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Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.

Milad Marvian1,2, Daniel A Lidar1,2,3,4

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Summary
This summary is machine-generated.

We developed a general method for quantum error suppression using subsystem codes to protect Hamiltonian-based quantum computations. This approach achieves complete error suppression by adding a penalty term, enhancing quantum computing reliability.

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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Quantum Error Correction

Background:

  • Hamiltonian-based quantum computation relies on precise control of quantum systems.
  • Quantum computations are susceptible to errors from environmental noise and imperfect operations.
  • Existing quantum error correction codes often require significant overhead.

Purpose of the Study:

  • To present general conditions for quantum error suppression in Hamiltonian-based quantum computation.
  • To introduce a novel scheme using subsystem codes for enhanced error protection.
  • To demonstrate the effectiveness of this method for specific quantum gates and systems.

Main Methods:

  • Encoding the computational Hamiltonian using an error-detecting subsystem code.
  • Introducing a penalty term that commutes with the encoded Hamiltonian.
  • Deriving performance bounds and analyzing the large penalty limit for error suppression.

Main Results:

  • The proposed scheme is general and encompasses stabilizer formalisms of subspace and subsystem codes.
  • Complete quantum error suppression is achieved in the limit of a large penalty term.
  • Fully two-local constructions are developed for protecting the swap gate and the Ising chain against local errors.

Conclusions:

  • Subsystem codes offer a powerful framework for quantum error suppression in Hamiltonian-based quantum computation.
  • The introduced penalty term method provides a viable path towards fault-tolerant quantum computing.
  • The demonstrated constructions highlight the practical applicability of subsystem codes for specific quantum operations.