Physicists simulate magnetic monopoles on a quantum spin chain

Quantum computers have advanced to the stage that interesting many-body quantum phenomena can be observed. A striking example is the magnetic monopole paradox, a problem that was only solved recently using the language of generalized symmetries.

Here the researchers demonstrate a quantum spin chain analogue of magnetic monopole scattering on Quantinuum System Model H2. The work efficiently converts localized particles into non-local string-like excitations by implementing a novel protocol and using a “duality defect.” This particle-to-string conversion was demonstrated across both the transverse-field Ising model and a symmetry-protected topological (SPT) phase of the cluster model, establishing duality defects and generalized symmetries as practical resources for probing quantum phenomena.

Quantum Spin Chains Simulate Magnetic Monopole Scattering

Understanding quantum many-body systems is a central goal of physics, but strong correlations often place them beyond the reach of mean-field theory or perturbative methods. Scattering offers a direct way to learn about them: prepare a low-energy excitation above the ground state, let it scatter, and examine what comes out. The outgoing state reveals both the excitations the system supports and how they interact. Recognizing the outgoing excitation, however, can be surprisingly subtle.

At certain interfaces between regions of a system, an excitation created by a local operator may pass through without reflection, yet emerge as the endpoint of a nonlocal string. The excitation keeps moving, but following it requires knowing what to measure. Without the right observables, a particle that continues to propagate can appear to “disappear.” An apparent disappearance can also arise when the outgoing state falls outside the scattering channels being considered.

In familiar scattering problems, the missing probability can often be recovered by including ordinary multiparticle states. A more puzzling disappearance arose in the work of Callan and Rubakov on chiral fermions scattering from magnetic monopoles. The conventional fermionic description appeared to offer no outgoing state consistent with the conserved quantum numbers. In this sense, an incoming fermion seemed unable to scatter back from the monopole.

Of course, it is not that quantum mechanics has failed. The difficulty lies in identifying the outgoing state, a problem that became known as the “monopole paradox.” Recent work has proposed a resolution in terms of twisted sectors. In the effective one-dimensional description of radial scattering, the monopole acts as a boundary whose degrees of freedom participate in the scattering. The outgoing excitation belongs to a twisted sector and is attached to the monopole by a topological defect line.

A unitary description therefore includes both the monopole degrees of freedom and the relevant twisted sectors. This structure has a direct lattice analogue in spin chains with topological duality defects. Such a defect joins two dual descriptions of a system, relating their excitation spectra and dynamics. The work demonstrates a novel method for converting localized quantum particles into non-local, string-like excitations, mirroring the behavior predicted when solving the long-standing magnetic monopole paradox.

This conversion relies on a “duality defect,” an interface that joins two distinct descriptions of a quantum system and alters the representation of excitations as they pass through it. The magnetic monopole paradox, stemming from the apparent disappearance of scattered particles, was recently resolved through the application of generalized symmetries, and this new simulation offers a practical demonstration of the underlying principles.

Unlike conventional scattering scenarios where missing probability is accounted for by additional particles, the monopole paradox suggested an outgoing excitation existed in an effectively non-locally connected to the monopole itself. Researchers replicated this behavior by creating a localized quasiparticle wavepacket and evolving it across the engineered duality defect, effectively transforming a localized particle into a non-local string extending from the interface. This process mirrors the theoretical resolution, where the defect acts as a boundary between topological sectors, analogous to the monopole’s role in the original problem.

The researchers implemented a matrix-product operator to represent the intertwiner between the dual models, allowing for the creation of the duality defect and the subsequent transmission of the wavepacket. This capability extends beyond the specific simulation of monopole scattering, potentially opening avenues for exploring other complex quantum phenomena and materials with exotic properties. This process realizes, in a controllable quantum many-body system, the mechanism proposed to resolve the monopole-scattering paradox, confirming that the apparent absence of an outgoing particle can be understood by recognizing its non-local connection to the defect.

Localized Wavepacket Preparation Identifies Momentum Sectors

Preparing localized quasiparticle wavepackets with controlled momentum proved essential for observing the conversion of particles into non-local string-like excitations, a process facilitated by a novel ancilla-assisted protocol implemented on Quantinuum’s H2 quantum computer. This protocol identifies each wavepacket’s momentum sector through measurement of ancilla outcomes, retaining all valid results without the need for feed-forward correction. By classifying outcomes after the computation, the researchers circumvented the need to discard valid data, maximizing the information gained from each quantum circuit execution.

The team achieved momentum-resolved wavepacket preparation by applying a post-classification technique, creating a superposition of excitations and then conditioning the system based on ancilla measurements. Specifically, they prepared a state represented as 1/($\sqrt{M})su{m}_{}$ = + k)⟩S, where M represents the number of momentum sectors. Measuring the ancilla register as k then conditions the system to apply ${\Psi }^{}$†(k + k_0), effectively assigning each computational path to a specific momentum sector.

Figures detailing the hardware data for both the Ising and cluster models presented the wavepacket’s behavior, with the cluster model demonstrating a transition from a visible wavepacket before the defect to a string excitation beyond it.

Duality Defects Link Local and Nonlocal Excitations

This process, analogous to simulating magnetic monopole scattering, hinges on the creation of a localized quasiparticle wavepacket, then evolving it through the duality defect itself. This behavior mirrors the complex interactions predicted when studying magnetic monopoles, a problem recently resolved using the language of generalized symmetries.

The experimental implementation involved a four-step process: preparing an approximation of the many-body ground state, exciting a local wavepacket, evolving it through the duality defects and finally, measuring the resulting excitation using appropriate local or non-local observables. In the Ising model, a wavepacket created from local spin excitations propagates through a Kramer-Wannier defect, transforming into a domain wall within the dual region.

This domain wall remains detectable through the local Ising order parameter, allowing researchers to directly follow the particle-to-string-to-particle sequence across both defects. “No separate reflected branch is resolved at the interface, and the continuation of the trajectory is consistent with the transmission expected for the ideal duality defect,” the researchers report in their work. The cluster model provides a complementary view of this conversion. After entering the SPT phase, the propagating excitation becomes undetectable using the original local spin observable, yet its trajectory remains visible through nonlocal string-order measurements.

This demonstrates that the duality defect functions not only as an object of study but also as a tool for actively preparing these elusive nonlocal excitations. The ability to switch between local and nonlocal descriptions of the excitation within the Ising model further highlights the power of duality defects in manipulating quantum states.

The researchers reconstructed momentum-resolved space-time trajectories in both lattice constructions, combining their preparation protocol with local and string observables. This allowed for detailed analysis of the excitation’s behavior as it traversed the duality defect, confirming the predicted transmission properties and the absence of unwanted reflections.

Transverse-Field Ising and Cluster Models Demonstrate Conversion

This conversion occurs at a “duality defect,” a carefully engineered point where the system’s fundamental properties change, allowing for manipulation of the excitation’s character. Detailed analysis involved reconstructing the excitation’s path through space and time using complementary lattice constructions, allowing for precise observation of the conversion process. In the Ising model, the initial localized excitation transforms into a domain wall upon encountering the first duality defect, a change in quantum state that is then reversed at a second defect, effectively creating a particle-to-string-to-particle sequence.

The researchers combined these observations with measurements of local and string-order parameters to fully characterize the excitation’s behavior. The cluster model offers a different perspective on this conversion, revealing a more subtle shift in detectability. The team’s approach relies on carefully preparing a localized quasiparticle wavepacket on top of the system’s ground state.

This initial state is then evolved through the duality defect, triggering the conversion to a non-local string-like excitation. The cluster model’s construction, involving interleaved open-boundary transverse-field Ising chains transformed by three dualities, highlights the complexity that can be achieved while still maintaining control over the excitation’s behavior.

Quantinuum System H2 Probes Generalized Symmetries

Researchers implemented a new protocol for creating a localized quasiparticle wavepacket, a key step in observing this complex phenomenon. This versatility highlights the robustness of the technique and its potential for broader application. This observation highlights the duality defect’s dual role as both an object of study and a tool for preparing non-local excitations.

The researchers employed a post-classification technique, retaining every valid computational “shot” by preparing a state that allowed for momentum-resolved wavepackets without discarding data or requiring feed-forward control. This approach involved preparing ancilla qubits and then conditioning the system on their measured outcomes, effectively labeling each shot with a specific momentum sector.

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