In principle, we can use quantum mechanics to exactly describe any system of quantum particles—from simple molecules to unwieldy proteins (and beyond, see figure)—but in practice this is impossible as the number of equations grows exponentially with the number of particles. Recognising this, Richard Feynman suggested that quantum systems be used to model quantum problems . For example, the fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a molecule as well as most other properties, can be calculated by solving the Schrödinger equation. However, the computational resources required increase exponentially with the number of atoms involved [1, 2].
In the late 1990’s an efficient algorithm was proposed to enable a quantum processor to calculate molecular energies using resources that increase only polynomially in the molecular size [2–4]. Despite the many different physical architectures that have been explored experimentally since that time—including ions, atoms, superconducting circuits, and photons—this appealing algorithm was not demonstrated until last year.
I will discuss how we have taken advantage of recent advances in photonic quantum computing  to present an optical implementation of the smallest quantum chemistry problem: obtaining the energies of H 2 , the hydrogen molecule, in a minimal basis . We perform a key algorithmic step—the iterative phase estimation algorithm [7–10]—in full, achieving a high level of precision and robustness to error. I’ll also report on our recent results in simulating quantum systems in material science—phase transitions in topological insulators—and in biology—light-harvesting molecules in photosynthesis. Together this body of work represents early experimental progress towards the long term goal of exploiting quantum information to speed up calculations in biology, chemistry and physics.
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