Quantum Computation with Fermions, Bosons, and Qubits with Eleanor Crane Episode 174 Abstract: Finding a scalable and universal framework for quantum simulation of strongly correlated fermions and bosons is important in fields ranging from material science to high-energy physics. While digital qubit-only quantum computers in principle offer such universality, the overhead encountered in mapping fermions and bosons to qubits renders this endeavour extremely challenging to implement in practice. In this talk, I will explain an approach to simulating bosonic matter, fermionic matter, and Abelian gauge fields in (2+1)D, which uses hybrid digital qubit-boson (or 'oscillator-qubit') and qubit-fermion operations, avoiding this overhead altogether. I will show how our compilation strategies for hybrid oscillator-qubit computation can be used to study dynamics as well as ground states, and develop measurement techniques of non-local observables, and mention the influence of hardware errors in circuit QED coupled to high-Q cavities. I will also show that it is possible to implement fully fault-tolerant operations using logical fermions comprised of physical fermions as can be found in neutral atoms. Illustrating the advantage of our hybrid qubit-oscillator approach over all-qubit hardware, the end-to-end comparison of the gate complexity for the Z2 gauge-invariant bosonic hopping term finds an improvement of the asymptotic scaling from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework, as well as a constant factor improvement of better than $10^3$, and the $U(1)$ plaquette term benefits from an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$. Illustrating the advantage of our hybrid qubit-fermion approach over all-qubit hardware, the fermionic fast Fourier transform, a widely-used subroutine in quantum algorithms for materials, finds an improvement from $\mathcal{O}(N\log(N))$ to $\mathcal{O}(\log(N))$ in circuit depth as well as from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ in Clifford gate complexity. Our work establishes hybrid qubit-oscillator quantum simulation and qubit-fermion fault-tolerant quantum computation as viable and advantageous methods for the study of the quantum aspects of nature.

свернуть