Glassy dynamics with softened kinetic constraints on a noisy quantum computer

AI summary

Overview

Research area: Quantum simulation of non-equilibrium many-body physics — specifically glassy dynamics and kinetically constrained models — using mid-circuit measurements on superconducting quantum hardware.

Technical level: Advanced. The paper assumes familiarity with quantum trajectories, Kraus operators, kinetically constrained models (the East model), and dynamical free energies.

Scope: A single experimental-theoretical study realizing the Floquet-East model on the ibm_kingston superconducting processor and extracting glassy, dynamical-heterogeneity signatures from roughly 10^5 measurement trajectories.

What This Paper Is About

Glassy systems are notoriously hard to characterize because their slow, heterogeneous relaxation is invisible in ensemble-averaged quantities — the stationary state can look completely featureless while individual stochastic realizations relax at wildly different rates. The authors ask whether a present-day noisy quantum processor can be used to directly observe this trajectory-level structure, by implementing the Floquet-East kinetically constrained model and reading out its dynamics through repeated mid-circuit ancilla measurements. The goal is to show that hardware noise, rather than being purely an obstacle, can be reinterpreted as a controllable "softening" of the kinetic constraint and that glassy signatures survive in the resulting measurement records.

Key Contributions

1. Hardware realization of the Floquet-East model with monitoring. The authors embed a 1D chain of L = 48 system qubits with periodic boundary conditions plus L/2 = 24 ancilla qubits (72 qubits total) onto the heavy-hex topology of the ibm_kingston processor, using controlled-rotation gates CRX(2ω) for the facilitated dynamics and system–ancilla couplings of strength γ for generalized measurements.

2. Trajectory-level characterization of dynamical heterogeneity. They define inactive space-time clusters — rectangular ℓ × τ regions containing exclusively '0' measurement outcomes — and measure their probability p_{ℓ×τ}, converting it into a dynamical free energy F_{ℓ×τ} = −log p_{ℓ×τ}.

3. Observation of an area-to-perimeter crossover. By fitting Δ_τ F_{ℓ×τ} = α_τ ℓ + β_τ over ℓ ∈ {2, …, 5}, they extract area-related (α_τ) and perimeter-related (β_τ) surface-tension metrics and find that β_τ eventually exceeds α_τ, the signature of proximity to a dynamical first-order phase transition in trajectory space.

4. Noise as softened kinetic constraints. They show that the dominant hardware error channel — independent bit flips with effective probability p_flip ≈ 0.05 — reproduces the observed cluster statistics when fed into tensor-network calculations of the softened-constraint model, establishing the device as an effective simulator of constraint-violating dynamics.

Main Findings

• Dynamical heterogeneity is visible per trajectory but not on average. At the classical deterministic point (ω = π/2, γ = π/2), single trajectories from ibm_kingston retain the correlated triangular void structure of the ideal East model, but the average ancilla excitation number ⟨k_i(t)⟩ over 10 000 trajectories rapidly washes out to a uniform value carrying no information about collective behavior.

• Noise produces individual defects. The hardware measurement record at the deterministic point shows isolated defects not present in the classical simulation, and the device dynamics is no longer deterministic — consistent with an effective bit-flip probability of p_flip ≈ 0.05 extracted from ancilla fidelity decay, with a comparison curve at p_flip = 0.1 also shown.

• Area-dominated scaling at small τ. For clusters with small temporal extent, the dynamical free energy grows with a slope proportional to the spatial extension ℓ, meaning the probability is suppressed exponentially with cluster area — the entropic cost of forming an ordered region out of random fluctuations.

• Perimeter-dominated scaling at large τ. As τ increases, F_{ℓ×τ} grows more slowly and its dependence on ℓ weakens, so suppression becomes perimeter-law rather than area-law. This crossover occurs at τ = 2 for the classical deterministic point (where it is instantaneous and analytically derivable) and is more gradual for the monitored quantum dynamics at ω = π/4 and γ = 1.0.

• Both scalings coexist, indicating near-coexistence rather than exact coexistence. The area contribution α_τ remains non-zero, which the authors interpret as the system sitting near, but not exactly at, the dynamical phase-coexistence point — an expected consequence of the softened constraint.

• Tensor-network calculations corroborate the interpretation. Simulations with p_flip = 0.05 match the measured dynamical free energy, supporting the claim that independent bit flips capture the dominant effect of noise on these trajectory-level observables.

• Data scale. On the order of 10^5 quantum trajectories were collected in less than 10 minutes of device runtime; the dynamical free-energy analysis in Fig. 3 uses 200 000 trajectories per parameter set, and Fig. 2 uses 10 000 shots.

Methodology in Plain English

The team built a repeating quantum circuit that mimics a classical "kinetically constrained" model of glassy matter: a qubit can only flip its neighbor if it is itself excited, so activity propagates in a directional, facilitated way and dead regions persist. Each discrete time step applies these constrained gates in a brickwork pattern, then couples every second system qubit to a dedicated ancilla qubit through a tunable interaction of strength γ. Measuring the ancillas constitutes a generalized (weak-to-projective) measurement of the system's excitation number, and the sequence of binary outcomes over space and time forms a quantum trajectory. The circuit needs no mid-circuit reset: because the system–ancilla interaction only flips the ancilla when the system is excited, a change in ancilla state is labeled '1' and no change '0', so a single compiled circuit can be run repeatedly.

Two parameter settings are studied: ω = π/2, γ = π/2, which is the classical deterministic East model and permits direct comparison with exact classical simulation, and ω = π/4, γ = 1.0, which is genuinely quantum (non-projective measurement, coherent superpositions) and markedly stochastic. Trajectories are converted into a 1+1D binary spin configuration, and the statistics of all-'0' rectangles are measured as a multi-point correlation function. The resulting free energy is then fitted as a linear function of ℓ at each τ to separate area and perimeter contributions, and compared against tensor-network calculations (ITensor) for perfect (p_flip = 0) and softened (p_flip = 0.05) constraints.

Why This Matters

Impact on research: The work shows that noisy intermediate-scale quantum hardware can serve as a scalable testbed for correlated many-body phenomena that are inaccessible to exact classical treatment, and that noise need not be eliminated to obtain physically meaningful collective behavior — it can be absorbed into the model as a physically motivated softening of constraints. It also demonstrates that trajectory-resolved observables reveal structure that ensemble averages destroy, reinforcing mid-circuit measurement as a primary tool for non-equilibrium quantum matter.

Real-world applications (as motivated by the paper's framing):

• Characterizing and benchmarking glassy and constrained dynamics in materials where relaxation is spatially heterogeneous.
• Validating approximate classical simulation methods (tensor networks) against hardware data in regimes where truncation is questionable.
• Providing large, structured datasets of measurement trajectories for data-driven and machine-learning analysis of many-body dynamics.
• Informing quantum error-correction efforts, since mid-circuit measurement combined with feedback is central to those protocols.

Industry relevance: The experiments ran on ibm_kingston, one of IBM's publicly accessible Heron r2 superconducting transmon devices with 156 qubits in heavy-hex connectivity, under the open plan agreement and within the 10 free runtime minutes — a direct demonstration of what commercially available cloud quantum hardware can deliver for many-body physics today.

Future Directions

• Data-driven analysis of trajectories. The authors suggest machine-learning methods (citing Refs. [8, 30]) as a complement to handcrafted observables such as inactive-cluster probabilities, potentially revealing features not anticipated by analytic reasoning.
• Quantifying and controlling the softening. Since the effective p_flip ≈ 0.05 moves the system away from exact dynamical phase coexistence, a natural next step is tuning noise or adding engineered bit-flip channels to map out the trajectory-space phase diagram systematically.
• Scaling to larger systems and longer times. The study uses L = 48 system qubits and 40 time steps (circuit depths of approximately 360 and 1040); whether the crossover sharpens into a genuine transition at larger L and τ remains open.
• Beyond the East model. The approach — monitored kinetically constrained circuits plus trajectory statistics — generalizes to other constrained or fragmented quantum models whose glassy signatures are only visible at the single-realization level.

Target Audience

Quantum-simulation researchers and condensed-matter/statistical-mechanics theorists interested in glassy dynamics, kinetically constrained models, and dynamical phase transitions; experimentalists working on mid-circuit measurement protocols and trajectory-resolved observables on superconducting hardware; and quantum-computing practitioners evaluating how far noisy devices can be pushed for many-body physics before fault tolerance. Readers without grounding in quantum trajectories, Kraus operators, and large-deviation/dynamical free-energy formalism will find the paper demanding despite its accessible motivation.

Authors’ abstract

Mid-circuit measurements provide direct access to trajectory-level observables, revealing dynamical structures in many-body systems that are invisible in ensemble-averaged quantities. We exploit this capability to realize and study an instance of the Floquet-East model on a superconducting quantum processor. Here, the combination of mid-circuit measurements, kinetically constrained unitary operations and hardware noise gives rise to intricate many-body phenomena. Analyzing trajectories obtained from temporally and spatially resolved mid-circuit measurements, we identify dynamical heterogeneity --- a hallmark of glassy dynamics. We quantify this emergent behavior by studying the probability of finding inactive space-time regions of a given size. This quantity displays a crossover from area- to perimeter-dominated scaling, which is a characteristic property of glasses and is associated with the proximity to a dynamical first-order phase transition. Our results establish current noisy intermediate-scale quantum devices as scalable testbeds for investigating correlated many-body phenomena at the level of measurement trajectories.