Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding

Abstract

The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and practical interest. Understanding the invariance of a set of states under certain transformations is mutually associated with a better understanding of some fundamental aspects of quantum mechanics as well as the practical utility of invariant subsystems. For example, DFS/NSs are potentially useful for protecting quantum information in quantum cryptography and quantum computing as well as enabling universal computation. Here we discuss transformations which are compatible with a DFS/NS that is composed of d-state systems which protect against collective noise. They are compatible in the sense that they do not take the logical (encoded) states outside of the DFS/NS during the transformation. Furthermore, it is shown that the Hamiltonian evolutions derived here can be used to perform universal quantum computation on a three qudit DFS/NS. Many of the methods used in our derivations are directly applicable to a large variety of DFS/NSs. More generally, we may also state that these transformations are compatible with collective motions.

30 pages, replaced with published version

References in corpus (45)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence Free Subspaces for Quantum Computation
• Noiseless Quantum Codes
• Universal Quantum Computation with the Exchange Interaction
• A Theory of Quantum Error-Correcting Codes
• Quantum cryptography with 3-state systems
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Quantum Cryptography using larger alphabets
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Universal quantum computation with spin-1/2 pairs and Heisenberg exchange
• Multi-valued Logic Gates for Quantum Computation
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Symmetrizing Evolutions
• Efficient Toffoli Gates Using Qudits
• Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
• Quantum Encodings in Spin Systems and Harmonic Oscillators
• A Quantum solution to the Byzantine agreement problem
• Dynamical Generation of Noiseless Quantum Subsystems
• Experimental application of decoherence-free subspaces in a quantum-computing algorithm
• Creating Decoherence-Free Subspaces with Strong and Fast Pulses
• Qutrit state engineering with biphotons
• Asymptotically Optimal Quantum Circuits for d-level Systems
• Reducing Constraints on Quantum Computer Design by Encoded Selective Recoupling
• A Magnetic Resonance Realization of Decoherence-Free Quantum Computation
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Implementation of Universal Control on a Decoherence-Free Qubit
• Efficient Universal Leakage Elimination for Physical and Encoded Qubits
• Qutrit Entanglement
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Experimental demonstration of a quantum protocol for Byzantine agreement and liar detection
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
• On Quantum Control via Encoded Dynamical Decoupling
• Criteria for Exact Qudit Universality
• Universal Leakage Elimination
• Entangled qutrits violate local realism stronger than qubits - an analytical proof
• Empirical Determination of Bang-Bang Operations
• Exact gate-sequences for universal quantum computation using the XY-interaction alone
• Entanglement sharing among qudits
• Simple Pulses for Universal Quantum Computation with a Heisenberg ABAB Chain
• Experimental Realization of Polarization Qutrits from Non-Maximally Entangled States
• Overview of Quantum Error Prevention and Leakage Elimination
• Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
• Few-body spin couplings and their implications for universal quantum computation
• Methods for Producing Decoherence-Free States and Noiseless Subsystems Using Photonic Qutrits
• Cooperative behavior of qutrits with dipole-dipole interactions

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• Robust and Reliable Transfer of a Quantum State Through a Spin Chain
• Numerical method for finding decoherence-free subspaces and its applications
• Affine Maps of the Polarization Vector for Quantum Systems of Arbitrary Dimension
• Minimal noise subsystems
• Geometry of pure states of N spin-J system
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Casimir Invariants for Systems Undergoing Collective Motion