  Simulation of materials is one of the most promising applications of quantum
computers. On near-term hardware the crucial constraint on these simulations is
circuit depth. Many quantum simulation algorithms rely on a layer of unitary
evolutions generated by each term in a Hamiltonian. This appears in
time-dynamics as a single Trotter step, and in variational quantum eigensolvers
under the Hamiltonian variational ansatz as a single ansatz layer. We present a
new quantum algorithm design for materials modelling where the depth of a layer
is independent of the system size. This design takes advantage of the locality
of materials in the Wannier basis and employs a tailored fermionic encoding
that preserves locality. We analyse the circuit costs of this approach and
present a compiler that transforms density functional theory data into quantum
circuit instructions -- connecting the physics of the material to the
simulation circuit. The compiler automatically optimises circuits at multiple
levels, from the base gate level to optimisations derived from the physics of
the specific target material. We present numerical results for materials
spanning a wide structural and technological range. Our results demonstrate a
reduction of many orders of magnitude in circuit depth over standard prior
methods that do not consider the structure of the Hamiltonian. For example our
results improve resource requirements for Strontium Vanadate (SrVO$_3$) from
864 to 180 qubits for a $3\times3\times3$ lattice, and the circuit depth of a
single Trotter or variational layer from $7.5\times 10^8$ to depth $884$.
Although this is still beyond current hardware, our results show that materials
simulation may be feasible on quantum computers without necessarily requiring
scalable, fault-tolerant quantum computers, provided quantum algorithm design
incorporates understanding of the materials and applications.
