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Simple proof of equivalence between adiabatic quantum computation and the circuit model
Ari Mizel1, Daniel A Lidar, Morgan Mitchell
1Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Physical Review Letters
|October 13, 2007
Summary
This study demonstrates the equivalence between adiabatic quantum computation and circuit-based quantum computation. An efficient procedure is presented for generating computational ground states, proving the viability of adiabatic quantum algorithms.
Area of Science:
- Quantum Information Science
- Theoretical Computer Science
- Computational Physics
Background:
- Quantum computation offers potential advantages over classical computation.
- Adiabatic quantum computation is a model for performing quantum computations.
- Understanding the relationship between different quantum computation models is crucial for advancing the field.
Purpose of the Study:
- To establish the theoretical equivalence between adiabatic quantum computation and the standard circuit model.
- To develop a practical procedure for adiabatic quantum computation.
- To analyze the computational efficiency of the proposed adiabatic procedure.
Main Methods:
- Proving the equivalence using theoretical computer science principles.
- Developing an explicit adiabatic quantum computation procedure.
- Analyzing the energy gap of the generated ground state to evaluate time complexity.
Main Results:
- Demonstrated a formal equivalence between adiabatic and circuit-based quantum computation.
- Provided a concrete procedure to generate the ground state encoding the solution.
- Showed that the time complexity is computationally efficient, dependent on the energy gap.
Conclusions:
- Adiabatic quantum computation is as powerful as the circuit model.
- The developed procedure offers an efficient method for solving problems via adiabatic quantum computation.
- This work bridges theoretical models and practical implementation in quantum computing.
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