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Better catalysts could change the cost of clean fuels, fertiliser, carbon utilisation, and industrial heat. Their active sites bind intermediates, move charge, and break or form bonds while coupled to a much larger chemical environment.
The capstone starts after a classical workflow has selected and embedded that active site. It runs one two-qubit variational solve for a precomputed effective Hamiltonian.
Catalysts, superconductors, battery materials, magnetic compounds, and transition-metal oxides derive useful behaviour from electrons acting collectively. Strong correlation can make a compact Hamiltonian into a difficult many-body calculation.
Unit 7 separates two jobs. It solves a two-site Hubbard model by exact classical diagonalisation, then feeds one known energy into a compiled three-bit quantum phase-estimation circuit.
A supply chain is a web of discrete choices: assign people to shifts, route trucks through depots, place inventory, and match jobs to machines. Difficulty accumulates when coverage, capacity, timing, preferences, and cost must hold together.
The companion notebook reduces that modelling problem to two nurses, two shifts, and two bits. One rule is hard, one preference is soft, and all four assignments can be checked by hand.
Finance often asks for an average over possible futures. Classical Monte Carlo is the workhorse for that job, but its error falls only as \(1/\sqrt{N}\). One more decimal digit of accuracy therefore needs roughly 100 times as many samples.
Unit 5 keeps the option price classical. Its quantum circuit reads a compiled phase for the fraction of eight uniformly weighted price bins above the strike, exposing the amplitude-estimation mechanism after state preparation and oracle construction have been supplied.
The two-qubit quantum kernel in the companion notebook does not beat its classical radial basis function baseline on the half-moons data. That result is useful: a feature space does not become valuable merely by being quantum.
The Netflix Prize remains a good parable. Recommendation quality depended on finding representations that exposed useful structure in sparse, noisy data, then comparing them against strong baselines.
To Prof Robert Ditchfield, who taught us Quantum Chemistry (Chem 81) in the fall of 1991, and ignited a spark that still burns today! Thank you for being one of my most memorable teachers at Dartmouth!
Published estimates of developing a new medicine span hundreds of millions to several billion US dollars once failed programmes and financing costs are included.1 That bill is not a quantum-chemistry budget; clinical trials, manufacturing, regulation, and failure account for much of it. Early decisions nevertheless depend on questions about molecular energies, bonding, and reaction pathways.
To expose the quantum workflow, Unit 3 uses the smallest chemistry example that carries the full loop: a reduced two-qubit Hamiltonian for \(\mathrm{H}_2\) at one bond length.
For Simon Middlemiss, in memory of that glorious talk we did together in Las Vegas in 2019! Truly one of the very best!
The Rivest-Shamir-Adleman (RSA) cryptosystem publishes a number \(N = pq\) while keeping its prime factors \(p\) and \(q\) secret. Multiplying the primes is routine; no efficient classical algorithm is known for recovering them from a suitably large product.
Shor's algorithm changes that security assumption by reducing factoring to period-finding. The notebook uses \(N = 15\) and \(a = 7\), with one known phase branch compiled into a small circuit. It demonstrates the phase readout and classical post-processing while leaving scalable modular exponentiation outside the circuit.
Dedicated to my friend, mentor and a boss who stood up for me when no one else would, Dave Fellows. You encouraged me when I told you I was writing a book on quantum computing, and this is a step in that direction.
UPS reports that removing one mile from each driver's daily route can save up to $50 million a year.1 At fleet scale, a route planner can create real value without proving it has found the perfect route; a repeatable improvement is enough.
Even a route with only 20 stops admits
possible orderings, before time windows, vehicle capacity, driver hours, or traffic enter the model.
The notebook reduces the optimisation machinery to MaxCut on a triangle: three nodes, three edges, and eight colourings. We can enumerate every candidate, inspect every gate, and compare the circuit's samples with uniform random choice.
i MakesThe classical eigensolvers of Part 3 stretch. Insert a factor of \(i\) into the exponent and stretching becomes rotation: the eigenvalues move onto the unit circle, lengths are preserved, and a quantum computer can run the evolution natively. That single letter is the entire difference.
Every eigensolver is a way of applying a function of the operator and letting the spectrum sort itself out. This post surveys the classical half: the methods that stretch.