139,307 research outputs found
Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance
Geometric phases have stimulated researchers for its potential applications
in many areas of science. One of them is fault-tolerant quantum computation. A
preliminary requisite of quantum computation is the implementation of
controlled logic gates by controlled dynamics of qubits. In controlled
dynamics, one qubit undergoes coherent evolution and acquires appropriate
phase, depending on the state of other qubits. If the evolution is geometric,
then the phase acquired depend only on the geometry of the path executed, and
is robust against certain types of errors. This phenomenon leads to an
inherently fault-tolerant quantum computation.
Here we suggest a technique of using non-adiabatic geometric phase for
quantum computation, using selective excitation. In a two-qubit system, we
selectively evolve a suitable subsystem where the control qubit is in state
|1>, through a closed circuit. By this evolution, the target qubit gains a
phase controlled by the state of the control qubit. Using these geometric phase
gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's
search algorithm in a two-qubit system
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Implementing universal nonadiabatic holonomic quantum gates with transmons
Geometric phases are well known to be noise-resilient in quantum
evolutions/operations. Holonomic quantum gates provide us with a robust way
towards universal quantum computation, as these quantum gates are actually
induced by nonabelian geometric phases. Here we propose and elaborate how to
efficiently implement universal nonadiabatic holonomic quantum gates on simpler
superconducting circuits, with a single transmon serving as a qubit. In our
proposal, an arbitrary single-qubit holonomic gate can be realized in a
single-loop scenario, by varying the amplitudes and phase difference of two
microwave fields resonantly coupled to a transmon, while nontrivial two-qubit
holonomic gates may be generated with a transmission-line resonator being
simultaneously coupled to the two target transmons in an effective resonant
way. Moreover, our scenario may readily be scaled up to a two-dimensional
lattice configuration, which is able to support large scalable quantum
computation, paving the way for practically implementing universal nonadiabatic
holonomic quantum computation with superconducting circuits.Comment: v3 Appendix added, v4 published version, v5 published version with
correction
Robust nonadiabatic geometric quantum computation by dynamical correction
Besides the intrinsic noise resilience property, nonadiabatic geometric
phases are of the fast evolution nature, and thus can naturally be used in
constructing quantum gates with excellent performance, i.e., the so-called
nonadiabatic geometric quantum computation (NGQC). However, previous
single-loop NGQC schemes are sensitive to the operational control error, i.e.,
the error, due to the limitations of the implementation. Here, we propose a
robust scheme for NGQC combining with the dynamical correction technique, which
still uses only simplified pulses, and thus being experimental friendly. We
numerically show that our scheme can greatly improve the gate robustness in
previous protocols, retaining the intrinsic merit of geometric phases.
Furthermore, to fight against the dephasing noise, due to the error, we can
incorporate the decoherence-free subspace encoding strategy. In this way, our
scheme can be robust against both types of errors. Finally, we also propose how
to implement the scheme with encoding on superconducting quantum circuits with
experimentally demonstrated technology. Therefore, due to the intrinsic
robustness, our scheme provides a promising alternation for the future scalable
fault-tolerant quantum computation.Comment: 6 pages, 5 figure
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