Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method

In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green's function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.Comment: 20 pages, 12 figure

A quantum circuit rule for interference effects in single-molecule electrical junctions

A quantum circuit rule for combining quantum interference effects in the conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules possessing three aromatic rings was investigated both experimentally and theoretically. Molecules were of the type X-Y-X, where X represents pyridyl anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a phenyl ring with p and m connectivities. The conductances GXmX (GXpX) of molecules of the form X-m-X (X-p-X), with meta (para) connections in the central ring, were predominantly lower (higher), irrespective of the meta, para or ortho nature of the anchor groups X, demonstrating that conductance is dominated by the nature of quantum interference in the central ring Y. The single-molecule conductances were found to satisfy the quantum circuit rule Gppp/Gpmp=Gmpm/Gmmm. This demonstrates that the contribution to the conductance from the central ring is independent of the para versus meta nature of the anchor groups

Tuning the Seebeck coefficient of naphthalenediimide by electrochemical gating and doping

We investigate the sign and magnitude of the single-molecule Seebeck coefficient of naphthalenediimide (NDI) under the influence of electrochemical gating and doping. The molecule consists of a NDI core with two alkyl chains in the bay-area position, connected to gold electrodes via benzothiophene (DBT) anchor groups. By switching between the neutral, radical and di-anion charge states, we are able to tune the molecular energy levels relative to the Fermi energy of the electrodes. The resulting single-molecule room-temperature Seebeck coefficents of the three charge states are -294.5 μV K(-1), 122 μV K(-1) and 144 μV K(-1) respectively and the room-temperature power factors are 4.4 × 10(-5) W m(-1) K(-2), 3 × 10(-5) W m(-1) K(-2) and 8.2 × 10(-4) W m(-1) K(-2). As a further strategy for optimising thermoelectric properties, we also investigate the effect on both phonon and electron transport of doping the NDI with either an electron donor (TTF) or an electron acceptor (TCNE). We find that doping by TTF increases the room-temperature Seebeck coefficient and power factor from -73.7 μV K(-1) and 2.6 × 10(-7) W m(-1) K(-2) for bare NDI to -105 μV K(-1) and 3.6 × 10(-4) W m(-1) K(-2) in presence of TTF. The low thermal conductance of NDI-TTF, combined with the higher Seebeck coefficient and higher electrical conductance lead to a maximum thermoelectric figure of merit of ZT = 1.2, which is higher than that of bare NDI in several orders of magnitude. This demonstrates that both the sign and magnitude of NDI Seebeck coefficient can be tuned reversibly by electrochemical gating and doping, suggesting that such redox active molecules are attractive materials for ultra-thin-film thermoelectric devices

Structural versus Electrical Functionalization of Oligo(phenyleneethynylene) Diamine Molecular Junctions

We explore both experimentally and theoretically the conductance and packing of molecular junctions based on oligo(phenyleneethynylene) (OPE) diamine wires, when a series of functional groups are incorporated into the wires. Using the scanning tunnelling microscopy break-junction (STM BJ) technique, we study these compounds in two environments (air and 1,2,4-trichlorobenzene) and explore different starting molecular concentrations. We show that the electrical conductance of the molecular junctions exhibits variations among different compounds, which are significant at standard concentrations but become unimportant when working at a low enough concentration. This shows that the main effect of the functional groups is to affect the packing of the molecular wires, rather than to modify their electrical properties. Our theoretical calculations consistently predict no significant changes in the conductance of the wires due to the electronic structure of the functional groups, although their ability to hinder ring rotations within the OPE backbone can lead to higher conductances at higher packing densities

Albiglutide and cardiovascular outcomes in patients with type 2 diabetes and cardiovascular disease (Harmony Outcomes): a double-blind, randomised placebo-controlled trial

Background: Glucagon-like peptide 1 receptor agonists differ in chemical structure, duration of action, and in their effects on clinical outcomes. The cardiovascular effects of once-weekly albiglutide in type 2 diabetes are unknown. We aimed to determine the safety and efficacy of albiglutide in preventing cardiovascular death, myocardial infarction, or stroke. Methods: We did a double-blind, randomised, placebo-controlled trial in 610 sites across 28 countries. We randomly assigned patients aged 40 years and older with type 2 diabetes and cardiovascular disease (at a 1:1 ratio) to groups that either received a subcutaneous injection of albiglutide (30–50 mg, based on glycaemic response and tolerability) or of a matched volume of placebo once a week, in addition to their standard care. Investigators used an interactive voice or web response system to obtain treatment assignment, and patients and all study investigators were masked to their treatment allocation. We hypothesised that albiglutide would be non-inferior to placebo for the primary outcome of the first occurrence of cardiovascular death, myocardial infarction, or stroke, which was assessed in the intention-to-treat population. If non-inferiority was confirmed by an upper limit of the 95% CI for a hazard ratio of less than 1·30, closed testing for superiority was prespecified. This study is registered with ClinicalTrials.gov, number NCT02465515. Findings: Patients were screened between July 1, 2015, and Nov 24, 2016. 10 793 patients were screened and 9463 participants were enrolled and randomly assigned to groups: 4731 patients were assigned to receive albiglutide and 4732 patients to receive placebo. On Nov 8, 2017, it was determined that 611 primary endpoints and a median follow-up of at least 1·5 years had accrued, and participants returned for a final visit and discontinuation from study treatment; the last patient visit was on March 12, 2018. These 9463 patients, the intention-to-treat population, were evaluated for a median duration of 1·6 years and were assessed for the primary outcome. The primary composite outcome occurred in 338 (7%) of 4731 patients at an incidence rate of 4·6 events per 100 person-years in the albiglutide group and in 428 (9%) of 4732 patients at an incidence rate of 5·9 events per 100 person-years in the placebo group (hazard ratio 0·78, 95% CI 0·68–0·90), which indicated that albiglutide was superior to placebo (p<0·0001 for non-inferiority; p=0·0006 for superiority). The incidence of acute pancreatitis (ten patients in the albiglutide group and seven patients in the placebo group), pancreatic cancer (six patients in the albiglutide group and five patients in the placebo group), medullary thyroid carcinoma (zero patients in both groups), and other serious adverse events did not differ between the two groups. There were three (<1%) deaths in the placebo group that were assessed by investigators, who were masked to study drug assignment, to be treatment-related and two (<1%) deaths in the albiglutide group. Interpretation: In patients with type 2 diabetes and cardiovascular disease, albiglutide was superior to placebo with respect to major adverse cardiovascular events. Evidence-based glucagon-like peptide 1 receptor agonists should therefore be considered as part of a comprehensive strategy to reduce the risk of cardiovascular events in patients with type 2 diabetes. Funding: GlaxoSmithKline

Interplay between quantum interference and conformational fluctuations in single-molecule break junctions

We theoretically explored the combined role of conformational fluctuations and quantum interference in determining the electrical conductance of single-molecule break junctions. In particular we computed the conductance of a family of methylsulfide-functionalized trans-alpha,omega-diphenyloligoene molecules, with terminal phenyl rings containing meta or para linkages, for which (at least in the absence of fluctuations) destructive interference in the former is expected to decrease their electrical conductance compared with the latter. We compared the predictions of density functional theory (DFT), in which fluctuational effects are absent, with results for the conformationally-averaged conductance obtained from an ensemble of conformations obtained from classical molecular dynamics. We found that junctions formed from these molecules exhibit distinct transport regimes during junction evolution and the signatures of quantum interference in these molecules survive the effect of conformational fluctuations. Furthermore, the agreement between theory and experiment is significantly improved by including conformational averaging

Correlation of breaking forces, conductances and geometries of molecular junctions

Electrical and mechanical properties of elongated gold-molecule-gold junctions formed by tolane-type molecules with different anchoring groups (pyridyl, thiol, amine, nitrile and dihydrobenzothiophene) were studied in current-sensing force spectroscopy experiments and density functional simulations. Correlations between forces, conductances and junction geometries demonstrate that aromatic tolanes bind between electrodes as single molecules or as weakly-conductive dimers held by mechanically-weak π − π stacking. In contrast with the other anchors that form only S-Au or N-Au bonds, the pyridyl ring also forms a highly-conductive cofacial link to the gold surface. Binding of multiple molecules creates junctions with higher conductances and mechanical strengths than the single-molecule ones

An MCBJ case study: The influence of π-conjugation on the single-molecule conductance at a solid/liquid interface

π-Conjugation plays an important role in charge transport through single molecular junctions. We describe in this paper the construction of a mechanically controlled break-junction setup (MCBJ) equipped with a highly sensitive log I–V converter in order to measure ultralow conductances of molecular rods trapped between two gold leads. The current resolution of the setup reaches down to 10 fA. We report single-molecule conductance measurements of an anthracene-based linearly conjugated molecule (AC), of an anthraquinone-based cross-conjugated molecule (AQ), and of a dihydroanthracene-based molecule (AH) with a broken conjugation. The quantitative analysis of complementary current–distance and current–voltage measurements revealed details of the influence of π-conjugation on the single-molecule conductance