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Interleaved randomised benchmarking of cross-resonance CNOT gate

This notebook measures the average CNOT gate fidelity using interleaved randomised benchmarking.

Description

Using high-fidelity quantum gates is crucial for implementing robust quantum computation. Therefore, benchmarking the average gate fidelity is essential for predicting the performance of a quantum computer1. Conventional randomised benchmarking (RB) determines the average quantum gate error in a way that is immune to state preparation and measurement (SPAM) errors. The protocol consists of appliying randomly generated sequences of gates selected from the Clifford group gate set to a given input state. The length of the randomly generated sequences varies, and one can compute an average fidelity for each length value. We can determine the average error rate per gate by fitting the average sequence fidelities against the sequence lengths. Interleaved Randomised Benchmarking2 is an extension to the RB protocol that allows estimating the fidelity of a specific gate by interleaving it with random Clifford gates.

Experiment steps

  1. Generating the basis gateset containing single-qubit rotations and a CNOT. Each single-qubit gate is described by the parameters: amplitude (amplitude), xy_angle (rotation angle), duration (pulse duration), and drag (DRAG parameter).

  2. Defining the sequence of lengths, which is stored in the array lengths.

  3. Preparing the qubit in the ground state \(|g\rangle\).

  4. Applying the conventional and interleaved RB sequences.

  5. Measuring the resonator transmission and collecting the \(I\) and \(Q\) signals for each length in lengths and the number of repetitions defined by num_samples.

Analysis steps

  1. Computing the Survival probability as a function of lengths. Here, we predict the qubit state from the \(IQ\) data by applying the discriminator trained in the Readout Discriminator Training experiment. Once we obtain the qubit state probabilities, we calculate the Survival probability by averaging the probabilities over the number of repetitions of the RB sequence (defined by RB_number). We do this for the conventional and interleaved sequences.

  2. Determining the average sequence fidelity by fitting \(f(x)\) to the experimental trace (Survival probability versus length). For the conventional sequence, the fitting function is \(f(x) = a \alpha^{x} + b\), where \(x\) is the sequence length and the parameter \(\alpha\) encodes the average sequence fidelity. For the interlaved sequence, the fitting function is \(f(x) = a (\alpha \alpha_c)^{x} + b\), where \(\alpha\) is fixed to the value found for the standard sequence and \(\alpha_c\) is related to the error per gate (epg).

  1. Matthew James Baldwin. Randomized benchmarking simulations of quantum gate sequences with z-gate virtualization. 2021. URL: https://hdl.handle.net/1721.1/139448. ↩

  2. Easwar Magesan, Jay M. Gambetta, B. R. Johnson, Colm A. Ryan, Jerry M. Chow, Seth T. Merkel, Marcus P. da Silva, George A. Keefe, Mary B. Rothwell, Thomas A. Ohki, Mark B. Ketchen, and M. Steffen. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett., 109:080505, Aug 2012. doi:10.1103/PhysRevLett.109.080505. ↩