Randomized Benchmarking of Quantum Gates (0707.0963v1)

Abstract: A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized pi/2 pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.

• The paper presents a randomized benchmarking protocol that evaluates quantum gate error rates using long sequences of random operations.
• The method achieves an estimated one-qubit error probability per π/2 pulse of 0.00482(17) and identifies contributions from coherent errors.
• The approach scales to multi-qubit systems, providing a framework to guide improvements in fault-tolerant quantum computing.

Overview of "Randomized Benchmarking of Quantum Gates"

The paper by Knill et al. focuses on presenting a method for evaluating the error rates of quantum gates, an essential component of scalable quantum computing. The authors introduce a randomized benchmarking protocol that circumvents the limitations of process tomography by relying on long sequences of randomly chosen gates to estimate gate errors. This approach allows for the accurate assessment of errors without necessitating perfect state preparation and measurement—a significant improvement given the stringent error probability requirements for fault-tolerant quantum computing.

Key Components and Findings

The primary contribution of this work lies in its development and implementation of a randomized benchmarking protocol, designed to calculate the error rate of quantum gates per computational step. The methodology includes random sequences of operations, where each sequence ends with a randomized measurement, ensuring the assessment of error rates is independent of any specific gate set. The paper focuses on one-qubit operations, extending to multiple qubits, in an experimental setup using trapped atomic ion qubits.

Significant Findings:

• The randomized benchmarking method provides a reliable estimate of computationally relevant error rates.
• The experiments yielded an estimated one-qubit error probability per randomized π/2 pulse of 0.00482(17), a result indicative of an error rate that could potentially be reduced with technical improvements.
• The measurements indicated that coherent errors substantially contributed to the fidelity loss, as evidenced by the variation in fidelity across different sequence lengths.
• Additional experiments helped in characterizing specific error types, such as phase and amplitude errors, supplementing the findings from the benchmarking protocol.

Implications and Future Developments

The implications of this research are significant for the field of quantum information processing. By providing a framework to accurately quantify gate errors, this paper assists in recognizing the technical hurdles present in current implementations of quantum gates and helps direct future technological enhancements. The randomized benchmarking approach promises scalability and applicability to multi-qubit systems, crucial for developing practical quantum computers.

Prospective Developments:

• The implementation of more complex multiqubit gate sets could be explored using a similar protocol, thereby expanding its applicability to broader systems.
• Future research might integrate this method with fault-tolerant quantum error correction schemes to better understand the interplay between gate errors and logical qubit performance.
• Advancements in reducing coherent and other systematic errors in quantum gates, as identified by the benchmarking results, could facilitate progress toward achieving the necessary error thresholds required for fault-tolerance.

This paper contributes critical methodologies and insights for experimentalists and theorists striving for high-fidelity quantum operations, marking a step forward in the development of robust quantum computing technology.