  Recent improvements in control of quantum systems make it seem feasible to
finally build a quantum computer within a decade. While it has been shown that
such a quantum computer can in principle solve certain small electronic
structure problems and idealized model Hamiltonians, the highly relevant
problem of directly solving a complex correlated material appears to require a
prohibitive amount of resources. Here, we show that by using a hybrid
quantum-classical algorithm that incorporates the power of a small quantum
computer into a framework of classical embedding algorithms, the electronic
structure of complex correlated materials can be efficiently tackled using a
quantum computer. In our approach, the quantum computer solves a small
effective quantum impurity problem that is self-consistently determined via a
feedback loop between the quantum and classical computation. Use of a quantum
computer enables much larger and more accurate simulations than with any known
classical algorithm, and will allow many open questions in quantum materials to
be resolved once a small quantum computer with around one hundred logical
qubits becomes available.
