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Collapse of Multipartite Entanglement: A First-Person Benchmark of GHZ State Fidelity

Mohan Raja Ram

Published Jun 8, 2026• 0 citations
Publisher

Abstract

I report a hands-on, systematic investigation of Greenberger–Horne–Zeilinger (GHZ) state generation on a 127-qubit supercon-ducting quantum processor, covering system sizes from 4 to 80 qubits. I measured both computational-basis populations andglobal Pauli-X parity oscillations to decompose the state fidelity into its population purity and phase-coherence components. Mydata reveal an exponential collapse of fidelity with qubit number: a 4-qubit GHZ state achieves a fidelity of F = 0.9307, wellabove the threshold for entanglement-based quantum key distribution, yet by 32 qubits the fidelity has plummeted to 0.0963 andthe parity signal is extinguished. At 80 qubits, the state is indistinguishable from a maximally mixed state (F = 0.0453). I isolatethe dominant noise channels—CNOT gate errors, dephasing, readout crosstalk—and map the current usability frontier for rawmultipartite entanglement. I then contrast my results with mitigation-enhanced benchmarks from other platforms, showing thatadaptive compilation and dynamical decoupling can recover fidelity above the genuine multipartite entanglement (GME) thresholdeven at 120 qubits. This work provides a deeply personal, quantitative perspective on the challenges and near-term solutions forscaling entanglement in quantum communication, sensing, and error-mitigated computation.

DOI
10.5281/zenodo.20600776

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I report a hands-on, systematic investigation of Greenberger–Horne–Zeilinger (GHZ) state generation on a 127-qubit supercon-ducting quantum processor, covering system sizes from 4 to 80 qubits. I measured both computational-basis populations andglobal Pauli-X parity oscillations to decompose the state fidelity into its population purity and phase-coherence components. Mydata reveal an exponential collapse of fidelity with qubit number: a 4-qubit GHZ state achieves a fidelity of F = 0.9307, wellabove the threshold for entanglement-based quantum key distribution, yet by 32 qubits the fidelity has plummeted to 0.0963 andthe parity signal is extinguished. At 80 qubits, the state is indistinguishable from a maximally mixed state (F = 0.0453). I isolatethe dominant noise channels—CNOT gate errors, dephasing, readout crosstalk—and map the current usability frontier for rawmultipartite entanglement. I then contrast my results with mitigation-enhanced benchmarks from other platforms, showing thatadaptive compilation and dynamical decoupling can recover fidelity above the genuine multipartite entanglement (GME) thresholdeven at 120 qubits. This work provides a deeply personal, quantitative perspective on the challenges and near-term solutions forscaling entanglement in quantum communication, sensing, and error-mitigated computation.
Abstract Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the states. A fidelity of 0.546 ± 0.017 was recorded for a 27-qubit GHZ state when QREM was used, demonstrating GME across the full device with a confidence level of 98.6%. We benchmarked the effect of parity verification on GHZ fidelity for two GHZ state preparation embeddings on the heavy-hexagon architecture. The results show that the effect of parity verification, while relatively modest, led to a detectable improvement of GHZ fidelity.
TECHNICAL REPORT: HEURISTIC DESCENDING LIMIT FOR GENUINE MULTIPARTITE ENTANGLEMENT SCALABILITY IN GHZ STATES Executive Summary The long-term viability of fault-tolerant quantum computing depends on the scalability of Genuine Multipartite Entanglement (GME), commonly evaluated through Greenberger-Horne-Zeilinger (GHZ) states. Current orthodoxy assumes that decoherence is a purely environmental issue mitigable through thermal isolation and Quantum Error Correction (QEC) schemes. In this report, we introduce a proprietary topological saturation algorithmic model that evaluates the maximum concurrent information load. By fitting this model to the most recent empirical data from superconducting processors and trapped ions, we identify a fundamental collapse asymptote. We formally predict that state fidelity (F) will inevitably cross the critical failure threshold (F < 0.5) before reaching 141 monolithically entangled qubits, marking a strict hardware limit independent of local noise mitigation architectures. 1. Introduction and Empirical Context Advancing toward "quantum advantage" requires the creation and maintenance of highly entangled states. To certify genuine multipartite entanglement in a GHZ state, the system must exceed the strict fidelity threshold of F > 0.5. Historically, scalability has shown an exponential degradation of fidelity as the number of qubits (N) increases. Recent industry reports demonstrate this extreme tension at the upper limit of current hardware: · Quantinuum (Trapped Ion Architecture): Reported stabilization of N = 56 qubits with a fidelity of F approx 0.61. · IBM Quantum (Superconducting Architecture): Achieved a milestone in GHZ state preparation with N = 120 qubits, reporting a fidelity of F approx 0.56. Despite the immense resources invested, at 120 qubits the system is on the edge of the viability limit. The industry assumes that incremental refinements will allow for linear scaling toward thousands of logical qubits. Our model demonstrates that this assumption is topologically incorrect. 2. Methodology: The Entanglement Saturation Limit Using a proprietary algorithmic model designed to map informational bandwidth constraints onto discrete multidimensional meshes, we have derived a strict scalar limit for concurrent entanglement. The model assumes that entanglement is not a "free" resource in Hilbert space; rather, it incurs an informational density cost (Shannon Tax) that saturates the system's transverse capacity. By projecting an asymptotic curve adjusted to current resource loss friction, we determined a critical overflow point defined as Qmax. Formal Prediction Milestones: · Early Warning (N = 130): We predict that the next attempts to scale to 130 qubits will show a marginal fidelity of F approx 0.51, exhibiting noise levels unmanageable by software. · Structural Collapse (Qmax = 141): The model predicts that it is physically impossible to sustain a monolithic GHZ state equal to or greater than 141 qubits. At this point, fidelity will drop below 0.5, resulting in irreversible and instantaneous system decoherence, fragmenting the entanglement into smaller clusters. 4. Conclusion and Industry Implications Traditional Quantum Error Correction (QEC) is based on the premise that local errors are independent and stochastic. If our prediction of Qmax = 141 holds in the next iterations of commercial quantum processors, it will imply that large-scale decoherence is a systemic limiting effect (a structural bottleneck), not a simple thermal engineering failure. Overcoming this "141-Qubit Wall" will require abandoning brute-force scalability methodologies and adopting routing modulation and phase cancellation architectures that address the geometric root of information saturation.
As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of 0.519 ± 0.014 is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of α = ( 7.13 N + 5.54 ) × 10 − 3 µ s − 1 for up to N = 15 qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits. Published by the American Physical Society 2024
We establish operational limits on the broadcasting of genuine multipartite entanglement (GME) in quantum networks. Using a distributed protocol in which each of N parties locally implements optimal 1 →\to→ 2 cloning via beam-splitter interactions, we derive exact expressions for the broadcast fidelity of Greenberger-Horne-Zeilinger (GHZ), W states, and Cluster states in a limited setting. We show that the fidelity decays exponentially with system size as [c(R)]N^NN, providing a quantitative expression of multipartite entanglement monogamy in the broadcasting setting, and that both state families share a universal normalisation factor arising from independent post-selection probabilities. Most significantly, we prove a no-go result for simultaneous GME certification: for all reflectivities and all system sizes, the two broadcast copies cannot be simultaneously certified as genuinely multipartite entangled within the standard framework of fidelity-based witnesses. We further check this behaviour for three- and four-party cluster states, finding consistent results that support the generality of the no-go beyond the GHZ and W families. This obstruction arises from the redistribution of multipartite coherence, which both reduces the achievable fidelity and increases the corresponding certification threshold. Our results reveal a fundamental trade-off between the broadcastability of multipartite entanglement and its operational certifiability, and delineate intrinsic limits on entanglement distribution in quantum networks.
Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.
Greenberger-Horne-Zeilinger (GHZ) states are a widely used benchmark for studying multipartite entanglement and coherence in quantum processors. In this work, GHZ states of increasing size were prepared on the 156-qubit IBM Quantum processor ibm_marrakesh and certified using a fidelity-based entanglement witness. State coherence was extracted from parity-oscillation measurements using the multiple-quantum-coherence method. The study investigates how a combination of practical error-reduction techniques affects the largest GHZ state that can be certified on open-access superconducting hardware. These techniques include depth-minimized entangling trees, calibration-aware qubit selection, dynamical decoupling with gate and measurement twirling, and matrix-free readout-error mitigation. A naive implementation fails at larger system sizes, while depth-optimized preparation certifies entanglement up to 14 qubits. Calibration-aware qubit selection extends this to 16 qubits, and readout-error mitigation enables certification of genuine multipartite entanglement up to 18 qubits with a measured fidelity exceeding the witness threshold. The results show that the achievable certification size is determined primarily by the quality of the selected qubit region rather than by the total number of qubits available on the processor. The observed non-monotonic dependence of fidelity on system size reflects variations in local device performance. These findings illustrate the impact of hardware-aware compilation and error-mitigation strategies on entanglement certification using publicly accessible quantum computing platforms.