Self-Consistent Quantum Process Tomography (1211.0322v1)

Abstract: Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography can not be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to define a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function.

• The paper demonstrates that a self-consistent tomography method effectively corrects for SPAM errors in quantum process tomography.
• It employs a unique likelihood function and linearization around a target model to achieve high-fidelity quantum gate characterization in simulations and experiments.
• Experimental validation on single-junction transmon qubits shows enhanced fidelity estimates compared to traditional methods, aligning with randomized benchmarking results.

Exploring Self-Consistent Quantum Process Tomography

The paper "Self-Consistent Quantum Process Tomography" addresses fundamental challenges associated with quantum process tomography (QPT) in quantum computing. The authors provide a detailed examination of the limitations of conventional QPT when implemented with systematic errors in state preparation and measurement (SPAM), proposing an alternative self-consistent method to improve the accuracy of quantum gate characterization.

Background and Challenges in Quantum Process Tomography

QPT is critical for the full characterization of quantum gates, which are essential for diagnosing faults in quantum architectures and improving gate designs. The process involves preparing quantum states, executing operations, and measuring outcomes to determine the process. The method scales unfavorably with the number of qubits, particularly because general maps require $O(2^{4n})$ parameters to describe, where $n$ is the number of qubits.

Traditional QPT approaches often overlook systematic errors introduced by SPAM, which arise when gates used for state preparation and measurements have systematic discrepancies. These errors can have a more significant impact on QPT outcomes than stochastic noise, especially in systems where measurement statistics are finite and systematic inaccuracies prevail. The authors argue that SPAM-related errors cannot be effectively mitigated through increased measurement statistics or typical physicality constraints alone.

Self-Consistent Tomography: A New Methodological Approach

This paper presents a novel self-consistent approach to quantum tomography, aiming to rectify the shortcomings of traditional QPT in the presence of SPAM. The authors offer a methodology where associated errors are treated on par with the gate operation errors being interrogated, resulting in enhanced estimation fidelity.

The core innovation in the self-consistent approach is a likelihood function that operates without assumptions about the SPAM-affected gates used for preparation and measurement. To make optimization computationally feasible, the method involves linearization about a target model, particularly appropriate for quantum computer benchmarking.

Numerical and Experimental Validation

Through a series of simulations, the authors demonstrate that the self-consistent method significantly improves the accuracy of QPT, especially as gate errors decrease. They provide evidence that, in the presence of coherent errors, this method yields superior fidelity estimates compared to traditional QPT, which can underestimate gate fidelities.

Experiments conducted on single-junction transmon qubits (SJT) further validate the technique. The self-consistent approach showed lower error margins compared to standard QPT and results were more consistent with fidelities obtained through randomized benchmarking, highlighting its practical applicability and enhanced precision.

Implications and Future Directions

Beyond highlighting the limitations and potential pitfalls of conventional QPT, the self-consistent technique allows for more reliable and precise quantum gate characterization. It provides a pathway towards reducing discrepancies between gate performance metrics and empowering accurate assessments essential for fault-tolerant quantum computing.

Future research motivated by this paper could explore further integration of this approach with more comprehensive error models, including dynamic errors over time and errors influencing initial state preparations and measurements. Additionally, scaling up this approach to more complex multi-qubit systems while maintaining computational efficiency is a critical avenue for ongoing development.

In conclusion, the self-consistent method outlined in this paper advances the understanding and methodology of QPT, emphasizing robust characterization techniques essential for the development and optimization of practical quantum computing systems.