Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

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 wavefunctions than classical computers.Comment: 11 pages, 13 figure

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Implications for registry-based vaccine effectiveness studies from an evaluation of an immunization registry: A cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Population-based electronic immunization registries create the possibility of using registry data to conduct vaccine effectiveness studies which could have methodological advantages over traditional observational studies. For study validity, the base population would have to be clearly defined and the immunization status of members of the population accurately recorded in the registry. We evaluated a city-wide immunization registry, focusing on its potential as a tool to study pertussis vaccine effectiveness, especially in adolescents.</p> <p>Methods</p> <p>We conducted two evaluations – one in sites that were active registry participants and one in sites that had implemented an electronic medical record with plans for future direct data transfer to the registry – of the ability to match patients' medical records to registry records and the accuracy of immunization records in the registry. For each site, records from current pediatric patients were chosen randomly. Data regarding pertussis-related immunizations, clinic usage, and demographic and identifying information were recorded; for 11–17-year-old subjects, information on MMR, hepatitis B, and varicella immunizations was also collected. Records were then matched, when possible, to registry records. For records with a registry match, immunization data were compared.</p> <p>Results</p> <p>Among 350 subjects from sites that were current registry users, 307 (87.7%) matched a registry record. Discrepancies in pertussis-related data were common for up-to-date status (22.6%), number of immunizations (34.7%), dates (10.2%), and formulation (34.4%). Among 442 subjects from sites that planned direct electronic transfer of immunization data to the registry, 393 (88.9%) would have matched a registry record; discrepancies occurred frequently in number of immunizations (11.9%), formulation (29.1%), manufacturer (94.4%), and lot number (95.1%.) Inability to match and immunization discrepancies were both more common in subjects who were older at their first visit to the provider site. For 11–17-year-old subjects, discrepancies were also common for MMR, hepatitis B, and varicella vaccination data.</p> <p>Conclusion</p> <p>Provider records frequently could not be matched to registry records or had discrepancies in key immunization data. These issues were more common for older children and were present even with electronic data transfer. These results highlight general challenges that may face investigators wishing to use registry-based immunization data for vaccine effectiveness studies, especially in adolescents.</p

Undecidability of the spectral gap

The spectral gap-the energy difference between the ground state and first excited state of a system-is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding 'halting problem'. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics