[Paper Review] Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer

R. Shen, Tianqi Chen+2 more|arXiv (Cornell University)|Nov 16, 2023

Quantum, superfluid, helium dynamics4 citations

TL;DR

This study reports the first experimental observation of the non-Hermitian skin effect (NHSE) and its many-body manifestation, the Fermi skin, on a digital quantum processor using a noisy intermediate-scale quantum (NISQ) device. By implementing non-unitary time evolution via post-selection on ancilla qubits and optimizing circuits with variational quantum algorithms, the authors demonstrate asymmetric spatial localization and Fermi skin profiles in fermionic systems, marking a milestone in simulating non-Hermitian many-body physics on current quantum hardware.

ABSTRACT

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.

Motivation & Objective

• To demonstrate the non-Hermitian skin effect (NHSE) in a many-body fermionic system on a universal quantum processor.
• To observe the emergence of the Fermi skin—a real-space Fermi surface-like profile—arising from Pauli exclusion statistics under NHSE dynamics.
• To overcome the challenge of simulating non-unitary dynamics on unitary quantum hardware using scalable, error-mitigated quantum circuits.
• To validate the feasibility of simulating complex non-Hermitian many-body phenomena on current noisy quantum processors.

Proposed method

• Non-unitary time evolution is implemented via post-selection on ancilla qubits to simulate non-reciprocal, non-unitary Hamiltonians.
• A trainable variational quantum circuit is used to optimize the time-evolution gate, minimizing errors from device noise.
• The effective Hamiltonian is engineered using a digital quantum circuit with tunable non-Hermitian hoppings, modeled after the Hatano-Nelson and SSH models.
• Fermi skin profiles are extracted from short-time evolution by weighting eigenstate overlaps, enabling early observation of the Fermi-Dirac-like density distribution.
• The spatial density profile is analyzed using a Fermi skin ansatz $ n_{\text{FS}}(x) = \left(1 + e^{\beta_{\text{eff}}(x - N)}\right)^{-1} $, with $ \beta_{\text{eff}} \approx 4\kappa $ in the strong NHSE limit.
• Numerical simulations confirm that the initial state's overlap with eigenstates governs early-time dynamics, enabling observation of Fermi skin in as few as 5–10 Trotter steps.

Figure 1: The non-Hermitian skin effect (NHSE) and its many-fermion counterpart. (a) At the single-particle level, the NHSE from asymmetric lattice hoppings amplifies all states towards one direction, resulting in boundary “skin” states with exponential localization lengths inversely proportional to

Experimental results

Research questions

• RQ1 Can the non-Hermitian skin effect be realized in a many-body fermionic system on a current quantum processor?
• RQ2 Does the interplay between NHSE and Pauli exclusion lead to a measurable Fermi skin profile in real space?
• RQ3 Can non-unitary dynamics be effectively simulated on a unitary quantum computer using post-selection and variational optimization?
• RQ4 How early can the Fermi skin profile emerge in time evolution, and what initial states best facilitate its observation?
• RQ5 What is the quantitative relationship between the non-Hermitian parameter $ \kappa $ and the effective inverse temperature $ \beta_{\text{eff}} $ of the Fermi skin?

Key findings

• The non-Hermitian skin effect was successfully observed on an IBM quantum processor using post-selected non-unitary evolution, with clear asymmetric spatial localization.
• The Fermi skin profile emerged in as few as 5–10 Trotter steps, demonstrating that many-body non-Hermitian effects can be probed early in time.
• The effective inverse temperature $ \beta_{\text{eff}} $ of the Fermi skin was empirically found to scale approximately as $ \beta_{\text{eff}} \approx 4\kappa $, consistent with theoretical predictions.
• Initial states with high overlap to edge-localized eigenstates (e.g., half-localized state) showed better agreement with the Fermi-Dirac profile than those with uniform or antiferromagnetic order.
• The use of variational quantum algorithms significantly reduced noise-induced errors, enabling reliable extraction of non-unitary dynamics.
• The study establishes a scalable framework for simulating non-Hermitian many-body physics on NISQ devices, paving the way for future studies of non-unitary quantum criticality and topological phases.

Figure 2: Overview of the ancilla-based framework. (a) and (b) show the process of implementing non-unitary dynamics by our local and global ancilla-based circuits respectively. For each Trotter step, the non-unitary process $U_{\rm non-unitary}$ can be realized by coupling N physical qubits (red qu