Exact dynamics of single qubit gate fidelities under the measurement-based quantum computation scheme
arXiv:1201.4894 · doi:10.1103/PhysRevA.86.042326
Abstract
Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single qubit gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N-qubit state, interacting with this type of error channel, to present an oscillatory behavior and we show that for the initial canonical cluster state the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, neither fast application of the set of projective measurements necessarily implies high gate fidelity, nor slow application thereof necessarily implies low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.
9 pages, 5 figures. Extra examples added
References in corpus (34)
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Measurement-based quantum computation
- Entanglement and non-Markovianity of quantum evolutions
- Universal Quantum Computation with Continuous-Variable Cluster States
- Non-Markovian effects on the dynamics of entanglement
- Universal dynamical decoupling of a single solid-state spin from a spin bath
- Experimental entanglement of six photons in graph states
- Assessing non-Markovian dynamics
- Measure for the Non-Markovianity of Quantum Processes
- Non-Markovian Dynamics of Quantum Discord
- Experimental Analysis of a 4-Qubit Cluster State
- Novel schemes for measurement-based quantum computation
- Measurement-based quantum computation beyond the one-way model
- Exact master equations for the non-Markovian decay of a qubit
- Experimental Uhrig Dynamical Decoupling using Trapped Ions
- Multiparticle entanglement under the influence of decoherence
- Experimental Entanglement and Nonlocality of a Two-Photon Six-Qubit Cluster State
- Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
- Optical one-way quantum computing with a simulated valence-bond solid
- Noise thresholds for optical cluster-state quantum computation
- Universal quantum computer from a quantum magnet
- Ultrafast optical spin echo for electron spins in semiconductors
- Open-system dynamics of graph-state entanglement
- Quantum computational webs
- Quantum computation in correlation space and extremal entanglement
- Noisy entanglement evolution for graph states
- Noisy One-Way Quantum Computations: The Role of Correlations
- Experimental Demonstration of Decoherence-Free One-Way Information Transfer
- Experimental measurement-based quantum computing beyond the cluster-state model
- Adiabatic Cluster State Quantum Computing
- Strong entanglement causes low gate fidelity in inaccurate one-way quantum computation
- Entanglement Sudden Death as an Indicator of Fidelity in a Four-Qubit Cluster State
- The decoherence dynamics of the multipartite entanglement in non-Markovian environment
- Storing Small Photonic Cluster States in a Dephasing Environment