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Encoding01:19

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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.
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Mechanisms of Membrane Domain Formation00:59

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Different physical properties of lipids and proteins allow them to localize and form distinct islands or domains in the membrane. Some membrane domains are formed due to protein-protein interactions, whereas others are formed due to the presence of specific lipids such as sphingolipids and sterols—for example, large proteins, such as bacteriorhodopsin, aggregate and create distinct domains.
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Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...
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Electrostatic Boundary Conditions in Dielectrics01:27

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When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
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Boundary Conditions: Lossless Lines01:21

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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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Van der Waals Interactions01:24

Van der Waals Interactions

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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.
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Related Experiment Video

Updated: Aug 19, 2025

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement
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Understanding domain-wall encoding theoretically and experimentally.

Jesse Berwald1, Nicholas Chancellor1,2, Raouf Dridi1

  • 1Quantum Computing Inc. Leesburg, VA, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 4, 2022
PubMed
Summary
This summary is machine-generated.

Encoding higher-than-binary discrete variables using domain walls on Ising chains is theoretically optimal for quantum computing. Experiments show this domain-wall encoding freezes dynamics later than one-hot encoding on quantum annealers.

Keywords:
QAOAVQEdomain encodingquantum annealing

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Area of Science:

  • Quantum Computing
  • Computational Physics

Background:

  • Encoding complex problems into quantum systems is crucial for quantum computation.
  • Discrete quadratic models with higher-than-binary variables are common in computational tasks.
  • Existing encoding methods like one-hot can be inefficient for quantum annealing.

Purpose of the Study:

  • To analyze the domain-wall encoding method for higher-than-binary discrete variables.
  • To compare the efficiency and performance of domain-wall encoding against traditional methods.
  • To investigate the implications of encoding strategies on quantum annealing and gate-model algorithms.

Main Methods:

  • Theoretical analysis of encoding efficiency for discrete quadratic models.
  • Implementation and experimentation on a D-Wave Advantage 1.1 quantum annealing computer.
  • Comparison of dynamics freezing times between domain-wall and one-hot encodings.

Main Results:

  • Theoretically, no general encoding is more efficient than domain-wall encoding in terms of binary variables per discrete variable for quadratic interactions.
  • Experimental results show domain-wall encoding leads to later dynamics freezing compared to one-hot encoding on a D-Wave quantum annealer.
  • This difference in dynamics freezing may explain observed performance improvements in recent experiments.

Conclusions:

  • Domain-wall encoding is a theoretically efficient and practically advantageous method for representing higher-than-binary discrete variables in quantum computing.
  • Considering the interplay between problem encoding and quantum system physics offers a more effective paradigm for algorithm design.
  • The findings have implications for both quantum annealing and gate-model algorithms like VQE and QAOA, as well as quantum-inspired approaches.