Quantum dynamical phase transition in a system with many-body interactions

We introduce a microscopic Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency $\omega_{0}$. For weak interactions with the environment $1/\tau_{\mathrm{SE}}<2\omega_{0},$ we find a slower oscillation whose amplitude decays with a decoherence rate $1/\tau_{\phi}=1/(2\tau_{\mathrm{SE}})$. However, beyond a finite critical interaction with the environment, $1/\tau_{\mathrm{SE}}>2\omega_{0}$, the decoherence rate becomes $1/\tau_{\phi}\propto(\omega_{0}^{2})\tau_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.Comment: 5 pages, 3 figures, minor changes, fig.2 modified, added reference

Quantum Interference Phenomena in the Local Polarization Dynamics of Mesoscopic Systems: An NMR Observation

It was predicted that local spin polarization in a ring of five dipolar coupled spins should present a particular fingerprint of quantum interferences reflecting both the discrete and finite nature of the system [Phys. Rev. Lett. 75 (1995) 4310]. We report its observation for the proton system of a (C$_5$H$_5$)$_2$Fe molecule using a rare $^{13}$C as {\it local probe}. Novel high frequency ($\simeq 60k$Hz) polarization oscillations appear because incomplete $^{13}$C-$^1$H cross-polarization transfer {\it splits} the polarization state, in a portion that wanders in the proton system and one that remains in the $^{13}$ C. They interfere with each other after rejoining.Comment: 12 pages, RevTex, 4 Figures available upon request, to appear in Chemical Physics Letter

Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains

The decay of a local spin excitation in an inhomogeneous spin chain is evaluated exactly: I) It starts quadratically up to a spreading time t_{S}. II) It follows an exponential behavior governed by a self-consistent Fermi Golden Rule. III) At longer times, the exponential is overrun by an inverse power law describing return processes governed by quantum diffusion. At this last transition time t_{R} a survival collapse becomes possible, bringing the polarization down by several orders of magnitude. We identify this strongly destructive interference as an antiresonance in the time domain. These general phenomena are suitable for observation through an NMR experiment.Comment: corrected versio

Code properties from holographic geometries

Almheiri, Dong, and Harlow [arXiv:1411.7041] proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes which admit a holographic interpretation. We introduce a new quantity called `price', which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit `uberholography', meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales small compared to the AdS curvature radius.Comment: 17 pages, 5 figure

Dynamical Origin of Decoherence in Clasically Chaotic Systems

The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma$ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically chaotic systems suggest that, under certain conditions, $\tau_{\phi}$ depends on H but not on $\Sigma$. By solving numerically a Hamiltonian model we find evidence of that property provided that the system shows a Wigner-Dyson spectrum (which defines quantum chaos) and the perturbation exceeds a crytical value defined by the parametric correlations of the spectra.Comment: Typos corrected, published versio

Generating topological order: no speedup by dissipation

We consider the problem of preparing topologically ordered states using unitary and non-unitary circuits, as well as local time-dependent Hamiltonian and Liouvillian evolutions. We prove that for any topological code in $D$ dimensions, the time required to encode logical information into the ground space is at least $\Omega(d^{1/(D-1)})$, where $d$ is the code distance. This result is tight for the toric code, giving a scaling with the linear system size. More generally, we show that the linear scaling is necessary even when dropping the requirement of encoding: preparing any state close to the ground space using dissipation takes an amount of time proportional to the diameter of the system in typical 2D topologically ordered systems, as well as for example the 3D and 4D toric codes.Comment: 7 pages, 1 figur

Fault-tolerant logical gates in quantum error-correcting codes

Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant depth geometrically local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dimensions, locality preserving gates are restricted to a set of unitary gates known as the D-th level of the Clifford hierarchy. In this paper, we elaborate this idea and provide several extensions and applications of their characterization in various directions. First, we present a new no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. Second, we prove that the code distance of a D-dimensional local stabilizer code with non-trivial locality-preserving m-th level Clifford logical gate is upper bounded by $O(L^{D+1-m})$. For codes with non-Clifford gates (m>2), this improves the previous best bound by Bravyi and Terhal. Third we prove that a qubit loss threshold of codes with non-trivial transversal m-th level Clifford logical gate is upper bounded by 1/m. As such, no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes, and is not restricted to geometrically-local codes. Fourth we extend the result of Bravyi and K\"onig to subsystem codes. A technical difficulty is that, unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of error threshold in a subsystem code, and the same conclusion as Bravyi-K\"onig is recovered.Comment: 13 pages, 4 figure

Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation

We develop the Keldysh formalism for the polarization dynamics of an open spin system. We apply it to the swapping between two qubit states in a model describing an NMR cross-polarization experiment. The environment is a set of interacting spins. For fast fluctuations in the environment, the analytical solution shows effects missed by the secular approximation of the Quantum Master Equation for the density matrix: a frequency decrease depending on the system-environment escape rate and the quantum quadratic short time behavior. Considering full memory of the bath correlations yields a progressive change of the swapping frequency.Comment: 16 pages, 3 figures, final for