Finding E_J Value of a Qubit: Step-by-Step Guide

In summary: Which theoretical expressions would I have to fit to this? I found an approximated version in lecture notes from a 2011 Les Houches School. The transition frequency of the qubit is given by $\sqrt{8EcEj} - Ec$. However, it's explicitly mentioned that it's an approximation. Is there any reference from which I can obtain the original/exact expression (for understanding purposes).
  • #1
ramyasuresh
2
0
Hi everyone,

I’ve performed microwave measurements on a 3D transmon and want to find the E_J value of the qubit. I’ve tried searching through many papers, particularly Koch et al, about how to do this, but I am stumped. Could someone please help me out?

Thanks in advance.
 
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  • #2
What is Koch et al.? Please give a link, also to an explanation of what a transmon is
 
  • #3
A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .
 
  • #4
f95toli said:
A transmon is a type of superconducting qubit.
Koch et al refers to a a series of papers from the Yale group.

What type of measurements have you done? Was it a fixed or variable frequency transmon?
Have you determined Ec? Could you get an idea of Ej by looking at the Ej/Ec ratio via the band structure?
I don't think there is a "direct" measurement of a Ej in a 3D transmon (most of the time we just "measure" it by measuring the resistance of a test junction fabricated at the same time) ; you would need to fit the theoretical expressions to different types of spectroscopy data .

Thanks for your reply! I guess I should have made my question a bit more lucid; I had the data of a two-tone spectroscopic measurement (which yielded the avoided crossing plot of a variable frequency transmon with a 3D cavity). This was all I had at the moment, from which I had to find Ec, Ej, etc.

Which theoretical expressions would I have to fit to this? I found an approximated version in lecture notes from a 2011 Les Houches School. The transition frequency of the qubit is given by $\sqrt{8EcEj} - Ec$. However, it's explicitly mentioned that it's an approximation. Is there any reference from which I can obtain the original/exact expression (for understanding purposes).
 

Related to Finding E_J Value of a Qubit: Step-by-Step Guide

1. What is a qubit and why is it important in quantum computing?

A qubit, or quantum bit, is the basic unit of information in quantum computing. It is the quantum equivalent of a classical bit, and can exist in a superposition of states, allowing for more complex calculations and faster processing. Qubits are important in quantum computing because they can represent and manipulate multiple states simultaneously, leading to more powerful and efficient computing.

2. How do I find the E_J value of a qubit?

The E_J value of a qubit, also known as the Josephson energy, can be found by measuring the energy difference between the two lowest energy states of the qubit. This can be done by applying a small voltage and measuring the resulting current, and then using this data to calculate the E_J value using the formula E_J = hf/2e, where h is Planck's constant, f is the frequency of the voltage, and e is the elementary charge.

3. What is the significance of the E_J value in qubits?

The E_J value is significant in qubits because it determines the energy required to change the state of the qubit. This energy barrier is what allows the qubit to maintain its state and makes it a stable unit of information. The E_J value also plays a role in determining the coherence time of the qubit, which is the length of time the qubit can maintain its superposition state before decoherence occurs.

4. Can the E_J value be controlled or adjusted?

Yes, the E_J value can be controlled and adjusted by changing the physical parameters of the qubit, such as the size and shape of the Josephson junction. This allows for fine-tuning of the qubit's energy levels and can improve its performance in quantum computing tasks.

5. Are there any limitations or challenges in accurately finding the E_J value of a qubit?

Yes, there are some limitations and challenges in accurately finding the E_J value of a qubit. One challenge is the sensitivity of the measurement, as small variations in the voltage or current can affect the accuracy of the E_J value. Additionally, the E_J value can be affected by external factors such as temperature and electromagnetic interference, making it difficult to obtain a precise measurement. As quantum computing technology continues to advance, researchers are working on improving methods for accurately determining the E_J value of qubits.

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