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Register a new userEfficient quantum computation in a network with probabilistic gates and logical encoding
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Added by
Johannes Borregaard phd
Publication date
2016
fields
Physics
and research's language is
English
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A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from linear optical quantum computation in order to perform high fidelity quantum gates across a quantum network. The error-detecting properties of the heralded operations ensure high fidelity while the encoding makes it possible to correct for failed attempts such that deterministic and high-quality gates can be achieved. Importantly, this is robust to photon loss, which is typically the main obstacle to photonic based quantum information processing. Overall this approach opens a novel path towards quantum networks with atomic nodes and photonic links.
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While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of computational and communicational tasks. Strong contextuality is an extremal form of contextuality describing systems that exhibit logically paradoxical behaviour. Here, we consider special magic states that deterministically enable quantum computation. After introducing number-theoretic techniques for constructing exotic quantum paradoxes, we present large classes of strongly contextual magic states that enable deterministic implementation of gates from the Clifford hierarchy. These surprising discoveries bolster a refinement of the resource theory of contextuality that emphasises the computational power of logical paradoxes.
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the quantum switch, which can be programmed to switch the order of two channels with a single use of each one.
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier transformation can be obtained with a single loop.
It has recently been shown that a parametrically driven oscillator with Kerr nonlinearity yields a Schrodinger cat state via quantum adiabatic evolution through its bifurcation point and a network of such nonlinear oscillators can be used for solving combinatorial optimization problems by bifurcation-based adiabatic quantum computation [H. Goto, Sci. Rep. textbf{6}, 21686 (2016)]. Here we theoretically show that such a nonlinear oscillator network with controllable parameters can also be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation based on quantum adiabatic evolution, which yields a Schrodinger cat state. All the elementary quantum gates are also achieved by quantum adiabatic evolution, in which dynamical phases accompanying the adiabatic evolutions are controlled by the system parameters. Numerical simulation results indicate that high gate fidelities can be achieved, where no dissipation is assumed.
We demonstrate coherent control of two logical qubits encoded in a decoherence free subspace (DFS) of four dipolar-coupled protons in an NMR quantum information processor. A pseudo-pure fiducial state is created in the DFS, and a unitary logical qubit entangling operator evolves the system to a logical Bell state. The four-spin molecule is partially aligned by a liquid crystal solvent, which introduces strong dipolar couplings among the spins. Although the system Hamiltonian is never fully specified, we demonstrate high fidelity control over the logical degrees of freedom. In fact, the DFS encoding leads to higher fidelity control than is available in the full four-spin Hilbert space.
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