⚛️ quantum physics

Experimental demonstration of non-local magic in a superconducting quantum processor

This paper presents the first experimental demonstration of non-local magic on a superconducting quantum processor, validating its theoretical definition through two independent measurement routes, characterizing dominant noise sources via a parameter-free model, and establishing it as a novel hardware benchmark for quantum advantage.

Original authors: Halima Giovanna Ahmad, Gianluca Esposito, Viviana Stasino, Jovan Odavic, Carlo Cosenza, Alessandro Sarno, Pasquale Mastrovito, Michele Viscardi, Stefano Cusumano, Francesco Tafuri, Davide Massarotti

Published 2026-07-01

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CC BY 4.0

Original authors: Halima Giovanna Ahmad, Gianluca Esposito, Viviana Stasino, Jovan Odavic, Carlo Cosenza, Alessandro Sarno, Pasquale Mastrovito, Michele Viscardi, Stefano Cusumano, Francesco Tafuri, Davide Massarotti, Alioscia Hamma

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

The Big Picture: What is "Magic" in a Quantum Computer?

Imagine you are trying to build a machine that can solve problems faster than any classical computer (like a regular laptop). To do this, the machine needs two special ingredients:

Entanglement: A spooky connection where two particles act as one, no matter how far apart they are.
Magic: A specific type of "weirdness" or complexity that makes the quantum state hard to predict.

Think of Entanglement like a perfectly synchronized dance between two partners. They move together, but if you look at just one partner, they aren't doing anything special on their own.

Think of Magic as the "spice" added to that dance. Without the spice, the dance is beautiful but predictable (a computer could simulate it easily). With the spice, the dance becomes chaotic and impossible for a normal computer to copy.

The Problem: Local vs. Non-Local Magic

The researchers discovered that "Magic" comes in two flavors, and this distinction is crucial:

Local Magic: This is spice you can add to just one partner in the dance. It's easy to remove. If you tell that partner to stop dancing weirdly, the "magic" disappears.
Non-Local Magic: This is the spice that is woven into the connection between the partners. It is shared. You cannot remove it by telling just one partner to stop. Even if you try to "clean" one partner, the weirdness remains because it lives in the bond between them.

The Paper's Claim: This is the first time anyone has successfully measured this "Non-Local Magic" on a real quantum computer chip.

The Experiment: The "Magic Eraser"

The team used a superconducting quantum processor (a chip made of tiny electrical circuits that act like atoms). They ran two different tests to prove they could find and measure this non-local magic.

Test 1: The "Optimal Eraser" (The Scavenger Hunt)
Imagine you have a messy room (the quantum state) filled with trash (Local Magic) and a hidden, unbreakable gem (Non-Local Magic).

The researchers tried to clean the room by applying specific "local" moves (like tidying up one corner).
They found the perfect combination of moves to remove all the trash.
The Result: When they were done, the trash was gone, but the gem remained. This proved that some magic cannot be erased by local actions; it is truly non-local.

Test 2: The "Purity Mirror" (The X-Ray)
Instead of cleaning, they looked at the "purity" of the connection between the two qubits (the partners).

Think of the connection as a mirror. If the mirror is perfectly clear, the partners are in a simple state. If the mirror is distorted, it means there is complex "magic" inside.
By measuring how "pure" or clear the connection was, they could mathematically calculate exactly how much non-local magic was hiding inside, without needing to clean the room first.

The Verdict: Both methods gave the same answer, and both matched the theory. They successfully found the "gem" that couldn't be erased.

Why This Matters: The Noise Detective

Real quantum computers are noisy. They are like a radio trying to play music in a storm; static (noise) gets in the way.

The researchers used their experiment to act as a noise detective. They realized that different types of noise affect the two types of magic differently:

Readout Errors (The Static): When the computer tries to "read" the result, it sometimes makes a mistake. This acts like "Local Magic"—it adds fake weirdness that can be cleaned up.
Depolarizing Errors (The Storm): A specific type of error on the connection between qubits acts like "Non-Local Magic." It leaves the core connection intact but makes it hard to clean up the local mess.

By understanding this, they built a model of the computer's errors that didn't need any "guesswork" (free parameters). They could predict exactly how the computer would behave just by knowing these two noise sources.

The Bigger Picture (As Stated in the Paper)

The paper claims this discovery is a new way to benchmark (test the quality of) quantum computers.

Current tests only check if the "gates" (the switches) work correctly.
This new test checks if the computer can actually generate and handle the "magic" needed for real quantum advantage.

The authors also mention that the tools they used to measure this could help in two specific future areas:

Black Holes: Using a "toy model" to decode radiation from black holes (Hawking radiation).
Faster Algorithms: A new way to estimate how "entangled" a system is, which could be exponentially faster than current methods.

Summary

The researchers proved they can spot the "untouchable" part of quantum weirdness (Non-Local Magic) on a real chip. They showed that while you can clean up the local mess, the deep, shared weirdness remains. This gives them a new, powerful tool to test how good a quantum computer really is and how to fix its errors.

Technical Summary: Experimental Demonstration of Non-Local Magic in a Superconducting Quantum Processor

Problem Statement
Identifying the physical resources responsible for quantum computational speedups over classical algorithms remains a central objective in quantum information science. While entanglement is necessary for universal fault-tolerant quantum computation, it is insufficient to guarantee quantum advantage. The stabilizer formalism provides a framework where "magic" (non-stabilizer resources) is identified as the additional resource required beyond Clifford operations. However, a critical distinction exists between local magic, which can be injected by local operations but generates no entanglement, and non-local magic, which arises from the interplay of entanglement and non-stabilizerness. Non-local magic ( $M_{NL}^2$ ) is defined as the fraction of non-stabilizer resources that cannot be removed by local unitary operations. Despite its theoretical importance in contexts ranging from magic state distillation to the AdS/CFT correspondence, non-local magic has never been experimentally measured on quantum hardware. Furthermore, existing benchmarking protocols, such as Randomized Benchmarking, quantify gate fidelities but do not directly assess a device's ability to generate and manipulate the specific resources (magic) required for quantum advantage.

Methodology
The authors report the first experimental demonstration of non-local magic on a superconducting quantum processing unit (sQPU), specifically a Contralto-D device from Quantware. The study employs two complementary protocols to measure non-local magic, both grounded in the Stabilizer Rényi Entropy (SRE), a computable measure of non-stabilizerness for pure states estimated via Randomized Clifford Measurements (RCM).

State-Dependent Protocol (Optimal Local Erasure): This approach quantifies non-local magic as the residual SRE remaining after applying an optimal local unitary operation ( $U_A \otimes U_B$ ) designed to erase all removable (local) magic from a bipartite state. The protocol involves preparing a target state, applying numerically optimized single-qubit unitaries to minimize the SRE, and measuring the residual entropy.
State-Agnostic Protocol (Subsystem Purity): This method relies on a theoretical derivation showing that for two-qubit pure states, non-local magic is a function solely of the purity of the reduced density matrix (RDM). By measuring the subsystem purity directly, the authors can infer non-local magic without needing to know the specific state or perform an optimization search.

The experimental workflow involves three stages:

State Preparation: Target states representing Local Magic (LM), Mixed (Local + Non-Local) Magic (M), and Non-Local Magic (NLM) are prepared using specific quantum circuits involving T-gates and entangling CZ gates.
Randomized Clifford Measurements (RCM): Random single-qubit Clifford unitaries are applied to the prepared states, followed by readout in the computational basis. Statistics from these measurements are used to estimate both the SRE and the subsystem purity.
Error Mitigation and Noise Modeling: A parameter-free noise model is constructed using independent benchmarking data. Readout errors are mitigated using a calibration matrix ( $\Lambda$ ) derived from device benchmarking. Theoretical predictions are adjusted to account for a depolarizing Controlled-Z (CZ) channel, with the depolarizing strength fixed by Interleaved Randomized Benchmarking (IRB) fidelity measurements. No free parameters are used to fit the experimental data to theory.

Key Contributions

First Experimental Measurement: This work provides the first experimental measurement of non-local magic on quantum hardware, validating the theoretical construct of non-stabilizerness that cannot be distilled by local operations.
Dual-Route Verification: The study demonstrates that the state-dependent (local erasure) and state-agnostic (subsystem purity) protocols yield consistent results, mutually corroborating the measurement of non-local magic.
Hardware-Aware Noise Characterization: By exploiting direct access to the device, the authors identify readout error and a depolarizing CZ channel as the dominant error mechanisms. They demonstrate that readout error injects spurious local magic, while the depolarizing CZ channel acts non-locally, preserving the structure of non-local magic while hindering local erasure.
Local Magic Erasure: The experiment successfully demonstrates the in-situ erasure of local magic using optimized local gates while preserving the non-local component, confirming the operational definition of non-local magic as a bound resource.

Results
The experiments were conducted on three classes of two-qubit states:

Local Magic (LM) State: A maximally entangled state with magic injected locally via a T-gate. The experiment showed that applying a specific local unitary (another T-gate) reduced the stabilizer entropy from $\sim 0.48$ to $\sim 0.1$ , effectively erasing the local magic. The non-local magic inferred from subsystem purity was near zero ( $0.0888 \pm 0.0004$ ), consistent with theory.
Mixed (M) State: A state containing both local and non-local magic. Numerical optimization identified local unitaries that reduced the total magic, leaving a residual non-local component. Experimental results ( $0.3 \pm 0.1$ ) aligned with theoretical predictions ($0.27$) and the subsystem purity inference ( $0.19 \pm 0.07$ ).
Non-Local Magic (NLM) State: A state designed to possess only non-local magic. The measured non-local magic matched theoretical expectations across a sweep of parameters, confirming that the state-agnostic purity method accurately captures the non-local resource.

The data showed that while readout errors introduced spurious local magic, the depolarizing noise on the CZ gate was the primary obstacle to perfect local erasure. The parameter-free noise model successfully predicted experimental outcomes, validating the correspondence between specific error channels and the types of magic they affect.

Significance
The paper claims that non-local magic serves as a hardware benchmark that reaches beyond standard gate-fidelity protocols. While current metrics quantify Clifford and non-Clifford gate fidelities, they do not directly measure a device's capacity to generate the specific resources (magic) necessary for quantum advantage. Measuring local and non-local magic provides a diagnostic tool for gate calibration and a benchmark for the computational resources underlying quantum advantage.

Furthermore, the ability to erase local magic in situ is identified as the elementary "cleansing" primitive for algorithms that estimate subsystem purity with exponential speedup. The same algorithmic kernel is noted to be relevant for decoding Hawking radiation in black-hole toy models. By demonstrating these capabilities on a real device, the work establishes a pathway for characterizing pre-fault-tolerant devices and suggests that non-local magic is a central resource for genuine quantum behaviors, including Bell inequality violations and holographic correspondences. The authors emphasize that their results are modest in scope (two-qubit demonstration) but scalable in principle, offering a new perspective on the interplay between entanglement, noise, and quantum computational resources.