Lady Margaret Hall, University of Oxford

Martin Kiffner - calculating intermolecular dispersion energies with quantum processors

London dispersion forces:

• fluctuating dipoles - correlated multipole moments
  • exchange of virtual photon pairs
• small correction to gross energy structure
• not pairwise additive
  • need to study the whole ensemble of the molecules to find a meaningful answer
• Although small - important for supramolecular chemistry, structural biology, nano tech etc.

How to approach this problem

• Ab-initio e.g. DFT
  • try and solve the schrodinger equation, computationally very demanding
• Empirical methods
  • cheap
  • but not very accurate
• Electric coarse graining
  • pair of 1D harmonic oscillator
    • Parameters: coupling, polarisability, separation, ground state energy
    • match model parameters to molecular species
  • Simple system, but still quantum do naturally reproduce dispersion forces

Quantum Algorithm

• Variational Quantum Eigensolver method
• For each oscillator, take into account d number of Fock states
• Need log2d qubits - each oscillator is represented by two qubits
• need to prepare each harmonic oscillator into a given quantum state
• number of unique circuits scales linearly with the number of molecules
• You have a classical algorithm on top of the quantum computer that picks a subset of parameters to feed back into the quantum computer
  • details in the paper (L. W. Anderson Phys Rev. A 105 2022)

Results

• Two iodine molecules (non-polar, strong London forces)
• reasonable fit between quantum (ibm-montreal/simulated) calc and theoretical results

Features

• number of qubits grows linearly with number of molecules
• number of uniques circuits measuring the hamiltonian of all-to-all dipolar interaction scales linearly with the number of molecules
• relatively cheap to extend quantum algorithm to an-harmonic molecule unlike classical coarse-grained counterpart

Aleks Kissinger - Picturing Quantum Software

• code that makes that code better
  • compilers
  • optimisation
  • vectorisation
• small advances in software give big gains on NISQ hardware
• quantum circuits are the assembly language of quantum computation
  • how to make quantum circuits more efficient
  • cut gates open and find things that are more fundamental inside
  • replace gates with ZX-diagram
    • made of spiders
    • two kinds
    • can make any quantum circuit from two basic spiders
    • small set of rules (8 rules) - imply hundreds of circuit identities
    • can realise in a much simpler circuit diagram
• How do we scale up?
  • GitHub.com/quantomatic/pyzx
  • python library
  • scale large circuit down to skeleton, take skeleton and expand into a simpler circuit than previously
    • have flexibility in the latter step, circuit routing
    • extract circuits based on Gaussian elimination

application

• T-count reduction, reduce the number of T-gates in a quantum circuit
  • reduce T-gates as they are much more overhead in fault-tolerant quantum computing
  • extremely important for long-term fault-tolerant QC (optimistically 20 years away)
  • matters today: simulating quantum circuits on a classical computer
    • classical simulation is hard
    • more qubits, the harder to simulate
    • the more entanglement between the qubits the harder it is to simulate
    • the more t-gates, the harder to simulated - as it is far from something that is easy to simulate
      • stabilarizer rank decomposition: simulate difficult circuits as a sum of simple circuits
      • If there aren’t too many terms you can use gauss-mania theorem
      • decomposing each T gate into 2 stabiliser terms, gives 2^t terms
    • interleave decomposition with zx-simplifications
      • 1400 t-gates, age of uni verse to simulate, can be broken down with zx-simulation to 6 minutes

Links: zxcalculus.com

Daniel Egger - quantum computing and its applications to optimisation and finance

why quantum

• still problems we can’t solve
• computation model in a nutshell
  • initial state
  • state evolves following a sequence of ops
  • measure state at end

Applications

• machine learning
  • classification task
    • fraud detection, credit risk rating, customer segmentation
  • feature map, classical support vector machine
  • can apply a quantum feature map, a feature map that can’t be calculated efficiently on classical machine
    • can leverage entanglement to find correlations between features in a quantum feature map
    • increase accuracy of classification, not necessarily faster
  • quantum neural networks
    • a bit more expressive
    • train a lot faster
    • brining quantities like entanglement trains to lower losses faster, ibm montreal backend

Combinatorial optimisation

• portfolio optimisation efficient frontier
  • max risk, minimise return
• binary decision variables
• MAXCUT
• take optimisation problem and transform to Ising Hamiltonians to GS problem
  • Hamiltonian corresponds to optimisation problem, ground state of hamiltonian is the solution
• heuristic may find better solutions faster

Transaction settlement

• clearing house that receives trades, which trades will settle, certain parties may not have the resources to settle the trades
• mixed binary optimisation problem
• enables new application such as transaction settlement

Financial simulations

• risk analysis with a quantum computer
• monte carlo simulation on Q for pricing and risk analysis
  • estimate expected value
  • value at risk
  • conditional value at risk
  • scales 2x
• Can rely on Amplitude estimation giving you a quadratic speed-up
• Option pricing
  • what system size for practical advantage, 7500 logical qubits
  • error correcting code needs to be 3 order of magnitude faster

Pauline Ollitrault - Molecular quantum dynamics: a quantum computing perspective

• born-oppenheimer approx: separation of the electronic and nuclear DOFs based on the different time-scales for their respective motion
  • solve electrons and nuclei individually
• classical approaches and limitations
  • we can do pyridine accurately, that is the current limit
• quantum algorithms for quantum dynamics simulations
  • solve electronic structure
  • solve time evolution Schrodinger equation based on previously attained electronic structure

time dependent Schrodinger

• decomposition methods
  • map to quantum circuit
  • requires no ancillary qubits
  • leads to shorter quantum circuits
• Variational methods
  • don’t encode time propagator
  • encode a trial state
    • solve the parameters’ equations of motion and adjust them (built classically and measured classically)
    • measure
    • iterate

Hendrik Hamann - Accelerated discovery for climate sustainability

• global emission rated will reach 80 Gt CO2/year by 2075
• path to 1.5degC means you have to remove CO2 from the atmosphere
• no matter what you have to deal with some level of climate change
• Geolab and MDLab are built on foundational AI capabilities

MDLab: Discovery materials for sustainability

• focus is mitigation
• finding materials for carbon removal or energy storage for example
• Accelerated discovery for materials for separation membranes for CO2 from air
  • deep search, ingest structure technical knowledge at scale from pdfs and scientific papers create knowledge graph
  • then use generative models from this knowledge, come up with new candidates
  • rely on AI models to accelerate learning. drive through monte carlo simulations
  • test models on simulated materials

Accelerated carbon accounting and measurements

• better carbon accounting (AI-enabled)
  • once you have a better assessment of your carbon footprint you can drive decisions
• Direct carbon GHG measurements
  • Satellite imagery to measure methane emission

Geolab: Geospatial data indexing for optimise performance and parallelism

• optimise data structures to optimise calculations
  • multidimensional-indicies
  • resolutions
  • space-filling curves
  • overview layers
• Geospatial temporal data access
  • help scientists access data faster
  • If you index data two order of magnitudes speed up (Geolab)
• 10,000x acceleration for feature generation and subsequent AI climate impact modelling
  • 400k timestamps for 4.5M locations —> 52 minutes, (to model high flood risk impact areas)
  • conventional system would take 14 months

Philip Stier - Climate Research at Oxford

https://www.climate.ox.ac.uk

State of research in Oxford

• over 200 researchers
• areas: biodiversity, climate, energy, future of food, water
• climate: physical climate, climate impact, climate action
• COP26 <- 80 oxford attendees

Next-gen models

• can simulate a few decades with current next-gen models
• how do you evaluate high res climate models
  • 6.6 million gis points, 2.5km 90 verticals
  • Turing test: a model is good enough when you can’t distinguish the model from the observation

Ship tracking based on aerosols

• Every cloud droplet forms on an aerosol particle, more pollution means more cloud droplets - want to find the affect of aerosols on models/climate
• Can see the tracks of ships in clouds, graduate students would find this by hand.
  • Can do this via standard computer vision ML model of hand labelled data
  • can get an output of global shipping corridors

Saiful Islam - From batteries to solar cells: Modelling insights into energy materials

• lithium battery materials
• beyond lithium ions
• perovskite solar cells

Context

• issues, is characterisation and deeper understanding
  • modelling is crucial to understand crystal structure
  • how do ions move
  • defects and disorder: “Like people, solids are imperfect - making them unique & interesting”
  • doping in the crystal lattice
  • surfaces and interfaces, grain boundaries of nano(materials)
• Lithium battery is a success story of materials science and chemistry in action.

Challenge

• the positive electrode of the battery (cathode)
• energy density of the cathode is half that of the graphite anode
• Looking at new materials such as
  • Li-rich NMC
  • DRS - disordered rock salts
  • anion redox methods: Invoking metal redox as well as an-ion redox to increase energy density

How fast can you charge

• how fast ions move across the lattice is related to charging speed
• Can we leave Cobalt behind for Iron based cathodes (Li Iron phosphate)
• Li-ions move through the structure, via a curved 1D path. predicted via modelling and shown via experiment

All solid state

• can we replace flammable liquid electrolyte with solid electrolyte
• Sodium batteries, abundant and low cost, good for storage for grid

Solar energy

• Perovskite cell predicted to overtake silicon in terms of solar cell efficiency
  • cheap to make
  • Problem: stability and ion migration
  • Mixed ionic -electronic structure, it was the iodide vacancy that moved

Volker Deringer - Machine-learning-drive advances in atomic scale materials modelling

• we want to know the energy of a system of where the atoms are - draw an energy potential surface about the structure
• we can only do this at a few points as the calculations are very demanding
• can use data based approaches, get a few points along the surface and predict the rest

How do we build these interatomic potential force field models

• reference data - need the correct data
• representations (descriptors) - the way you encode the atomistic structure
• Regression (the fit itself)
  • neural network based methods
  • kernel methods
  • linear fitting

what now - we want to see things we haven’t seen before

• can we build general purpose machine learning force fields
• 10nm long amorphous silicon
• can understand structural transitions under pressure
  • can see phase change
  • crystallinity formation and grain boundaries

Flaviu Cipcigan - Materials discovery lab for climate sustainability

• scientific tools and data for materials researcher in CCUS and energy storage
• discover optimised materials
  • generate
  • screen
  • simulate
• validate outcome for scale
  • process simulation
  • lab synthesis and screening with autonomous labs

deep search and knowledge graphs

• annotations and natural language processing tasks to mine patents papers and other data sets to create a knowledge graph of existing CCUS methods and materials
• AI for prediction of nonporous material properties
• ML classifiers enable rapid computational screen of carbon capture materials

automated laboratory for CCUS material testing

• data generation, validation and process optimisation
• rapid assay platform for thermodynamic and kinetic measurement software solvents
• automated lab for polymer synthesis found discovery of catalysts for CO2 utilisation
• pilot-scale testing of rapid thermal swing processes with solid sorbents

accelerated discovery for sustainable batteries

• rely on AI as an expert in the loop for battery optimisation. Train the AI to think like an expert based on expert knowledge, rather than having a human in the loop