Abstract
One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions.
Highlights
One of the key applications of quantum information is simulating nature
The universal quantum simulation of fermionic systems is daunting due to their particle statistics[2], and Feynman left as an open question whether it could be done, because of the need for physically implementing non-local control
The digital approach is in its infancy—so far, the only experiment is the simulation of a spin Hamiltonian in ion traps7—because it requires complex sequences of logic gates, especially for non-local control, which hinge on carefully constructed interactions between subsets of qubits in a larger system; a demanding task for any platform
Summary
One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. Focusing on the Hubbard model[8,9], we perform time evolutions with constant interactions as well as a dynamic phase transition with up to four fermionic modes encoded in four qubits, using the Jordan–Wigner transformation[10]. The implemented digital approach is universal and allows for the efficient simulation of fermions.
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