Related Experiment Video
Updated: Sep 1, 2025
05:30
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
Published on: September 8, 2023
649
Quantifying Nonlocality: How Outperforming Local Quantum Codes Is Expensive
Nouédyn Baspin1, Anirudh Krishna2
1Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1.
Physical Review Letters
|August 12, 2022
Summary
Implementing quantum low-density parity-check (LDPC) codes requires understanding the trade-offs between code parameters and interaction types. This study quantifies the number of long-range interactions needed for quantum LDPC codes with specific dimensions and distances.
Area of Science:
- Quantum Information Science
- Quantum Error Correction
- Theoretical Computer Science
Background:
- Quantum low-density parity-check (LDPC) codes offer a path to efficient, scalable quantum circuit construction.
- Previous work established limitations on quantum LDPC codes using only local interactions for dimension (k) and distance (d).
Purpose of the Study:
- To investigate the number of long-range interactions necessary for implementing quantum LDPC codes with specific parameters (k, d).
- To establish quantitative bounds on code parameters based on limited long-range connectivity.
Main Methods:
- Analysis of 2D quantum LDPC codes.
- Derivation of lower bounds on the number and length of interactions required.
- Application to a stacked architecture model.
Main Results:
- A quantum LDPC code with distance d∝n^{1/2+ϵ} requires Ω(n^{1/2+ϵ}) long-range interactions of length Ω[over ˜](n^{ϵ}).
- A code with k∝n and d∝n^{α} necessitates Ω[over ˜](n) interactions of length Ω[over ˜](n^{α/2}).
- Limited long-range connectivity in a stacked architecture imposes bounds on achievable distance and code dimension.
Conclusions:
- The number of long-range interactions is a critical factor in the practical implementation of quantum LDPC codes.
- Understanding these interaction requirements is essential for designing efficient and scalable quantum error correction schemes.
- The findings provide quantitative insights into the resource costs associated with achieving desired code performance.
Related Concept Videos
01:21Linear Approximation in Time Domain
120
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
120
01:24Area Computation by the Alternative Coordinate Method
141
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
141
00:59Propagation of Uncertainty from Random Error
998
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
998
01:26Linear Approximation in Frequency Domain
129
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
129
01:05Estimation of the Physical Quantities
5.2K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
5.2K
01:17Space-Time Curvature and the General Theory of Relativity
3.0K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
3.0K