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Lecture notes in computer science

A Logical Basis for Quantum Evolution and Entanglement

Richard F. Blute, Alessio Guglielmi, Ivan T. Ivanov, Prakash Panangaden, Lutz Straßburger

Published Jan 1, 2014• 10 citations
Publisher
DOI
10.1007/978-3-642-54789-8_6

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We present a universal quantum computing architecture which combines the measurement-driven aspect of MBQC with the circuit model's algorithm dependent generation of qubit entanglement. Our architecture, which we call QGATE, is tailored for discrete-variable photonic quantum computers with deterministic photon sources capable of generating 1D entangled photonic states. QGATE achieves universal quantum computing on a logical data qubit register via the implementation of Clifford operations, QGATE ancilla, and arbitrary angle single-qubit measurements. We realise unitary evolutions defined by multi-qubit Pauli strings via the generation of entanglement between a sub-set of logical qubits and a mutual QGATE ancilla qubit. Measurement of the QGATE ancilla in the appropriate basis then implements a given term of the desired unitary operation. This enables QGATE to both directly perform Hamiltonian evolutions in terms of a series of multi-qubit Pauli operators, in terms of projectors for an arbitrary sparse Hamiltonian, or realise multi-controlled gates enabling direct translation of circuit models to QGATE. We consider examples inspired by quantum chemistry and computational fluid dynamics. We propose an example photonic implementation of QGATE and calculate thresholds of 10.36±0.02%10.36\pm0.02\%10.36±0.02% or 25.98±0.28%25.98\pm0.28\%25.98±0.28% on the photonic loss for logical qubits constructed from foliated rotated surface codes, dependent on the deployment of intra-layer or inter-layer fusion respectively.
Current schemes for implementing quantum logic involve controlled coupling between two-level systems, or qubits, which requires a large number of qubits to be entangled coherently for information processing. A multilevel basis for quantum information minimizes the number of systems that need to be entangled. We present the requirements for multilevel quantum logic in a dual basis formalism that emphasizes the key role played by the Fourier transform in quantum algorithms. We discuss a realization in atomic systems, where the two bases consist of energy levels and wave packets, and examine the practical resources needed for controlling each basis.
We study a means of creating multiparticle entanglement of neutral atoms using pairwise controlled dipole-dipole interactions. For tightly trapped atoms the dipolar interaction energy can be much larger than the photon scattering rate and substantial coherent evolution of the two-atom state can be achieved before decoherence occurs. Excitation of the dipoles can be made conditional on the atomic states, allowing for deterministic generation of entanglement. We derive selection rules and a figure of merit for the dipole-dipole interaction matrix elements, for alkali atoms with hyperfine structure and trapped in localized center of mass states. Different protocols are presented for implementing two-qubit quantum logic gates such as the controlled-phase and swap gates. We analyze the error probability of our gate designs, finite due to decoherence from cooperative spontaneous emission and coherent couplings outside the logical basis. Outlines for extending our model to include the full molecular interactions potentials are discussed.