microwave-only control allows fixed-frequency transmons, which avoid some noise.

Tuning up the gate, 2016

The same paper presents improvements in both theoretical understanding and experimental implementation that led to shorter two-qubit gate times and interleaved randomized benchmarking fidelities exceeding 99 percent. Its title refers to a procedure for systematically tuning up crosstalk in the gate. The abstract calls the CR gate well suited to quantum computing architectures based on two-dimensional superconducting qubits because it does not require tunability.

An error budget, 2019

A 2019 Physical Review A paper by Tripathi, Khezri and Korotkov analyzes the gate analytically, semi-analytically and numerically. The authors find that a relatively simple semi-analytical method gives accurate CNOT-equivalent gate durations and compensating single-qubit rotations, but that full numerical simulation is needed to calculate the intrinsic fidelity. They decompose the numerical infidelity into contributions from different mechanisms. At small drive amplitudes, they find the fidelity is limited by imperfections of the target-qubit rotations, while at large amplitudes it is limited by leakage. They also analyze the dependence on detuning between qubits, coupling, drive frequency, ramp durations and microwave crosstalk, and the effect of the echo sequence. Their results show that the gate can provide an intrinsic infidelity of less than 10^-3 when a simple pulse shape is used. That is a simulated, intrinsic figure and excludes other noise in real devices.

A calibration procedure, 2019

A 2019 Physical Review Applied paper from a group at the University of Oxford implements the gate between two transmon qubits with a direct static dispersive coupling. They demonstrate a calibration procedure combining continuous and repeated-gate Hamiltonian tomography with stepwise reduction of dominant two-qubit coherent errors by mapping to microwave control parameters. They report a ZX-pi/2 gate with a fidelity of 97.0 plus or minus 0.7 percent, measured with interleaved randomized benchmarking, in an architecture with out-of-plane control and readout that they say is readily extensible to larger circuits.

What this does not tell you

The numbers come from different devices, years and methods, so they should not be ranked against each other. None of these abstracts reports results for a large processor.

FAQ

What is the cross-resonance gate?

A microwave-only two-qubit entangling gate for fixed-frequency superconducting transmon qubits.

Why use it?

It needs no tunability and little control overhead, per the 2016 paper.

How good is it?

One experiment reported fidelities above 99 percent, another 97.0 percent, and a 2019 simulation an intrinsic infidelity below 10^-3.

What limits fidelity?

At small drive amplitudes, imperfect target-qubit rotations. At large amplitudes, leakage, per the 2019 analysis.

How is it calibrated?

The Oxford paper describes Hamiltonian tomography combined with stepwise reduction of coherent errors.