Experimental quantum simulation of a topologically protected Hadamard gate via braiding Fibonacci anyons.

Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC-the Fibonacci anyon system-lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can simulate the Fibonacci anyon system and construct the topologically protected logical spaces with the Fibonacci anyons. Via braiding the Fibonacci anyons, we can implement universal quantum gates on the logical space. Our disk model merely requires two physical qubits to realize three Fibonacci anyons at the boundary. By 15 sequential braiding operations, we construct a topologically protected Hadamard gate, which is to date the least-resource requirement for TQC. To showcase, we implement a topological Hadamard gate with two nuclear spin qubits, which reaches 97.18% fidelity by randomized benchmarking. We further prove by experiment that the logical space and Hadamard gate are topologically protected: local disturbances due to thermal fluctuations result in a global phase only. As a platform-independent proposal, our work is a proof of principle of TQC and paves the way toward fault-tolerant quantum computation.

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

Ground-state degeneracy of topological phases on open surfaces.

We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Tao-Wu charge-pumping argument for Abelian fractional quantum Hall states to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a nontrivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.

Subpeaks in the Brillouin loss spectra of distributed fiber-optic sensors.

Subpeaks in the Brillouin loss spectra of distributed fiber-optic sensors were observed for what is believed to be the first time and studied. We discovered that the Fourier spectrum of the pulsed signal and the off-resonance oscillation both contributed to subpeaks. The off-resonance oscillation at frequency /v - vB/ is the oscillation in the Brillouin time domain when beat frequency v of the two counterpropagating laser beams does not match local Brillouin frequency vB. This study is important in differentiating the subpeaks from actual strain-temperature peaks.

Effect of optical phase on a distributed Brillouin sensor at centimeter spatial resolution.

Because of the power imbalance between the two arms of an interferometer in an electro-optic modulator (EOM), the output of the EOM is combined amplitude modulation (AM) and phase modulation (PM) for the probe signal consisting of the pulse and the dc component. Because of this PM, the Brillouin gain-loss spectrum becomes asymmetric. The central Brillouin frequency is shifted from that of an AM pulse. The maximum extinction ratio of the EOM is limited to approximately 29 dB for a power-splitting ratio of 51% to 49%. The asymmetric property induced by PM is not pulse shape dependent; for both Gaussian- and super-Gaussian-shaped pulses the Brillouin loss spectrum is symmetric for AM and asymmetric for combined AM and PM (power imbalance).

Coherent probe-pump-based Brillouin sensor for centimeter-crack detection.

We provide a theoretical explanation for a coherent probe-pump-based Brillouin sensor system that achieves centimeter spatial resolution with high-frequency resolution. It was recently discovered that, when a combination of cw and pulsed light (the probe beam) interacts with a cw laser (the pump beam), centimeter spatial resolution with high-frequency resolution can be achieved even though the probe-pulse duration is 1.5 ns [Opt. Lett. 29, 1485 (2004)]. Our study reveals that the coherent portion inside the pulse length of these two interactions caused by the same phase is responsible for this behavior. It allows us to detect 1.5-cm outer-layer cracks on an optical ground-wire cable.