The Forbidden Quantum Adder

Quantum information provides fundamentally different computational resources than classical information. We prove that there is no unitary protocol able to add unknown quantum states belonging to different Hilbert spaces. This is an inherent restriction of quantum physics that is related to the impossibility of copying an arbitrary quantum state, i.e., the no-cloning theorem. Moreover, we demonstrate that a quantum adder, in absence of an ancillary system, is also forbidden for a known orthonormal basis. This allows us to propose an approximate quantum adder that could be implemented in the lab. Finally, we discuss the distinct character of the forbidden quantum adder for quantum states and the allowed quantum adder for density matrices.

Long-lived oscillatory incoherent electron dynamics in molecules: trans-polyacetylene oligomers

We identify an intriguing feature of the electron-vibrational dynamics of molecular systems via a computational examination of trans-polyacetylene oligomers. Here, via the vibronic interactions, the decay of an electron in the conduction band resonantly excites an electron in the valence band, and vice versa, leading to oscillatory exchange of electronic population between two distinct electronic states that lives for up to tens of picoseconds. The oscillatory structure is reminiscent of beating patterns between quantum states and is strongly suggestive of the presence of long-lived molecular electronic coherence. Significantly, however, a detailed analysis of the electronic coherence properties shows that the oscillatory structure arises from a purely incoherent process. These results were obtained by propagating the coupled dynamics of electronic and vibrational degrees of freedom in a mixed quantum-classical study of the Su-Schrieffer-Heeger Hamiltonian for polyacetylene. The incoherent process is shown to occur between degenerate electronic states with distinct electronic configurations that are indirectly coupled via a third auxiliary state by vibronic interactions. A discussion of how to construct electronic superposition states in molecules that are truly robust to decoherence is also presented

Metallic thin fi lms on stepped surfaces: lateral scattering of quantum well states

Quantum well states of Ag films grown on stepped Au(111) surfaces are shown to undergo lateral scattering, in analogy with surface states of vicinal Ag(111). Applying angle resolved photoemission spectroscopy we observe quantum well bands with zone-folding and gap openings driven by surface/interface step lattice scattering. Experiments performed on a curved Au(111) substrate allow us to determine a subtle terrace-size effect, i.e., a fine step-density-dependent upward shift of quantum well bands. This energy shift is explained as mainly due to the periodically stepped crystal potential offset at the interface side of the film. Finally, the surface state of the stepped Ag film is analyzed with both photoemission and scanning tunneling microscopy. We observe that the stepped film interface also affects the surface state energy, which exhibits a larger terrace-size effect compared to surface states of bulk vicinal Ag(111) crystals

Dual-path methods for propagating quantum microwaves

We study quantum state tomography, entanglement detection and channel noise reconstruction of propagating quantum microwaves via dual-path methods. The presented schemes make use of the following key elements: propagation channels, beam splitters, linear amplifiers and field quadrature detectors. Remarkably, our methods are tolerant to the ubiquitous noise added to the signals by phase-insensitive microwave amplifiers. Furthermore, we analyse our techniques with numerical examples and experimental data, and compare them with the scheme developed in Eichler et al (2011 Phys. Rev. Lett. 106 220503; 2011 Phys. Rev. Lett. 107 113601), based on a single path. Our methods provide key toolbox components that may pave the way towards quantum microwave teleportation and communication protocols.

Quantum ricochets: surface capture, release and energy loss of fast ions hitting a polar surface at grazing incidence

A diffraction mechanism is proposed for the capture, multiple bouncing and final escape of a fast ion (keV) impinging on the surface of a polarizable material at grazing incidence. Capture and escape are effected by elastic quantum diffraction consisting of the exchange of a parallel surface wave vector G= 2p/ a between the ion parallel momentum and the surface periodic potential of period a. Diffraction- assisted capture becomes possible for glancing angles F smaller than a critical value given by Fc 2- 2./ a-| Vim|/ E, where E is the kinetic energy of the ion,. = h/ Mv its de Broglie wavelength and Vim its average electronic image potential at the distance from the surface where diffraction takes place. For F< Fc, the ion can fall into a selected capture state in the quasi- continuous spectrum of its image potential and execute one or several ricochets before being released by the time reversed diffraction process. The capture, ricochet and escape are accompanied by a large, periodic energy loss of several tens of eV in the forward motion caused by the coherent emission of a giant number of quanta h. of Fuchs- Kliewer surface phonons characteristic of the polar material. An analytical calculation of the energy loss spectrum, based on the proposed diffraction process and using a model ion-phonon coupling developed earlier (Lucas et al 2013 J. Phys.: Condens. Matter 25 355009), is presented, which fully explains the experimental spectrum of Villette et al (2000 Phys. Rev. Lett. 85 3137) for Ne+ ions ricocheting on a LiF(001) surface.

Quantum Emulation of Gravitational Waves

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials.

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.