Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.

Much progress has been made recently in the study of the effects of electron-phonon (el-ph) coupling in doped insulators using angle resolved photoemission (ARPES), yielding evidence for the dominant role of el-ph interactions in underdoped cuprates. As these studies have been limited to doped Mott insulators, the important question arises how this compares with doped band insulators where similar el-ph couplings should be at work. The archetypical case is the perovskite SrTiO 3 (STO), well known for its giant dielectric constant of 10000 at low temperature, exceeding that of La 2 CuO 4 by a factor of 500. Based on this fact, it has been suggested that doped STO should be the archetypical bipolaron superconductor. Here we report an ARPES study from high-quality surfaces of lightly doped SrTiO 3 . Comparing to lightly doped Mott insulators, we find the signatures of only moderate electron-phonon coupling: a dispersion anomaly associated with the low frequency optical phonon with a λ ′ ∼ 0.3 and an overall bandwidth renormalization suggesting an overall λ ′ ∼ 0.7 coming from the higher frequency phonons. Further, we find no clear signatures of the large pseudogap or small polaron phenomena. These findings demonstrate that a large dielectric constant itself is not a good indicator of el-ph coupling and highlight the unusually strong effects of the el-ph coupling in doped Mott insulators.Strong energy-momentum dispersion in the lightly doped SrTiO 3 2

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers

Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging quantum chemistry problems. Here we report an experimental demonstration that a small nuclear-magnetic-resonance (NMR) quantum computer is already able to simulate the dynamics of a prototype chemical reaction. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on current classical computers is feasible in the near future. 1Introduction. In addition to offering general-purpose quantum algorithms with substantial speed-ups over classical algorithms (1) [e.g., Shor's quantum factorizing algorithm (2)], a quantum computer can be used to simulate specific quantum systems with high efficiency (3). This quantum simulation idea was first conceived by Feynman (4). Lloyd proved that with quantum computation architecture, the required resource for quantum simulation scales polynomially with the size of the simulated system (5), as compared with the exponential scaling on classical computers. During the past years several quantum simulation algorithms designed for individual problems were proposed (6-10) and a part of them have been realized using physical systems such as NMR (11-13) or trapped-ions (14). For quantum chemistry problems, Aspuru-Guzik et al. and Kassal et al. proposed quantum simulation algorithms to calculate stationary molecular properties (15) as well as chemical reaction rates (16), with the quantum simulation of the former experimentally implemented on both NMR (17) and photonic quantum computers (18). In this work we aim at the quantum simulation of the more challenging side of quantum chemistry problems -chemical reaction dynamics, presenting an experimental NMR implementation for the first time.Theoretical calculations of chemical reaction dynamics play an important role in understanding reaction mechanisms and in guiding the control of chemical reactions (19,20). On classical computers the computational cost for propagating the Schrödinger equation increases exponentially with the system size. Indeed, standard methods in studies of chemical reaction dynamics so far have dealt with up to 9 degrees of freedom (DOF) (21). Some highly sophisticated approaches, such as the multi-configurational time-dependent Hartree (MCTDH) method (22), can treat dozens of DOF but various approximations are necessary. So generally speaking, classical computers are unable to perform dynamical simulations for large molecules.For example, for a 10-DOF system and if only 8 grid points are needed for the coordinate representation of each DOF, classical computation will have to store and operate 8 10 data points, 2 already a formidable task for current classical computers. By contrast, such a system size is manageable by a quantum computer with only 30 qubits. Furthermore, the whole set of data c...

We have investigated the molecular environment of the semicircular composite supernova remnant (SNR) 3C 396 and performed a Chandra spatially resolved thermal X-ray spectroscopic study of this young SNR. With our CO millimeter observations, we find that the molecular clouds (MCs) at V LSR ∼ 84 km s −1 can better explain the multiwavelength properties of the remnant than the V LSR = 67-72 km s −1 MCs that are suggested by Lee et al. (2009). At around 84 km s −1 , the western boundary of the SNR is perfectly confined by the western molecular wall. The CO emission fades out from west to east, indicating that the eastern region is of low gas density. In particular, an intruding finger/pillar-like MC, which may be shocked at the tip, can well explain the X-ray and radio enhancement in the southwest and some infrared filaments there. The SNR-MC interaction is also favored by the relatively elevated 12 CO J=2-1/J=1-0 line ratios in the southwestern "pillar tip" and the molecular patch on the northwestern boundary. The redshifted 12 CO (J=1-0 and J=2-1) wings (86-90 km s −1 ) of an eastern 81 km s −1 molecular patch may be the kinematic evidence for shock-MC interaction. We suggest that the 69 km s −1 MCs are in the foreground based on HI self-absorption while the 84 km s −1 MCs at a distance of 6.2 kpc (the tangent point) are in physical contact with SNR 3C 396. The X-ray spectral analysis suggests an SNR age of ∼ 3 kyr. The metal enrichment of the X-ray emitting gas in the north and south implies a 13-15M ⊙ B1-B2 progenitor star.