Simulating Quantum Circuits with Hard-Core Bosons

Kurzfassung

Simulating quantum systems without the exponential overhead characteristic of classical simulations is a challenging task. Complex Clifford algebras can unify all components of a quantum circuit, with only elements of the algebra together with the geometric product. However, due to its non-Abelian nature, the geometric product realizes the tensor product by constantly correcting the sign of the expressions. In this work, hard-core bosons are shown as the most natural way to fully represent multiqubit systems and the tensor product is naturally realized without the need of any sign correction. It is proved that the two approaches are strictly equivalent up to a Jordan-Wigner transformation. Multiqubit gates in terms of annihilation and creation operators are described. Finally, a method to simulate a quantum circuit is developed.