Observation of the non-Hermitian skin effect and Fermi skin on a digital
  quantum computer
Non-Hermitian physics has attracted considerable attention in recent years,
particularly the non-Hermitian skin effect (NHSE) for its extreme sensitivity
and non-locality. While the NHSE has been physically observed in various
classical metamaterials and even ultracold atomic arrays, its highly-nontrivial
implications in many-body dynamics have never been experimentally investigated.
In this work, we report the first observation of the NHSE on a universal
quantum processor, as well as its characteristic but elusive Fermi skin from
many-fermion statistics. To implement NHSE dynamics on a quantum computer, the
effective time-evolution circuit not only needs to be non-reciprocal and
non-unitary but must also be scaled up to a sufficient number of lattice qubits
to achieve spatial non-locality. We show how such a non-unitary operation can
be systematically realized by post-selecting multiple ancilla qubits, as
demonstrated through two paradigmatic non-reciprocal models on a noisy IBM
quantum processor, with clear signatures of asymmetric spatial propagation and
many-body Fermi skin accumulation. To minimize errors from inevitable device
noise, time evolution is performed using a trainable, optimized quantum circuit
produced with variational quantum algorithms. Our study represents a critical
milestone in the quantum simulation of non-Hermitian lattice phenomena on
present-day quantum computers and can be readily generalized to more
sophisticated many-body models with the remarkable programmability of quantum
computers.
Ruizhe Shen Tianqi Chen Bo Yang Ching Hua Lee