2,397 research outputs found
Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits
To implement a set of universal quantum logic gates based on non-Abelian
geometric phases, it is a conventional wisdom that quantum systems beyond two
levels are required, which is extremely difficult to fulfil for superconducting
qubits, appearing to be a main reason why only single qubit gates was
implemented in a recent experiment [A. A. Abdumalikov Jr \emph{et al}., Nature
496, 482 (2013)]. Here we propose to realize non-adiabatic holonomic quantum
computation in decoherence-free subspace on circuit QED, where one can use only
the two levels in transmon qubits, a usual interaction, and a minimal resource
for the decoherence-free subspace encoding. In particular, our scheme not only
overcomes the difficulties encountered in previous studies, but also can still
achieve considerably large effective coupling strength, such that high fidelity
quantum gates can be achieved. Therefore, the present scheme makes it very
promising way to realize robust holonomic quantum computation with
superconducting circuits.Comment: V4: published version; V1: submitted on April
Ternary Logic Design in Topological Quantum Computing
A quantum computer can perform exponentially faster than its classical
counterpart. It works on the principle of superposition. But due to the
decoherence effect, the superposition of a quantum state gets destroyed by the
interaction with the environment. It is a real challenge to completely isolate
a quantum system to make it free of decoherence. This problem can be
circumvented by the use of topological quantum phases of matter. These phases
have quasiparticles excitations called anyons. The anyons are charge-flux
composites and show exotic fractional statistics. When the order of exchange
matters, then the anyons are called non-Abelian anyons. Majorana fermions in
topological superconductors and quasiparticles in some quantum Hall states are
non-Abelian anyons. Such topological phases of matter have a ground state
degeneracy. The fusion of two or more non-Abelian anyons can result in a
superposition of several anyons. The topological quantum gates are implemented
by braiding and fusion of the non-Abelian anyons. The fault-tolerance is
achieved through the topological degrees of freedom of anyons. Such degrees of
freedom are non-local, hence inaccessible to the local perturbations. In this
paper, the Hilbert space for a topological qubit is discussed. The Ising and
Fibonacci anyonic models for binary gates are briefly given. Ternary logic
gates are more compact than their binary counterparts and naturally arise in a
type of anyonic model called the metaplectic anyons. The mathematical model,
for the fusion and braiding matrices of metaplectic anyons, is the quantum
deformation of the recoupling theory. We proposed that the existing quantum
ternary arithmetic gates can be realized by braiding and topological charge
measurement of the metaplectic anyons
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