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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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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.