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Related Concept Videos

Encoding01:19

Encoding

Information enters the brain through encoding, which is the input of information into the memory system. Once sensory information is received from the environment, the brain labels or codes it. The information is then organized with similar information and connected to existing concepts. Encoding occurs through automatic processing and effortful processing.
Automatic processing involves the encoding of details like time, space, frequency, and the meaning of words, usually done without conscious...
Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
Quartile01:15

Quartile

Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...
Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
The Quotient Rule01:30

The Quotient Rule

The quotient rule is a fundamental differentiation technique in calculus used to differentiate functions expressed as a ratio of two differentiable functions. Given a function of the form:Where g(x) and h(x) are both differentiable and h(x) ≠ 0, the derivative of f(x) is given by:Example:The quotient rule is beneficial when differentiating rational functions, trigonometric ratios, and exponential functions. For example, given:applying the quotient rule,This rule is essential in solving problems...
Cartesian Vector Notation01:28

Cartesian Vector Notation

Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...

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Related Experiment Videos

A smaller and more efficient one-hot encoding for QUBO.

Shinji Takasugi1, Hideo Nakaya2, Yoshihiro Nakao2

  • 1LG Japan Lab Inc., Yokohama, Japan. shinji.takasugi@lgjlab.com.

Scientific Reports
|June 4, 2026
PubMed
Summary

Researchers explored Quadratic Unconstrained Binary Optimization (QUBO) encodings for optimization problems. A new method, reduced commander, offers an excellent balance between QUBO size and solution quality.

Related Experiment Videos

Area of Science:

  • Computational Optimization
  • Quantum Computing
  • Artificial Intelligence

Background:

  • One-hot constraints are crucial for Quadratic Unconstrained Binary Optimization (QUBO) in quantum and simulated annealing.
  • These constraints are equivalent to exactly-one constraints in Boolean Satisfiability (SAT) problems.
  • Various SAT encodings exist to minimize problem size.

Purpose of the Study:

  • To evaluate existing and novel QUBO encodings.
  • To identify the optimal encoding for balancing QUBO size and solution quality.
  • To improve the efficiency of solving optimization problems using annealing methods.

Main Methods:

  • Systematic examination of QUBO encodings, including established SAT encodings and new inventions.
  • Comparative analysis of encoding performance based on QUBO size and solution accuracy.
  • Experimental validation on benchmark optimization problems.

Main Results:

  • The 'reduced commander' encoding demonstrated a superior trade-off between QUBO size and solution quality.
  • Performance was evaluated against previously proposed SAT encodings.
  • The new encoding proved effective for the studied benchmark problems.

Conclusions:

  • The 'reduced commander' QUBO encoding is a promising advancement.
  • It offers an improved approach for tackling optimization challenges.
  • Further research can explore its application in diverse computational problems.