Beecroft Building, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Dr Alexander Schuckert, École Normale Superieure, Paris
Abstract
Simulating the dynamics of electrons in quantum chemistry, materials science, and nuclear physics is one of the most technologically and scientifically promising applications of fault-tolerant quantum computers.
I will present 3+1 results that bring this dream closer.
Firstly, I will introduce fermionic fault-tolerant quantum computing [1], a framework which removes the usual fermion-to-qubit encoding overhead altogether. Using native fermionic operations, we show how to realize a universal fermionic gate set, including transversal fermionic Clifford gates, which, among other things, required overcoming the apparent inability of neutral atoms to implement non-number-conserving gates.
Secondly, I will discuss recent breakthroughs in qubit-only quantum simulation of fermions [2] which yield the same asymptotic depth for simulating materials as fermionic quantum computers, at the cost of a large number of ancillas and a large constant prefactor overhead. For generic fermionic problems, we show that qubit quantum computers have a Theta(log(N)) overhead compared to fermionic ones even for all-to-all connectivity, which is exponentially better than the previously-believed O(N) bound from a naive Jordan-Wigner encoding.
Thirdly, I will present a compilation of a real-world nuclear physics [3] problem — electron scattering on oxygen nuclei— to a near-term fault-tolerant neutral-atom quantum computer. Combining advances in qLDPC architectures, arithmetic circuits, and Trotter algorithms, we show that this problem can be solved with a few thousand qubits, a scale targeted in the first-generation fault-tolerant machines being built right now.
As a bonus (if time permits), I will present a new numerical technique [4] for simulating the continuous-time dynamics of local observables under Hamiltonian and Lindbladian dynamics based on a continuous-time version of Pauli Propagation. It can extract the transport coefficient of an 82-qubit XY spin ladder within a minute on a laptop without the need for any parameter extrapolation - a task which previously took> 100 h while requiring heuristic (e.g., bond-dimension) extrapolation. I will then show results on 1D and 3D long-range interacting dipolar systems of up to 125 spins, for which no previous results were available. I hope this method will offer new possibilities for benchmarking analog simulators, defining their regime of quantum advantage, and for real-world applications such as NMR, spin transport, and spintronics.
[1] Schuckert et al., Nat. Phys (accepted); arXiv:2411.08955
[2] Constantinides et al., arXiv:2510.05099
[3] Weiss, Mark et al., in prep.
[4] Schuckert et al., in prep.