Principles of Control for Decoherence-Free Subsystems

Abstract

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.

12 pages, 7 figures

References in corpus (38)

• Decoherence Free Subspaces for Quantum Computation
• Dynamical Decoupling of Open Quantum Systems
• Dynamical suppression of decoherence in two-state quantum systems
• Noiseless Quantum Codes
• Universal Quantum Computation with the Exchange Interaction
• Time Optimal Control in Spin Systems
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Fault-Tolerant Quantum Dynamical Decoupling
• Preserving coherence in quantum computation by pairing quantum bits
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Universal Control of Decoupled Quantum Systems
• Symmetrizing Evolutions
• Robust dynamical decoupling with bounded controls
• Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing
• Arbitrarily accurate composite pulses
• 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
• Reducing Constraints on Quantum Computer Design by Encoded Selective Recoupling
• A Magnetic Resonance Realization of Decoherence-Free Quantum Computation
• Implementation of Universal Control on a Decoherence-Free Qubit
• Efficient Universal Leakage Elimination for Physical and Encoded Qubits
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Robust Control of Quantum Information
• Robust Ising Gates for Practical Quantum Computation
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
• On Quantum Control via Encoded Dynamical Decoupling
• Multipulse Control of Decoherence
• Universal Leakage Elimination
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
• Resonant cancellation of off-resonant effects in a multilevel qubit
• Exploring Noiseless Subsystems via Nuclear Magnetic Resonance
• A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations
• Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy
• A Simplified Approach to Optimally Controlled Quantum Dynamics
• Synchronized pulse control of decoherence

Cited by in corpus (32)

• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Colloquium: Quantum Batteries
• Quantum Computing with NMR
• Optimal Control for Generating Quantum Gates in Open Dissipative Systems
• Coherence and control of quantum registers based on electronic spin in a nuclear spin bath
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Application of Optimal Control to CPMG Refocusing Pulse Design
• Quantum correlation in disordered spin systems: entanglement and applications to magnetic sensing
• Continuous dynamical decoupling magnetometry
• Optimization of Short Coherent Control Pulses
• Accelerated Randomized Benchmarking
• Adiabatic Markovian Dynamics
• Incoherent Control of Locally Controllable Quantum Systems
• Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
• The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses
• Engineering Effective Hamiltonians
• Making Distinct Dynamical Systems Appear Spectrally Identical
• Soft-Pulse Dynamical Decoupling with Markovian Decoherence
• Experimental Implementation of Logical Bell State Encoding
• Numerical Analysis of Optimized Coherent Control Pulses
• Fidelity enhancement by logical qubit encoding
• Improved entanglement detection with subspace witnesses
• Cavity cooling to the ground state of an ensemble quantum system
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect
• Decoherence-free quantum register of nuclear spins in diamond
• The effect of random coupling coefficients on decoherence
• Spin Dynamics of CPMG sequence in time-dependent magnetic fields
• Estimation of the Laser Frequency Nosie Spectrum by Continuous Dynamical Decoupling
• Subsystem Pseudo-pure States
• Observation of adiabatic and non-adiabatic behavior for CPMG sequence in time-dependent magnetic fields
• Bath Dynamical Decoupling with a Quantum Channel
• Engineering Precise and Robust Effective Hamiltonians