A method to find quantum noiseless subsystems

Abstract

We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective, or the algebraic noise commutant formalism. As an application, we propose a method for finding all such subspaces and subsystems for arbitrary quantum operations. We suggest that this work brings the fundamental passive technique for error correction in quantum computing an important step closer to practical realization.

5 pages, to appear in Physical Review Letters

References in corpus (4)

• A Unified and Generalized Approach to Quantum Error Correction
• Classical and quantum communication without a shared reference frame
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame

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• Adiabatic Markovian Dynamics
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• Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• Decoherence-free linear quantum subsystems
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• Avoiding coherent errors with rotated concatenated stabilizer codes
• The multiplicative domain in quantum error correction
• Fixed points of commutative Lüders operations
• Quantum error correction on infinite-dimensional Hilbert spaces
• Multi-particle decoherence free subspaces in extended systems
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Generalized Multiplicative Domains and Quantum Error Correction
• Cryptography in a Quantum World
• Quantum Zeno Effect of General Quantum Operations
• On Groups in the Qubit Clifford Hierarchy
• Quantum states characterization for the zero-error capacity
• Optical implementation of a unitarily correctable code
• Quantum computation in silicon-vacancy centers based on nonadiabatic geometric gates protected by dynamical decoupling
• Bath Dynamical Decoupling with a Quantum Channel
• Non-stationarity and Dissipative Time Crystals: Spectral Properties and Finite-Size Effects
• Recursive encoding and decoding of the noiseless subsystem for qudits