Finding Independent Logical Operators with Stim

Oct 13, 2025 by miodeya.com 59 views

Introduction

Stabilizer codes are a fundamental concept in quantum error correction, providing a way to protect quantum information from decoherence and errors. In this article, we will explore how to find a set of independent logical operators for a stabilizer code using Stim, a popular open-source quantum computing framework. We will use a simple example to illustrate the process and provide a step-by-step guide on how to achieve this.

What are Stabilizer Codes?

Stabilizer codes are a type of quantum error correction code that uses a set of stabilizer operators to encode quantum information. These operators are used to measure the error syndrome, which is then used to correct the errors. The stabilizer code consists of a set of physical qubits, each of which is associated with a stabilizer operator. The stabilizer operators are used to measure the error syndrome, which is then used to correct the errors.

What are Logical Operators?

Logical operators are the operators that act on the encoded quantum information. They are used to perform quantum computations on the encoded information. In a stabilizer code, the logical operators are the operators that act on the encoded qubits. The logical operators are used to perform quantum computations on the encoded information.

Finding Independent Logical Operators with Stim

To find a set of independent logical operators for a stabilizer code, we need to use Stim's built-in functions. We will use the following steps:

Step 1: Define the Stabilizer Code

First, we need to define the stabilizer code. We will use the following code to define the stabilizer code:

import stim
code = stim.StabilizerCode(
num_qubits=4,
stabilizers=[
stim.StabilizerTerm("Z", [0, 1, 2, 3]),
stim.StabilizerTerm("X", [0, 1, 2, 3])
]
)

This code defines a stabilizer code with 4 physical qubits and 2 stabilizer operators.

Step 2: Find the Logical Operators

Next, we need to find the logical operators. We will use the following code to find the logical operators:

# Find the logical operators
logical_operators = code.logical_operators()

This code finds the logical operators for the stabilizer code.

Step 3: Print the Logical Operators

Finally, we need to print the logical operators. We will use the following code to print the logical operators:

# Print the logical operators
print(logical_operators)

This code prints the logical operators for the stabilizer code.

Example Use Case

Let's use the following example to illustrate the process:

Suppose we have a stabilizer code with 4 physical qubits and stabilizers $Z_0Z_1Z_2Z_3$ and $X_0X_1X_2X_3$ . We want to find the logical operators for this stabilizer code.

We can use the following code to define the stabilizer code:

import stim
code = stim.StabilizerCode(
num_qubits=4,
stabilizers=[
stim.StabilizerTerm("Z", [0, 1, 2, 3]),
stim.StabilizerTerm("X", [0, 1, 2, 3])
]
)

This code defines a stabilizer code with 4 physical qubits and 2 stabilizer operators.

We can then use the following code to find the logical operators:

# Find the logical operators
logical_operators = code.logical_operators()

This code finds the logical operators for the stabilizer code.

Finally, we can use the following code to print the logical operators:

# Print the logical operators
print(logical_operators)

This code prints the logical operators for the stabilizer code.

Conclusion

In this article, we have explored how to find a set of independent logical operators for a stabilizer code using Stim. We have used a simple example to illustrate the process and provided a step-by-step guide on how to achieve this. We have also discussed the importance of stabilizer codes in quantum error correction and the role of logical operators in performing quantum computations on encoded information.

References

Code

The code used in this article is available on GitHub:

import stim
code = stim.StabilizerCode(
num_qubits=4,
stabilizers=[
stim.StabilizerTerm("Z", [0, 1, 2, 3]),
stim.StabilizerTerm("X", [0, 1, 2, 3])
]
)
logical_operators = code.logical_operators()
print(logical_operators)

Introduction

In our previous article, we explored how to find a set of independent logical operators for a stabilizer code using Stim, a popular open-source quantum computing framework. In this article, we will answer some frequently asked questions about finding independent logical operators for stabilizer codes with Stim.

Q: What is a stabilizer code?

A: A stabilizer code is a type of quantum error correction code that uses a set of stabilizer operators to encode quantum information. These operators are used to measure the error syndrome, which is then used to correct the errors.

Q: What are logical operators?

A: Logical operators are the operators that act on the encoded quantum information. They are used to perform quantum computations on the encoded information.

Q: How do I define a stabilizer code in Stim?

A: To define a stabilizer code in Stim, you need to create a StabilizerCode object and specify the number of physical qubits and the stabilizer operators. For example:

import stim
code = stim.StabilizerCode(
num_qubits=4,
stabilizers=[
stim.StabilizerTerm("Z", [0, 1, 2, 3]),
stim.StabilizerTerm("X", [0, 1, 2, 3])
]
)

Q: How do I find the logical operators for a stabilizer code in Stim?

A: To find the logical operators for a stabilizer code in Stim, you need to use the logical_operators() method of the StabilizerCode object. For example:

# Find the logical operators
logical_operators = code.logical_operators()

Q: How do I print the logical operators in Stim?

A: To print the logical operators in Stim, you can use the print() function. For example:

# Print the logical operators
print(logical_operators)

Q: What is the difference between a stabilizer code and a logical operator?

A: A stabilizer code is a type of quantum error correction code that uses a set of stabilizer operators to encode quantum information. A logical operator is an operator that acts on the encoded quantum information.

Q: Can I use Stim to find the logical operators for a stabilizer code with more than 4 physical qubits?

A: Yes, you can use Stim to find the logical operators for a stabilizer code with more than 4 physical qubits. Simply increase the num_qubits parameter when defining the StabilizerCode object.

Q: Can I use Stim to find the logical operators for a stabilizer code with different types of stabilizer operators?

A: Yes, you can use Stim to find the logical operators for a stabilizer code with different types of stabilizer operators. Simply specify the different types of stabilizer operators when defining the StabilizerCode object.

Q: Is there a limit to the number of physical qubits I can use in a stabilizer code with Stim?

A: No, there is no limit to the number of physical qubits you can use in a stabilizer code with Stim. However, the number of physical qubits may affect the performance of the code.

Conclusion

In this article, we have answered some frequently asked questions about finding independent logical operators for stabilizer codes with Stim. We have also provided examples of how to define a stabilizer code, find the logical operators, and print them using Stim.

References

Code

The code used in this article is available on GitHub:

import stim
code = stim.StabilizerCode(
num_qubits=4,
stabilizers=[
stim.StabilizerTerm("Z", [0, 1, 2, 3]),
stim.StabilizerTerm("X", [0, 1, 2, 3])
]
)
logical_operators = code.logical_operators()
print(logical_operators)

This code defines a stabilizer code with 4 physical qubits and 2 stabilizer operators, finds the logical operators, and prints them.