About this post
Thank you for visiting this post. I'm Takanori Sugiyama, a principal researcher at Fujitsu Research of Japan. I belong to an experimental team of superconducting quantum computer as a theorist. I gave a poster presentation about my research progress at an event, Fujitsu Quantum Day 2025 Japan, on March 28, 2025. www.fujitsu.com In this post, I'm going to briefly explain the content of my poster, which is about a characterization of gate operations used in a quantum computer. You can see more detailed and technical explanation on our recent preprint. arxiv.org
Background 1: Development of Quantum Computer, Characterization Method, and Error Amplification
Huge theoretical and experimental efforts have been made over the past three decades for realizing a practical quantum computer, and its development is progressing rapidly on a global scale. For further developing the project, it's necessary to increase the number of data unit, called a quantum bit or qubit, and accuracies of elementary operations simultaneously. A characterization method is used for checking what kinds of errors occur during an elementary operation and how much these are. Since a calibration, a trial of further improvement of the accuracy of the operation, is performed based on a result of the characterization, reliability and efficiency of a characterization method is important.
There are three categories of elementary quantum operations, state preparations, measurements, and quantum gates.
I'm working on development of a more reliable and efficient method for characterizing quantum gates.
Error sizes of quantum gates in current state-of-the-art experiments have attained below for one qubit and below
for two qubit.
The degrees of freedom of a gate error is 12 for one qubit and 240 for two qubit, and we need to extract these multiple information from such a tiny error.
It is hard to precisely extract the information from single execution of a gate operation since its error is so small.
In order to make an effect of the tiny error more easily detectable, a gate operation is executed many many times, and the effect of the error is amplified.
This is called an error amplification, and it is used in most of modern characterization methods by default.
Background 2: Difficulties of Error Amplification
An error amplification has a strong advantage that the effect of a tiny error is amplified and becomes easily detectable, but as compensation of the advantage, it makes a data-processing for extracting the error information harder. This is related to an interesting property of quantum gates, called non-commutativity.
Roughly speaking, an action of a quantum gate can be identified as a rotation of a ball. Suppose that we can perform two types of rotations, one is along with x axis and the other is along with z axis. Imagine two situations: (1) we first perform 90-degree x-axis rotation, and second we perform 90-degree z-axis rotation. (2) We perform two rotations in the reversed order, i. e., first 90-dergree z-axis rotation, and second 90-degree x-axis rotation. The results of (1) and (2) are different, and then the two rotations are called non-commutative.
In error amplification, several different and non-commutative quantum gates are combined as an amplification unit. Errors of each gates in the unit are mixed by the combination and amplified after the mixing. The effect of the mixing is not obvious because of the non-commutativity of gates, and there were no theoretical tools for analyzing the effect of the mixing. This lack of knowledge on mathematical structure of error amplification is an origin of the difficulties at the data-processing for extracting error information from results of error amplification.
There are other origins of the difficulties, nonlinearity of cyclicity, and existence of dissipation, but I omit its explanation for saving space of this post. If you are interested in those, please see Appendix B of our preprint.
Our approach: Small Error Approximation
We consider it worthwhile to reveal the mathematical structure of error amplification, because if we know the structure, it must become possible to design more reliable and efficient characterization experiments and data-processing with error amplification. However, it is very hard to strictly treat the non-commutativity. So, we introduced an approximation that an error of gate is sufficiently small. As explained in Background 1, the size of gate error is very small in current experiments at development of quantum computer, and we consider this approximation valid.
Based on the approximation, we derived mathematical formulae for analyzing effects of error amplification on gate errors, and it became possible to know which components of and how much a gate error is amplified. We introduced a new data-processing method using the knowledge of the structure of error amplification and succeeded to reduce cost of data-processing and to increase its numerical stability.
What I need to do next
In the poster presentation, we explained some results on numerical simulations of our data-processing method, which indicates high reliability of our method. The numerical results have not been included in the preprint yet, and an updated version including the numerical results will be submitted soon. In addition to theoretical and numerical study, I'm also working on experiments with the developed characterization method for investigating errors of quantum gates implemented in our lab in order to verify practical usefulness of the method.
This is a brief explanation of my recent research progress. Thank you for reading this post up to the end!
Have a nice day!
