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A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green&#39;s function for use in condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.

CAP Virtual Congress 2021

Lanczos recursion on a quantum computer for the Green&#39;s function and ground state

quantum chemistry

quantum algorithm

green's function

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A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function for use in condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining the ground state is also discussed.

Lanczos recursion on a quantum computer for the Green's function and ground state

technical paper

We present a study of the evolution of entanglement entropy of matter and geometry in quantum cosmology. We show that entanglement entropy increases rapidly as the Universe expands, and then saturates to a constant non-zero value. The saturation value of the entropy is a linear function of the energy E associated to the quantum state: S=γE. This result suggests a ‘First Law’ of matter-gravity entanglement entropy in quantum gravity.

Matter-Geometry Entanglement in Quantum Cosmology

Over the last few decades, the study of nuclei and neutron-rich matter from first principles has entered a new era. This has partly been driven by the development of novel interactions between two or three nucleons. In an attempt to produce a systematic expansion, several groups have produced Effective Field Theory (EFT) interactions, whether of finite range (chiral EFT) or zero range (pionless EFT). Pionless EFT has been quite successful in studies of cold-atomic Fermi gases. In this talk, I will present recent Quantum Monte Carlo calculations of 8-particle systems and discuss their impact on 8Be and the physics of alpha clustering. I will also discuss recent work on trying to connect ab initio theory with simpler qualitative pictures. Specifically, I will address the first ever systematic non-perturbative calculations of the single-particle excitation spectrum and of the static response (both for strongly interacting neutron matter). In addition to impacting light and neutron-rich nuclei, this work and this talk also touch upon the physics of ultracold gases and of neutron stars.

From alpha clustering to homogeneous matter

Two-pulse COSY (correlation spectroscopy) EPR (Electron Paramagnetic resonance) sequence, utilized for distance measurements in biological systems using nitroxide biradicals, is investigated both analytically and numerically. The analytical expressions derived here for any orientations of the two nitroxide dipoles with respect to the dipolar axis, oriented at an angle \theta with respect to the magnetic field with respect to the dipolar axis joining the two nitroxide dipoles at the angle, \theta, show that, in general, the coherence transfer from p=0 to the single quantum p=1 state is peaked at the orientation \theta being the magic-angle, {54.7}^\circle, and its supplementary angle, {125.3}^\circle, with a narrow width, implying that there is produced orientational selectivity, by the first \pi/2 pulse. This results in the signal being predominantly determined by those biradicals, whose dipolar axes are at, or near, the magic and its supplementary angle. This is entirely a novel finding, not published in the literature. Furthermore, the analytical treatment shows that the Fourier transforms of the two-pulse COSY signal exhibit peaks at \pm d\times \left(3cos^2\theta-1\right); here d=\frac{2}{3}D, with D being the dipolar-coupling constant.). In addition, there occurs also structural sensitivity of the signal, i.e., its dependence on the orientations of the two nitroxide dipoles during to free evolution over the two coherence states p=+1 and -1. The powder (polycrystalline) averages over the unit sphere, accumulated over 20 sets of Monte-Carlo orientations of the two nitroxide dipole moments reveal that the Pake doublets occur at \pm d. It is concluded that the two-pulse COSY experiment is a preferred technique for distance measurements as compared to other multi-pulse (four, five, six) sequences, as well as two-pulse DQ (double quantum) and five-pulse DQM (double quantum modulation) sequences, because its Pake doublet is the most intense of all the other multi-pulse sequences.

Magic-angle orientation selectivity in two-pulse EPR COSY (correlation spectroscopy) sequence: Distance measurements in biological systems

While Big Bang cosmology successfully explains much of the history of our universe, there are certain features it does not explain, for example the spatial flatness and uniformity of our universe. One widely studied explanation for these features is cosmological inflation. I will discuss the gravitational wave spectra generated by inflaton field configurations oscillating after inflation for E-Model, T-Model, and additional inflationary models. I will show that these gravitational wave spectra provide access to some inflation models beyond the reach of any planned cosmic microwave background (CMB) experiments, such as LiteBIRD, Simons Observatory, and CMB-S4. Specifically, while these experiments will be able to resolve a tensor-to-scalar ratio ($r$) down to $10^{-3}$, I show that gravitational wave background measurements have the potential to probe certain inflation models for $r$ values down to $10^{-10}$. Importantly, all the gravitational wave spectra from E- and T-model inflation lie in the MHz-GHz frequency range, motivating development of gravitational wave detectors in this range.

Gravitational Wave Backgrounds from Low Scale Inflation

The CLS2 is a concept design of a next generation synchrotron light source to keep Canada at the forefront of scientific research that is uniquely available to researchers with access to such national infrastructure. Canada's research priorities in health and medicine, agriculture and food security, advance materials and industrial research, will all be enabled with national access to a next generation synchrotron. The CLS has provided critical research for Canada and the world, including covid-19 research that can only be performed on a synchrotron, and all OECD countries are in the process of commissioning, investing in or planning a next generation light source such as CLS2. This presentation of a new concept for a next generation synchrotron is a world leading design with the highest brightness in its class. The Conceptual Design Report currently being written is aimed at the government, industry and scientific community who will be the users of the facility and to engage them in the creation of a Technical Design Report and a project proposal to realise a future light source for Canada beyond the CLS which is approaching end-of-life.

A Next Generation Light Sournce for Canada

Radiotherapy and chemotherapy are the gold standard for treating patients with cancer in the clinic but, despite modern advances, are limited by normal tissue toxicity. The use of nanomaterials, such as gold nanoparticles (GNPs), to improve radiosensitivity and act as drug delivery systems can mitigate toxicity while increasing deposited tumor dose. To expedite a quicker clinical translation, three-dimensional (3D) tumor spheroid models that can better approximate the tumor environment compared to a two-dimensional (2D) monolayer model have been used. We tested the uptake of 15 nm GNPs and 50 nm GNPs on a monolayer and on spheroids of two cancer cell lines, CAL-27 and HeLa, to evaluate the differences between a 2D and 3D model in similar conditions. The anticancer drug docetaxel (DTX) which can act as a radiosensitizer, was also utilized, informing future potential of GNP-mediated combined therapeutics. The radiosensitization effects on monolayer vs spheroids with the different sized GNPs was also elucidated. In the 2D monolayer model, the addition of DTX induced a small, non-significant increase of uptake of GNPs of approximately 20% while in the 3D spheroid model, DTX increased uptake by between 50% and 200%, with CAL-27 having a much larger increase relative to HeLa. Further, the depth of penetration of 15 nm GNPs over 50 nm GNPs increased for both cancer spheroids. Measurement of the responses to radiation with GNPs yielded a large radiosensitization effect, with more of the cells on the periphery of the spheroid being affected. These results highlight the necessity to optimize GNP treatment conditions in a more realistic tumor-life environment. A 3D spheroid model can capture important details, such as different packing densities from different cancer cell lines and the introduction of an extracellular matrix, which are absent from a simple 2D monolayer model.

Three-dimensional tumor spheroids as a tool to optimize the nano-bio interface

Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is non-relativistic, making it unclear whether the minimum length is Lorentz invariant. We formulate a Relativistic Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum measurable length and the resolution of the composition law problem. This proved to be an important step in the formulation of Quantum Field Theory with minimum length. We derived the Lagrangians consistent with the existence of minimal length and describing the behaviour of scalar, spinor, and $U(1)$ gauge fields. We calculated the Feynman rules (propagators and vertices) associated with these Lagrangians. Furthermore, we calculated the Quantum Gravity corrected scattering cross-sections for a lepton-lepton scattering. Finally, we compared our results with current experiments, which allowed us to improve the bounds on scale at which quantum gravity phenomena will become relevant.

Quantum field theory with minimum length

Effective local therapy is needed to avoid local progression of the tumor, which may further decrease the development of systemic metastases and increase the possibility for resection. Radiation therapy (RT) is frequently used to locally treat the tumor. One of the major issues in RT for treating cancer is the close proximity of adjacent organs at risk, resulting in treatments doses being limited by significant tissue toxicities, preventing dose escalation necessary to guarantee local control. One of the currently adapted approaches to overcome this challenge is to add radiosensitizers to current RT protocol to unlock the full potential of RT. In this talk, I will focus on gold nanoparticles (GNPs), docetaxel, and cisplatin as radiosensitizers. About half of cancer patients (50%) receive radiotherapy, and all of these patients would benefit from this type of novel approaches.

Combining gold nanoparticles with other radiosensitizers for unlocking the full potential of cancer radiotherapy

Blister formation occurs when a laser pulse is focussed through a transparent substrate onto a coated polymer thin film. A pocket of expanding vapor is formed beneath the film, which pushes the film upward locally. This process has been used for Laser-Induced Forward Transfer (LIFT) of materials. Most studies of blister formation and blister-based LIFT use linear absorption of nanosecond or picosecond lasers to obtain large target areas (~100s of µm$^2$). We are the first to achieve nanoscale blisters, through nonlinear absorption of femtosecond pulses.

We spin-coated polyimide films achieving a thickness of 1.3 µm. We used a Ti:Sapphire laser producing pulses of 45-fs duration at a central wavelength of 800 nm. We mounted samples onto a 3D motion stage, and focused single pulses of various energies through the glass substrate onto the polymer-glass interface. Since polyimide is transparent to 800 nm light, we used tightly-focused (NA ≥ 0.4) femtosecond pulses to induce nonlinear absorption. We characterized samples after blister fabrication using atomic force microscopy (AFM). At intensities above 10$^{13}$ W/cm$^2$, interactions of the pulse with both the film and substrate must be considered. We model these interactions and find that the resulting blister volume is proportional to the energy deposited in the film.

The use of 0.95 NA focusing led to a minimum structure diameter of 700 nm, smaller than the wavelength of the laser pulse. In the future, we propose the use of thinner films and shorter wavelengths to reach further into the nanoscale. This technique can be used for direct micro- and nano-fabrication, and potentially to LIFT sensitive materials on the nanoscale. It is a possible alternative to lithography, laser milling, and laser-based additive machining that also leaves the surface composition unchanged, since the laser energy is deposited beneath the film.

Nanoscale polymer blister formation using single femtosecond pulses

The prototypical superfluid, Helium-4 ($^4$He), transitions to its superfluid state below ~2 K. In contrast, its isotopic counterpart Helium-3 ($^3$He) has a transition temperature of ~2 mK. This thousand-fold disparity is due to the nature of the superfluid transition; while $^4$He Bose condenses directly, the fermionic $^3$He atoms must first form composite bosons through Cooper pairing. The $p$-wave, spin-triplet pairing of the $^3$He atoms gives rise to many possible superfluid phases, though only two distinct phases are realized in the bulk.

Recent experimental and theoretical advances have suggested that a third phase emerges when superfluid $^3$He is confined to a slab --- a pair-density-wave (PDW) phase. Analogous to a supersolid, the PDW phase is characterized by the spontaneous breaking of translational symmetry that coexists with superfluid order. The precise spatial structure of this "superfluid crystal" has been the subject of ongoing debate: existing theories favor a unidirectional PDW, the stripe phase, while recent nuclear magnetic resonance (NMR) experiments seem to indicate a two-dimensional PDW with square or hexagonal symmetry. In this talk, I will outline a mechanism, based on Landau's theory of weak crystallization, which stabilizes a two-dimensional PDW with the hexagonal symmetry of a triangular lattice.

Lanczos recursion on a quantum computer for the Green's function and ground state

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