Benchmarking and Fidelity
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Programs run on a quantum computer may not produce perfect results - each quantum gate has a chance of producing an error in the output. While practical quantum error correction is a rapidly-developing area in the field of quantum computing, current-generation quantum devices have much higher error rates than their classical counterparts. Output circuit quality is strongly correlated with the quality of individual gates on a device, so it is important to measure and study the error rates of individual operations on the QPU.
Performance benchmarks may be performed with quantum gates appearing in isolation or running in parallel with other operations. Due to effects like crosstalk, simultaneous operations are typically more prone to errors than isolated operations. Benchmarks performed in parallel are therefore likely to be lower than those performed in isolation, but more representative of circuit-level performance.
Note: "Fidelity" is often used to describe gate quality and refers to
1 - error rate.
There are many ways to benchmark the performance of individual gates; however, a few techniques have become standard. For more details, please see the comprehensive review presented in Ref [1].
Ref. [2]
Uses sequences of random unitaries sampled from the Clifford group. At the end of the sequence, the qubits are returned to their initial state, allowing the measurement of the survival probability - if one of the qubits is not in the correct state, an error has occurred. The error rate per Clifford is estimated by fitting to the exponential decay of the survival probability as a function of the sequence length. Note that for two-qubit randomized benchmarking this process conflates single- and two-qubit errors as both gate types are required to decompose each Clifford.
Ref. [3]
We often want to know what the error rate is of a specific quantum gate, however standard randomized benchmarking combines errors from the entire set of gates used to decompose the Clifford group. To isolate the performance of a single gate type, we can first perform standard randomized benchmarking and then perform a second experiment with the target gate type inserted in between each Clifford. By comparing the additional error rate per sequence length introduced by the additional gates to the reference error rate we can isolate the error of the target gate.
Ref. [4]
Rather than using the survival probability as our success metric, we can forgo the final inversion step and measure the bitstrings of the random state produced by each circuit. The fidelity of a given circuit is estimated using the cross-entropy between the expected and measured output distributions. The expected bitstring distribution is determined by calculating the final state of the qubits , which is computationally tractable for circuits which entangle only a few qubits, but rapidly becomes intractable for circuits involving many qubits.
Rigetti uses the result of a combination of these benchmarking protocols to maintain an up-to-date and accurate estimate of gate performance. The specific technique used differs depending on the gate type:
RX(pi/2) - Randomized benchmarking, both in isolation and simultaneously across the entire device. Both numbers are published through the QCS API within the InstructionSetArchitecture. To generate the native gate sequences, Cliffords are decomposed using the ZXZXZ decomposition (Euler angles). This method of decomposition produces regular layers of gates that, in the parallel case, should represent in-context performance.
RX(pi) - Not benchmarked separately from RX(pi/2)
ISWAP / CZ - Interleaved randomized benchmarking. When the uncertainty in the interleaved error rate is too high, or the interleaved value is non-physical due to fitting errors (e.g., the interleaved fidelity is estimated to be over 1), the non-interleaved RB value is reported. Two-qubit Cliffords are decomposed greedily into the target native one- and two-qubit gate set, and as such do not follow the same structure as the single-qubit, ZXZXZ-decomposed sequences used for RX(pi/2) benchmarking. For this reason we do not publish two-qubit RB fidelities measured in parallel.
MEASURE - Qubits are first prepared in the |0> state and measured, then prepared in the |1> state and measured. For each qubit an individual confusion matrix is produced - the reported readout fidelity is computed by taking the trace of the individual confusion matrix and dividing by two. This is equivalent to averaging the assignment fidelities of the input states of all zeros and all ones. Rigetti publishes readout performance data measured in parallel.
[1] A. Hashim et al., "A Practical Introduction to Benchmarking and Characterization of Quantum Computers," arXiv:2408.12064 [quant-ph] (2024).
[2] J. Emerson, R. Alicki, and K. Zyczkowski, "Scalable noise estimation with random unitary operators," J. Opt. B: Quantum Semiclass. Opt., 7, S347 (2005), arXiv:quant-ph/0503243, doi:10.1088/1464-4266/7/10/021.
[3] E. Magesan et al., "Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking," Phys. Rev. Lett., 109, 080505 (2012).
[4] S. Boixo et al., "Characterizing quantum supremacy in near-term devices," Nat. Phys., 14, 595–600 (2018), doi:10.1038/s41567-018-0124-x.
