The study of quasiparticle dynamics is central to understanding non-equilibrium phenomena in quantum many-body systems. Direct simulation of such dynamics on quantum hardware has been limited by circuit depth and noise constraints. In this work, we use a recently developed constant-depth circuit algorithm to examine the real-time evolution of site-resolved magnetization in a transverse-field Ising chain on noisy intermediate-scale quantum devices. By representing each spin as a pair of Majorana fermions, we identify two distinct dynamical regimes governed by the relative strength of spin interaction. Furthermore, we show how local impurities can serve as probes of Majorana modes, acting as dynamical barriers in the weak coupling regime. These results demonstrate that constant-depth quantum circuits provide a viable route for studying quasiparticle propagation and for probing Majorana signatures on currently available quantum processors.
The study of quasiparticle dynamics is central to understanding non-equilibrium phenomena in quantum many-body systems. Direct simulation of such dynamics on quantum hardware has been limited by circuit depth and noise constraints. In this work, we use a recently developed constant-depth circuit algorithm to examine the real-time evolution of site-resolved magnetization in a transverse-field Ising chain on noisy intermediate-scale quantum devices. By representing each spin as a pair of Majorana fermions, we identify two distinct dynamical regimes governed by the relative strength of spin interaction. Furthermore, we show how local impurities can serve as probes of Majorana modes, acting as dynamical barriers in the weak coupling regime. These results demonstrate that constant-depth quantum circuits provide a viable route for studying quasiparticle propagation and for probing Majorana signatures on currently available quantum processors.
We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the anisotropic Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap while retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the interdimer coupling to generate a finite-size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the one-dimensional transverse field Ising model through a combined perspective that includes exact diagonalisation, variational quantum eigensolver (VQE) simulations, and simulations on realistic physical quantum devices. We focus on a lattice of four spins, where we calculate the ground-state energies, magnetic order parameters and correlation functions at uniformly applied conditions, which is repeated by all systems. Precise diagonalisation provides both a benchmark, which is symmetry-conserving, and a depth-two, physics inspired variational approximation, which provides simulations accessible to hardware. The circuits that have been optimised identically are then placed on the IQM Garnet quantum processor, using a resource-efficient batched protocol. We find that the ground-state energies of shallow variational circuits are reliably captured by the circuit over the entire parameter space; the magnetic arrangement parameters and observables sensitive to correlation signal significantly more noise. The error analysis of quantitative analysis reveals a strong broadening of critical crossover on hardware, which is consistent with the noise attenuation of long-range correlations. These findings highlight the current capabilities as well as the fundamental limitations of noisy intermediate-scale quantum systems in modelling quantum critical phenomena as a benchmark to future enhancements in obtaining quantum hardware and quantum algorithms development.
Control of topological edge modes is desirable for encoding quantum information resiliently against external noise. Their implementation on quantum hardware, however, remains a long-standing problem due to current limitations of circuit depth and noise, which grows with the number of time steps. By utilizing recently developed constant-depth quantum circuits in which the circuit depth is independent of time, we demonstrate successful long-time dynamics simulation of bulk and surface modes in topological insulators on noisy intermediate-scale quantum (NISQ) processors, which exhibits robust signatures of localized topological modes. We further identify a class of one-dimensional topological Hamiltonians that can be readily simulated with NISQ hardware. Our results provide a pathway towards stable long-time implementation of topological quantum spin systems on present-day quantum processors.
We study the generation and propagation of local perturbations in a quantum many-body spin system. In particular, we study the Ising model in transverse field in the presence of a local field defect at one edge. This system possesses a rich phase diagram with different regions characterized by the presence of one or two Majorana zero modes. We show that their localized character (i) enables a characterization of the Ising phase transition through a local-only measurement performed on the edge spin, and (ii) strongly affects the propagation of quasiparticles emitted after the sudden removal of the defect, so that the dynamics of the local magnetization show clear deviations from a ballistic behavior in the presence of the Majorana fermions.
Majorana fermions arise in a broad range of systems in condensed matter physics, not only as a useful abstraction but also as emergent quasiparticles, e.g., at the boundaries of topological insulators. In this dissertation, we consider two distinct settings wherein Majorana fermions play a central role: (i) non-abelian Kitaev spin liquids and (ii) entanglement dynamics in monitored quantum circuitsThe Kitaev spin liquid is a paradigmatic model featuring non-abelian anyons and a chiral Majorana edge mode when time-reversal symmetry is broken. To this end, it presents an alluring platform for realizing topologically protected quantum information. However, experimental efforts to identify this putative phase have been hampered both by the difficulty of probing the charge neutral quasiparticles and by the presence of phonons and other deviations from the idealized toy model. Here we examine how judicious device design may suppress bulk phonon contributions to thermal transport, allowing for refined observation of transport mediated by the chiral Majorana edge mode. Moreover, we show that the bulk topological order can be revealed through universal features in the tunneling conductance across a point contact. Looking forward, we develop a roadmap for near-term experimental devices to demonstrate robust control of topologically protected qubits encoded in the bulk anyons.Much as Majorana models form the building blocks for symmetry-protected topological order, Majorana circuits provide a powerful framework for studying the entanglement dynamics and phases of monitored quantum circuits. Here we show that the entanglement dynamics of Majorana circuits can be mapped exactly to the statistical mechanics of classical loop models. Harnessing this framework, we undertake a precise numerical characterization of the universality of entanglement transitions in symmetry classes BDI and D in both (1+1) and (2+1)-dimensional circuits. Furthermore, we employ duality relations for loop models to construct an analytically solvable interacting circuit which features not only the usual percolation criticality but also Berezinskii-Kosterlitz-Thouless critical lines and a tricritical point with Ising universality. Lastly, by generalizing to colored loop models for Majorana circuits with classical control, we provide a blueprint for engineering even more diverse entanglement dynamics which may include Hilbert-space fragmentation and subdiffusive transport.
Topological states of matter are promising resources for composing fault-tolerant quantum computers, advancing beyond the limitations of current noisy intermediate-scale quantum devices. To enable this progress, a deep understanding of topological phenomena within actual quantum computing platforms is essential. However, existing quantum-circuit algorithms to examine topological properties remain limited. Here we introduce three quantum-circuit algorithms designed to (i) determine the ground state within a specified parity subspace, (ii) identify the many-body topological invariant, and (iii) visualize zero-energy edge modes. We illustrate these algorithms with the interacting Kitaev chain, a typical model of one-dimensional topological superconductors. These approaches are versatile, extending beyond one-dimensional systems to various topological states, including those in higher dimensions.