Experimental Demonstration of the PBR Test on a Superconducting Processor

TL;DR

This work implements the Pusey-Barrett-Rudolph (PBR) no-go test on IBM's 156-qubit Heron2 superconducting processor to discriminate between $\psi$-ontic and $\psi$-epistemic$-$preparation independent$-$hidden-variable models. It generalizes the protocol to $n=2$ and $n=5$ using two non-orthogonal states with overlap $|\langle\psi_0|\psi_1\rangle|^2=\cos^2\theta$ and an entangling circuit designed so certain outcomes are forbidden for specific inputs, while incorporating noise via depolarizing channels and a thermodynamic decoherence model with $T_1$, $T_2$, and readout errors. Experimental results show a large majority of adjacent two- and five-qubit configurations yield forbidden-outcome statistics below the epistemic bound, with passing probability deteriorating as circuit depth, qubit separation, and SWAP insertions increase. This establishes the PBR test as a practical, device-level benchmark for quantumness in NISQ systems, while also highlighting the need for more detailed noise models at larger scales and engaging with theoretical critiques of the PBR assumptions.

Abstract

We present an experimental implementation of the Pusey-Barrett-Rudolph (PBR) no-go theorem on IBM's 156-qubit Heron2 Marrakesh superconducting quantum processor. By preparing qubits in a set of non-orthogonal states and evolving them under carefully compiled unitary circuits, we test whether one can interpret the hidden variable model for quantum states as merely epistemic -- reflecting ignorance about some underlying physical reality. To account for realistic hardware imperfections, we derive noise-aware error tolerance based on decoherence models calibrated to the device's performance. Our results show that a significant majority of adjacent qubit pairs and adjacent five-qubit configurations yield outcome statistics that violate the epistemic bound, thus ruling out the epistemic interpretation of quantum mechanics. Furthermore, we observe a clear trend: the probability of passing the PBR test decreases as the spatial separation within the quantum processor between qubits increases, highlighting the sensitivity of this protocol to connectivity and coherence in Noisy Intermediate-Scale Quantum (NISQ) systems. These results demonstrate the PBR test as a promising device-level benchmark for quantumness in the presence of realistic noise.

Figures (4)

• Figure 1: Illustration of three interpretations of the quantum states in the physical state (bottom) and the ontic space $\Lambda$: (Top left) Epistemic—different quantum states correspond to overlapping distributions over $\Lambda$---implying $\psi$ reflects knowledge---ruled out by the PBR theorem. (Top middle) Hidden variable—the same ontic state consisting of multiple physical states, suggesting incomplete knowledge of the quantum state, thus the need for a hidden variable model. (Top right) Ontic—distinct quantum states map to disjoint state, implying representation of physical reality.
• Figure 2: The general PBR test circuit for $n=2$. Input qubits are prepared in either $|\psi_0\rangle$ or $|\psi_1\rangle$. The entangling measurement includes $Z_\beta = R_z(\beta)$ and $CR_\alpha = CR_z(\alpha)$ rotations conditioned on the '0’ state and final Hadamards before measurement. Each measurement outcome $k$ is guaranteed (by the choice of $\alpha,\beta$) to have zero probability on one of the four input states. In the presence of noise, 'forbidden’ outcomes occur with a small probability.
• Figure 3: The layout of qubits on the Marrakesh processor. Each edge represents a physical two-qubit connection. Red circles indicate the adjacent two-qubit pairs test, while the black circles indicate those for an adjacent five-qubit test. The spatial distribution reflects how connectivity and localized noise affect the test outcome. Note that not all qubit pairs are shown in the figure for a clear visualization.
• Figure 4: An example of a distance-2 two-qubit PBR test is shown here. The background illustrates the qubit layout of the Marrakesh architecture, with the four relevant qubits highlighted: [103, 104, 105, 106]. The inset displays the circuit automatically generated by Qiskit’s transpiler for this specific configuration.