#sykmodel

Trapped-Ion Quantum Computer Simulation of the Simplified Sachdev-Ye-Kitaev Model: A Quantum Computing Breakthrough.

A trapped-ion model of Sachdev Ye Kitaev

Simulating highly interacting many-body systems is a major goal of quantum physics research, as it yields crucial data for theoretical models. Researchers at the Quantinuum quantum computing firm have successfully simulated a scaled-down version of the Sachdev-Ye-Kitaev (SYK) model using a trapped-ion quantum computer. This novel simulation enhances the understanding of chaotic quantum systems, which are notoriously intractable by conventional computer methods.

The SYK model is very relevant for two reasons: it is a model for strongly interacting fermions in condensed matter physics and it is the simplest toy model for exploring quantum gravity in the lab using the concept of holographic duality.

For this difficult task, the researchers chose to use 24 Majorana fermions in a sparsified version of the SYK model. They used the Quantinuum System Model H1, a trapped-ion quantum processor with high-fidelity quantum operations and all-to-all communication among qubits, to model the non-local SYK interactions.

To navigate the complex dynamics, the team employed a novel randomized quantum technique known as TETRIS (Time Evolution Through Random Independent Sampling). This method is particularly well-suited for simulating the SYK model, which is characterized by random couplings, due to its structure and randomized nature. Furthermore, the researchers developed and applied specialized error mitigation techniques like Large Gate Angle Extrapolation (LGAE) and echo verification, which significantly increased the results' resistance to quantum noise.

Over long periods, the simulation could calculate the Loschmidt amplitude and see the characteristic decay associated with the model dynamics. This invention demonstrates that commercial quantum technology may effectively replicate complicated interactions. The results suggest that quantum computers may soon be able to solve other previously difficult systems, including the Fermi-Hubbard model and lattice gauge theories.

An explanation of the Sachdev-Ye-Kitaev (SYK) model

The Sachdev-Ye-Kitaev (SYK) model is a fundamental theoretical concept in modern physics that spans the fields of quantum chaos, condensed matter, and quantum gravity.

Character of the System

SYK model describes a quantum system with strong correlation. In essence, it is described as a system of strongly interacting N Majorana fermions. These fermions participate in interactions between a q number of fermions in a single interaction term, known as random q-body interactions (the simplest non-trivial instance is often q=4). A Gaussian distribution is used to generate the random coefficients that make up the couplings' strength.

The strong quantum chaotic signature of the SYK model is complimented. Because of its dynamics, quantum information that was initially shared by a small number of degrees of freedom rapidly expands out into an exponentially huge number of degrees of freedom, a phenomenon known as "scrambling." At low temperatures, the model is shown to saturate a universal bound on the quantum Lyapunov exponent, which quantifies the chaotic behavior of quick scramblers like black holes.

function in the physics of condensed matter

In condensed matter physics, the SYK model is thought to be an attractive platform for studying strong electrical correlations and disorder in materials. The model exhibits clear non-Fermi liquid (NFL) behavior under the specific circumstances of high N and low temperature. Non-Fermi liquids, sometimes referred to as "strange metals," are poorly understood states with nonzero entropy density even at vanishing temperature.

Connection to Quantum Gravity and Holography

The SYK model is particularly crucial to high-energy physics since it is the most basic toy model illustrating the holographic duality. Holographic duality establishes a connection between quantum gravity in d+1 dimensions and a quantum field theory in d dimensions. Specifically, a two-dimensional gravitational holographic description in the infrared spectrum is admitted by the SYK model. This connection has led to efforts to use the SYK model as a paradigmatic example to study quantum gravity phenomena in a controlled laboratory setting.

The Challenge of Simulation

Quantinuum researchers digitally simulated a simplified Sachdev-Ye-Kitaev (SYK) model, a testbed for strongly interacting quantum matter and a toy model for quantum gravity, on a trapped-ion quantum computer, advancing chaotic many-body dynamics simulation beyond classical reach. A randomized “TETRIS” time-evolution algorithm and bespoke error-mitigation using Quantinuum’s System Model H1 hardware are used in the preprint.

The SYK model is valued in condensed-matter physics for capturing “all-to-all” fermion interactions and in high-energy theory for permitting laboratory probes of holographic duality theories. In the latest study, the scientists simulated a sparsified SYK instance with 24 interacting Majorana fermions, which are their own antiparticles, mapping them onto 13 physical qubits (called “12+1 qubits”) on the trapped-ion device.

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“We were interested in the SYK model for two reasons: it is a prototypical model of strongly interacting fermions in condensed matter physics, and it is the simplest toy model for studying quantum gravity in the lab via the holographic duality,” said Quantinuum Lead R&D Scientist Enrico Rinaldi, the paper's senior author.

What the team did The experiment uses Quantinuum's 2024 randomized algorithm TETRIS to accomplish time evolution without systematic Trotter errors for real-time quantum dynamics of a SYK Hamiltonian. The algorithm's randomized structure, H1's inherent all-to-all connectivity, and high-fidelity gates allowed the researchers to increase circuit depth while minimizing noise with natural error-mitigation “tricks.” Rinaldi says, “These algorithmic advances and System Model H1’s high-fidelity and all-to-all operations allowed us to realize the largest SYK simulations to date.”

On the analysis side, the preprint calculates the Loschmidt amplitude at long enough times to witness its decay—a characteristic of confused dynamics—demonstrating controlled access to out-of-equilibrium behavior in a strongly interacting system. For a 24-Majorana instance on a trapped-ion processor, the arXiv publication describes the randomized protocol and specific error-mitigation for TETRIS, while the Phys.org study stresses hardware-algorithm synergy

Hardware, algorithms Quantinuum's H1 technology captures and manipulates charged atomic ions as qubits, providing reconfigurable, full connectivity for models like SYK with nonlocal, all-to-all couplings. The researchers encoded (N=24) Majorana fermions utilizing a compact qubit mapping (12+1 qubits) and TETRIS-scheduled time-evolution gates. It eliminates systematic mistakes in Trotterized dynamics and pairs well with error-mitigation solutions that use the algorithm's randomization.

“Our study shows for the first time, such complicated interactions can be simulated on Quantinuum's current generation of commercial quantum devices by cleverly designing new algorithms and noise-modifying techniques,” Rinaldi added. In larger systems, “other difficult-to-simulate systems, such as the Fermi-Hubbard model, or lattice gauge theories, will be soon simulated by the quantum computers on our roadmap.”

How this fits in the field SYK has long been used to examine quantum confusion, information scrambling, and gravitational dualities. Simulations on noisy intermediate-scale quantum (NISQ) hardware are difficult, but recent architecture-wide work—including superconducting-qubit studies—has increased system sizes and observables. The trapped-ion demonstration extends that trajectory by pushing a huge Majorana count and presenting confusing decay-related dynamical observables using an algorithmic framework to reduce systematic mistakes.

The authors suggest that randomized digital simulation and error-mitigation on ion-trap hardware could be applied to other nonlocal and strongly correlated models. As Quantinuum upgrades to future “Helios” platforms, Rinaldi says the team is exploring new methods to simulate SYK models that use new capabilities. Increasing circuit depth and gate fidelities while reducing complexity and gate count.

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