Implementation of Measurement Reduction for the Variational Quantum Eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.Comment: Revised order of paper, and further background details about the LCU method added. A unary implementation of LCU is also explored. Results unchange

A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations.Comment: 46 pages, 11 figure

A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth

Long Time Scale Ensemble Methods in Molecular Dynamics: Ligand–Protein Interactions and Allostery in SARS-CoV-2 Targets

We subject a series of five protein-ligand systems which contain important SARS-CoV-2 targets, 3-chymotrypsin-like protease (3CLPro), papain-like protease, and adenosine ribose phosphatase, to long time scale and adaptive sampling molecular dynamics simulations. By performing ensembles of ten or twelve 10 μs simulations for each system, we accurately and reproducibly determine ligand binding sites, both crystallographically resolved and otherwise, thereby discovering binding sites that can be exploited for drug discovery. We also report robust, ensemble-based observation of conformational changes that occur at the main binding site of 3CLPro due to the presence of another ligand at an allosteric binding site explaining the underlying cascade of events responsible for its inhibitory effect. Using our simulations, we have discovered a novel allosteric mechanism of inhibition for a ligand known to bind only at the substrate binding site. Due to the chaotic nature of molecular dynamics trajectories, regardless of their temporal duration individual trajectories do not allow for accurate or reproducible elucidation of macroscopic expectation values. Unprecedentedly at this time scale, we compare the statistical distribution of protein-ligand contact frequencies for these ten/twelve 10 μs trajectories and find that over 90% of trajectories have significantly different contact frequency distributions. Furthermore, using a direct binding free energy calculation protocol, we determine the ligand binding free energies for each of the identified sites using long time scale simulations. The free energies differ by 0.77 to 7.26 kcal/mol across individual trajectories depending on the binding site and the system. We show that, although this is the standard way such quantities are currently reported at long time scale, individual simulations do not yield reliable free energies. Ensembles of independent trajectories are necessary to overcome the aleatoric uncertainty in order to obtain statistically meaningful and reproducible results. Finally, we compare the application of different free energy methods to these systems and discuss their advantages and disadvantages. Our findings here are generally applicable to all molecular dynamics based applications and not confined to the free energy methods used in this study

A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules.Comment: 42 pages, 4 figure

Shear-Induced Isotropic-to-Lamellar Transition in a Lattice-Gas Model of Ternary Amphiphilic Fluids

Although shear-induced isotropic-to-lamellar transitions in ternary systems of oil, water and surfactant have been observed experimentally and predicted theoretically by simple models for some time now, their numerical simulation has not been achieved so far. In this work we demonstrate that a recently introduced hydrodynamic lattice-gas model of amphiphilic fluids is well suited for this purpose: the two-dimensional version of this model does indeed exhibit a shear-induced isotropic-to-lamellar phase transition.Comment: 17 pages, LaTeX with epsf and REVTeX, PostScript and EPS illustrations included. To appear in J. Phys. Cond. Ma

Lattice-gas simulations of Domain Growth, Saturation and Self-Assembly in Immiscible Fluids and Microemulsions

We investigate the dynamical behavior of both binary fluid and ternary microemulsion systems in two dimensions using a recently introduced hydrodynamic lattice-gas model of microemulsions. We find that the presence of amphiphile in our simulations reduces the usual oil-water interfacial tension in accord with experiment and consequently affects the non-equilibrium growth of oil and water domains. As the density of surfactant is increased we observe a crossover from the usual two-dimensional binary fluid scaling laws to a growth that is {\it slow}, and we find that this slow growth can be characterized by a logarithmic time scale. With sufficient surfactant in the system we observe that the domains cease to grow beyond a certain point and we find that this final characteristic domain size is inversely proportional to the interfacial surfactant concentration in the system.Comment: 28 pages, latex, embedded .eps figures, one figure is in colour, all in one uuencoded gzip compressed tar file, submitted to Physical Review

Activation of both TLR and NOD signaling confers host innate immunity-mediated protection against microbial infection

The detection of microbial pathogens relies on the recognition of highly conserved microbial structures by the membrane sensor Toll-like receptors (TLRs) and cytosolic sensor NOD-like receptors (NLRs). Upon detection, these sensors trigger innate immune responses to eradicate the invaded microbial pathogens. However, it is unclear whether TLR and NOD signaling are both critical for innate immunity to initiate inflammatory and antimicrobial responses against microbial infection. Here we report that activation of both TLR and NOD signaling resulted in an augmented inflammatory response and the crosstalk between TLR and NOD led to an amplified downstream NF-kB activation with increased nuclear transactivation of p65 at TNF-a and IL-6 promoters. Furthermore, co-stimulation of macrophages with TLR and NOD agonists maximized antimicrobial activity with accelerated phagosome maturation. Importantly, administration of both TLR and NOD agonists protected mice against polymicrobial sepsis-associated lethality with increased serum levels of inflammatory cytokines and accelerated bacterial clearance from the circulation and visceral organs. These results demonstrate that activation of both TLR and NOD signaling synergizes to induce efficient inflammatory and antimicrobial responses, thus conferring protection against microbial infection

The role and uses of antibodies in COVID-19 infections: a living review

Coronavirus disease 2019 has generated a rapidly evolving field of research, with the global scientific community striving for solutions to the current pandemic. Characterizing humoral responses towards SARS-CoV-2, as well as closely related strains, will help determine whether antibodies are central to infection control, and aid the design of therapeutics and vaccine candidates. This review outlines the major aspects of SARS-CoV-2-specific antibody research to date, with a focus on the various prophylactic and therapeutic uses of antibodies to alleviate disease in addition to the potential of cross-reactive therapies and the implications of long-term immunity