⚛️ quantum physics

Quantum computer-based simulation of Stark many-body localization in a 1D Fermi-Hubbard model

This paper demonstrates a quantum computer-based simulation of Stark many-body localization in a 12-qubit 1D Fermi-Hubbard model on IBM hardware, utilizing advanced compilation and optimization techniques to significantly reduce circuit complexity and successfully observe the crossover from thermalizing to localized dynamics.

Original authors: Abdul Kalam, Prasenjit Deb, Akitada Sakurai, Tapan Mishra, V. S. Prasannaa, B. P. Das

Published 2026-08-04

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CC BY 4.0

Original authors: Abdul Kalam, Prasenjit Deb, Akitada Sakurai, Tapan Mishra, V. S. Prasannaa, B. P. Das

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, chaotic dance floor. Usually, when you drop a few dancers onto this floor, they bump into each other, swap partners, and eventually mix so thoroughly that you can't tell where anyone started. In physics, this chaotic mixing is called "thermalization," and it's how most things in nature reach a state of equilibrium, like a hot cup of coffee cooling down to room temperature. But what if the dance floor had invisible walls or a strange, tilted slope that forced the dancers to stay in their own little corners, refusing to mix? This is the mystery of "Many-Body Localization" (MBL). It's a phenomenon where a quantum system forgets how to thermalize, keeping a long-term memory of its starting position. While scientists have long known that random messiness (disorder) can cause this, a newer idea suggests that even a perfectly smooth, straight slope (a uniform electric field) could trap particles just as effectively. This is called "Stark MBL." Understanding this is a big deal because it challenges our basic rules of how energy and information move, and it might be the key to building better quantum computers that don't lose their data.

In this paper, a team of researchers decided to test this "Stark MBL" idea using a real, physical quantum computer, rather than just a simulation on a regular laptop. They set up a model called the "Fermi-Hubbard model," which is like a digital playground for electrons hopping between lattice sites, but they added a strong, uniform electric field to tilt the whole playground. The goal was to see if the particles would get stuck in place (localized) or if they would eventually run wild and mix (thermalize). The challenge was that current quantum computers are a bit "noisy"—like trying to solve a complex puzzle while someone is shaking the table. To get a clear answer, the team had to be incredibly clever with their code. They used a special mapping technique to translate the electron problem into qubits (the bits of a quantum computer) and then applied a "circuit compression" routine. Think of this as taking a massive, tangled ball of yarn and shrinking it down into a neat, tiny knot without losing the pattern. This optimization was a huge success, cutting the number of complex two-qubit operations by about 88% and the depth of the circuit by 87%, making the experiment possible on today's imperfect hardware.

The results were a clear victory for the "tilted slope" theory. When the researchers applied a weak electric field, the particles behaved normally: they hopped around, mixed up, and the system lost its memory of where it started, just like a normal dance floor. However, when they cranked up the electric field strength to a high level (specifically a tilt strength of 15), the behavior changed dramatically. The particles stopped moving. They stayed exactly where they were placed, refusing to hop to neighboring spots. The system retained a strong "memory" of its initial state, and the entanglement between particles grew very slowly, which is the hallmark of localization. The team verified these findings by comparing their noisy quantum computer results with perfect, noiseless simulations and exact mathematical calculations, and they matched up remarkably well. They observed this "freezing" effect using several different measurements, such as tracking how many particles stayed on one side of the chain and measuring the "charge imbalance" (how unevenly the particles were distributed).

The paper explicitly rules out the idea that this localization is caused by random disorder or messiness in the system; instead, it confirms that a deterministic, uniform electric field is enough to trap the particles. The authors are confident in these findings because their hardware results closely mirrored the exact simulations, even though they had to fight against the noise of the quantum processor. They didn't just suggest this happens; they measured it in real-time dynamics on a 12-qubit system. The study shows that with the right optimization tricks, current quantum computers can successfully simulate complex, non-thermalizing quantum states. This proves that we can use these noisy machines to explore deep physics questions, like how particles get stuck in a perfectly ordered world, paving the way for future experiments that might one day help us build more stable quantum technologies.

Technical Summary: Quantum Computer-Based Simulation of Stark Many-Body Localization

Problem Statement
Many-body localization (MBL) represents a breakdown of thermalization in isolated quantum systems, characterized by the retention of initial state memory and slow entanglement growth. While traditionally associated with quenched disorder, recent theoretical work suggests that a uniform linear electric field (Stark potential) can induce MBL in disorder-free systems, known as Stark MBL. A primary challenge in studying such phenomena is the limitation of classical computers in simulating the dynamics of interacting many-body systems, particularly as system size and evolution time increase. Furthermore, simulating MBL on current Noisy Intermediate-Scale Quantum (NISQ) devices is hindered by circuit depth and gate count constraints, which lead to rapid decoherence and error accumulation. This work addresses the feasibility of simulating Stark MBL in a 12-qubit correlated fermionic system using current IBM quantum hardware, specifically focusing on overcoming the resource constraints of noisy processors.

Methodology
The study models the system using a one-dimensional tilted Fermi-Hubbard model (t-FHM), where a linear Stark potential is applied to a standard Fermi-Hubbard lattice. The Hamiltonian includes nearest-neighbor hopping ( $J$ ), on-site Coulomb interaction ( $U$ ), and a Stark tilt term ( $\Delta_0$ ).

To simulate this on a quantum computer, the authors employed the following technical pipeline:

Mapping: A spin-resolved Jordan-Wigner transformation was used to map the fermionic Hamiltonian to qubits. Unlike conventional interleaved mappings, this approach assigns spin-up and spin-down fermions to separate parity chains (even and odd qubits, respectively). This reduces the length of Pauli strings associated with hopping operators.
Circuit Construction: The time evolution was approximated using a first-order Trotter-Suzuki decomposition. The circuit was organized into three blocks: Stark potential, on-site interaction, and hopping. To handle the non-local hopping terms arising from the spin-resolved mapping on hardware with nearest-neighbor connectivity, a SWAP-network architecture was implemented.
Optimization: A multi-stage optimization workflow was applied to reduce circuit depth and gate counts:
- Tensor-Network Compression: The AQC-Tensor routine was used to compress the Trotterized circuit by optimizing a parameterized ansatz to maximize fidelity with the target state.
- Transpilation: The compressed circuits underwent a standard optimization pipeline involving Qiskit Level-3, pytket passes, and a final Qiskit Level-3 optimization.
- Error Suppression: Dynamical decoupling (DD) and Pauli twirling (PT) were applied to mitigate decoherence and coherent errors.
Hardware Execution: Experiments were conducted on the IBM_Marrakesh processor (Heron r2 architecture) using 12 qubits. The system was initialized in two product states: Charge-Density-Wave (CDW) and Domain-Wall (DW).

Key Contributions

Resource Efficiency: The integration of tensor-network-based compression with standard transpilation resulted in a significant reduction in resource requirements. The authors report an approximate 88% reduction in two-qubit gate count and an 87% reduction in circuit depth compared to unoptimized Trotter circuits.
Demonstration of Stark MBL: The study successfully demonstrated the crossover from thermalizing dynamics (at weak tilts, $\Delta_0 = 1, 3$ ) to strongly localized behavior (at strong tilts, $\Delta_0 = 15$ ) on actual quantum hardware.
Benchmarking: The hardware results were rigorously benchmarked against exact diagonalization and noiseless simulations, showing good qualitative and quantitative agreement for the observables measured.

Results
The dynamics were characterized using several observables:

Charge Imbalance ( $I_c$ ): For weak and intermediate tilts, the imbalance decayed rapidly, indicating thermalization. For the strong tilt ( $\Delta_0 = 15$ ), the imbalance remained high, preserving the memory of the initial CDW state.
Quantum Fisher Information (QFI) and Participation Entropy ( $S^P_2$ ): In the localized regime, the growth of QFI and participation entropy was strongly suppressed, indicating limited spreading of correlations and wavefunction confinement in Hilbert space.
Entanglement Entropy: Subsystem entanglement entropy remained low and showed weak dependence on subsystem size for strong tilts, consistent with area-law scaling typical of MBL.
Density Evolution: Site-resolved density measurements showed that particles remained confined to their initial positions under strong tilts, whereas they spread across the lattice for weaker fields.
Particle Transport: For the DW initial state, the number of particles in the initially occupied half ( $N_{half}$ ) remained constant for strong tilts, confirming the suppression of transport.

Significance and Claims
The paper claims that present-day quantum hardware, when coupled with resource-efficient compilation and optimization strategies, is capable of studying dynamical phenomena like MBL in correlated quantum many-body systems. The authors emphasize that the disorder-free nature of Stark MBL is particularly advantageous for quantum simulation, as it eliminates the need for averaging over multiple disorder realizations, thereby reducing experimental overhead. The work serves as a benchmark for the utility of NISQ devices in exploring non-ergodic quantum dynamics, demonstrating that despite hardware noise, the essential signatures of Stark localization can be captured through optimized circuit implementations and error suppression techniques. The study does not claim to solve the full phase diagram of the model but focuses on demonstrating the suppression of transport and memory retention in the strongly tilted regime for a fixed interacting system.

Technical Summary: Quantum Computer-Based Simulation of Stark Many-Body Localization

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