⚛️ high-energy theory

Running Quantum Computers in Discovery Mode

This paper demonstrates that a hybrid quantum-classical learning agent can autonomously discover significant many-body quantum phenomena, such as discrete time crystals and dual-unitary circuits, by optimizing an "interest function" on a 36-qubit superconducting processor.

Original authors: Aydin Deger, Benedikt Placke, G. J. Sreejith, Alessio Lerose, S. L. Sondhi

Published 2026-08-07

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Aydin Deger, Benedikt Placke, G. J. Sreejith, Alessio Lerose, S. L. Sondhi

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 a vast, dark library where every book contains a secret recipe for how the universe behaves at its smallest scales. For decades, scientists have been trying to write these recipes by hand, guessing the ingredients and hoping the dish turns out right. This is the world of quantum physics, a realm where particles can be in two places at once and where the rules of everyday life seem to dissolve. The "ingredients" in these recipes are called quantum circuits—complex sequences of instructions that tell quantum bits (or qubits) how to dance. The goal is to find specific dances that create new, strange, and useful states of matter, like time crystals or super-fast chaotic systems. But with so many possible dances (more than there are atoms in the universe), guessing one by one is like trying to find a single specific grain of sand on a beach by picking up one grain at a time. It's too slow, and we might miss the magic entirely.

This is where the idea of "discovery mode" comes in. Instead of a human guessing the recipe, imagine giving a robot chef a taste-tester that can instantly tell if a dish is "interesting." The robot tweaks the recipe, tastes it again, and tweaks it again, learning what makes a dish special without ever knowing the name of the dish beforehand. This paper explores exactly that: a new way to use quantum computers not just to solve problems we already know, but to go hunting for things we haven't even imagined yet. The researchers propose a partnership between a quantum computer (which does the heavy lifting of simulating the quantum dance) and a classical computer (which acts as the smart, learning robot). Together, they use a special "interest function"—a score that tells the system how cool or unusual a result is—to steer the quantum computer toward discovering new physics.

The Great Quantum Treasure Hunt

The authors of this paper, a team from Oxford and India, are proposing a radical new way to use quantum computers. They call it "Discovery Mode." Think of it like this: usually, when we use a quantum computer, we tell it, "Here is a specific problem, please solve it." But in Discovery Mode, we tell the computer, "Here is a vague idea of what 'cool' looks like; go find it for yourself."

To do this, they set up a feedback loop between two types of computers. The Quantum Computer is the explorer. It runs a specific quantum circuit (a sequence of operations) and generates a massive amount of data about how particles behave. The Classical Computer is the detective. It looks at the data, calculates a score called an "interest function," and then tells the quantum computer how to tweak its settings to get a higher score. The goal isn't to solve a math equation; it's to find a circuit that produces a result that is statistically "interesting" or unusual.

The paper tests this idea with two different "interest functions," which are like different definitions of "cool."

1. The Clustering Detective: Finding Time Crystals

The first definition of "interesting" is based on clustering. Imagine you have a long video of a ball bouncing. If the ball bounces randomly, the pattern is boring and hard to predict. But if the ball bounces in a perfect, repeating rhythm that defies the usual rules of energy loss, that's special.

In the quantum world, the researchers asked the computer to look at a sequence of states (snapshots of the quantum system over time) and see if they could be easily sorted into two distinct groups. If the states are all jumbled together, the "interest score" is low. If the states naturally fall into two clear, separate clusters, the score is high.

They tested this on a real quantum processor with up to 36 qubits. The computer was given a circuit with knobs it could turn (parameters like magnetic field strength). The classical agent kept turning the knobs to maximize the clustering score. The result? The computer almost automatically discovered a Discrete Time Crystal (DTC).

A DTC is a weird state of matter that oscillates in time, like a clock that ticks at half the speed of the force pushing it. It's a phase of matter that was only theoretically predicted a few years ago. The amazing part is that the computer didn't know what a DTC was. It just knew that the "clustering" score was highest when the system behaved like a DTC. The researchers found that the computer successfully tuned the circuit to create these time crystals with high probability, proving that this "discovery mode" works on real, noisy hardware.

2. The Chaos Hunter: Finding Dual-Unitary Circuits

The second definition of "interesting" was about chaos. In physics, some systems are too predictable (like a pendulum), and some are so chaotic they look like random noise. But there is a special, rare type of chaos called "dual-unitary" where the system is maximally chaotic but still follows strict, beautiful mathematical rules.

To find this, the researchers used a different interest function based on the spectral properties of the circuit. Imagine the circuit as a musical instrument. The "spectrum" is the set of notes it can play. If the notes are random, the music is noise. If the notes are perfectly spaced, it's a simple tune. But "dual-unitary" circuits are like a symphony that sounds chaotic but has a hidden, perfect structure.

The researchers couldn't run this specific search on the real quantum computer because it required too much data to measure accurately. Instead, they ran simulations on a classical computer to see if the "discovery mode" would work. They created a virtual quantum computer and let the learning agent search for the circuit that minimized the "noise" in the spectrum.

The simulations suggested that the agent would successfully steer the circuit toward the "dual-unitary" setting. The landscape of the search was "concave," meaning there was a clear path to the top of the hill (the most interesting circuit). While they didn't physically build this on a chip yet, the math strongly suggests that if they tried, the computer would find these special, maximally chaotic circuits.

Why This Matters

The big takeaway is that we don't need to know exactly what we are looking for to find it. By defining a simple rule for what is "interesting" (like "can we sort these states?" or "is the chaos structured?"), we can let quantum computers and AI work together to uncover new laws of physics.

The paper shows that this approach is feasible. They proved it works on a real 36-qubit device for finding time crystals, and their simulations suggest it would work for finding dual-unitary circuits too. They aren't claiming to have found everything, but they have shown a new path forward. Instead of humans guessing the next big discovery, we can build a system that hunts for it, using the unique power of quantum computers to explore the vast, uncharted territory of the quantum world. It's a shift from asking the computer to do our homework to asking it to help us write the next chapter of the science textbook.

Technical Summary: Running Quantum Computers in Discovery Mode

Problem Statement

The rapid scaling of quantum hardware toward "physical megaquops" (devices with $\sim$ 1000 qubits and depth $\sim$ 1000) presents a fundamental challenge: how to effectively utilize these devices to explore the vast space of possible quantum circuits ( $\sim 10^{105.8}$ distinct circuits). Traditional approaches rely on either universal digital quantum computing (requiring error correction) or analogue quantum simulation (investigating pre-defined models). This paper proposes a third paradigm, termed "discovery mode," where the goal is to search the space of quantum circuits to find instances exhibiting "interesting" dynamics without prior knowledge of the specific physical realization.

The core challenges identified are:

Defining what constitutes an "interesting" circuit instance.
Establishing procedures to identify these instances efficiently, avoiding the "barren plateau" problems common in variational quantum algorithms where optimization signals vanish exponentially.
Organizing the search to scale from small systems to larger, more complex ones.

Methodology

The proposed framework integrates a quantum processor with a classical machine learning agent in a closed-loop feedback system (illustrated in Fig. 1).

Interest Functions: The central component is the definition of an "interest function," $f(U)$ , which maps a unitary circuit $U$ (and its action on specific states) to a scalar value. This function quantifies the "interestingness" of the dynamics.
Hybrid Optimization Loop:
- The Quantum Processor executes parameterized circuits to generate data (measurement outcomes).
- The Classical Agent evaluates the interest function based on this data and uses optimization algorithms (e.g., COBYLA, Nelder-Mead) to update the circuit parameters to maximize $f(U)$ .
Curriculum Learning: To address scalability and optimization landscapes, the search is organized as a curriculum: starting with small systems and restricted circuit families, then transferring learned parameters to progressively larger systems.

The paper validates this approach through two distinct examples:

Example 1: Discovering Discrete Time Crystals (DTCs)

Interest Function: Based on the binary classifiability of a time series of states $S = \{U^t|\psi\rangle\}$ $S = {U^{t} ∣ ψ ⟩}$ .
- States are represented using classical shadows (random Pauli measurements).
- Dimensionality is reduced via Kernel Principal Component Analysis (PCA).
- Hierarchical Agglomerative Clustering (HAC) is applied to the reduced data. The "interest" is defined by the distance between the final two merged clusters in the dendrogram; a large separation indicates distinct, non-thermalizing clusters (i.e., high classifiability).
Implementation: Executed on IBM superconducting quantum processors (12, 24, and 36 qubits) using a Floquet unitary circuit (Kicked Ising model).
Optimization: Gradient-free optimizers (COBYLA) were used to tune the transverse field strengths $\{h_i\}$ and Ising couplings $\{J_i\}$ .

Example 2: Discovering Dual-Unitary Circuits

Interest Function: Based on the spectral properties of the unitary $U$ $U$ , specifically minimizing the fluctuations of traces of powers of $U$ $U$ , $z_t(U) = \text{tr}(U^t)/D$ $z_{t} (U) = tr (U^{t}) / D$ .
- This relates to the Spectral Form Factor (SFF), a probe of quantum chaos.
- The interest function is constructed as a negative potential $f(U) = -\sum V_t(z_t(U))$ , aiming to minimize $|z_t(U)|$ for various $t$ .
Implementation: Simulated classically for systems up to $n=14$ qubits due to the computational cost of averaging over Haar-random single-qubit gates to smooth the landscape.
Goal: To find circuits with extremal spectral correlations (maximally chaotic behavior) that are robust to perturbations.

Key Results

1. Discovery of Discrete Time Crystals

Experimental Validation: On a 36-qubit device, the interest function successfully identified the DTC phase. As the average kick strength $\langle h \rangle$ was tuned toward $\pi/2$ , the interest function peaked, corresponding to the emergence of period-doubled order.
Optimization Success: In 24-qubit optimization runs, the agent autonomously converged to configurations resembling DTCs.
- One run produced a "bimodal" profile with disconnected DTC regions separated by sites with $h \approx 0$ .
- Another run converged to a large, coherent DTC bulk with $h \approx \pi/2$ , achieving a higher interest score.
Scaling: The interest function was found to be intensive (independent of system size $n$ ) in the DTC phase but scales as $\sim \sqrt{T}$ with the observation window $T$ . In the trivial phase, the function was small and weakly dependent on $T$ .
Generalization: Simulations on more general circuit families (without $Z_2$ symmetry) showed that maximizing classifiability consistently steered the system toward $Z_2$ -symmetric DTC configurations, recovering the orthogonality of interaction and rotation axes.

2. Discovery of Dual-Unitary Circuits

Landscape Analysis: Numerical simulations revealed that the interest landscape for spectral minimization is locally concave.
Convergence: Optimization drives the parametrized brickwork circuits toward the submanifold where parameters satisfy the dual-unitarity condition ( $J_x = J_y = J_z = \pi$ ).
Significance: This maximum coincides with the theoretical value for fully random unitaries (Circular Unitary Ensemble), despite the finite-depth constraint. The landscape suggests that dual-unitary circuits are robust attractors for this interest function, characterized by an inverse "domain-wall tension" $\tau = 0$ .
Feasibility: While direct SFF measurement is sample-complexity limited for large systems, the paper notes that the partial spectral form factor (pSFF) offers a more efficient proxy for this discovery protocol.

Significance and Claims

The paper claims to provide the first demonstration of a "discovery mode" for quantum computers, where a hybrid classical-quantum system autonomously identifies non-trivial many-body phenomena.

Paradigm Shift: The work establishes the design of interest functions as a primary activity in many-body physics, shifting focus from simulating known Hamiltonians to searching for unknown, interesting dynamics.
Autonomy: The results suggest that learning agents with access to quantum resources can discover phenomena (DTCs, dual-unitarity) that were previously identified through human intuition and specific theoretical insights, but here are found with minimal encoding of the outcome.
Scalability: The "curriculum" approach (transferring parameters from small to large systems) is proposed as a viable strategy to overcome barren plateaus and scale discovery to larger devices.
Counterfactual Validation: While the dual-unitary discovery was validated via simulation (due to current hardware limitations), the DTC discovery was experimentally verified on real noisy hardware, proving the protocol's feasibility.
Future Outlook: The authors anticipate that this approach will lead to the discovery of new phases of matter and logical gates, envisioning "CERN-like facilities" for many-body physics that combine state-of-the-art quantum platforms with powerful classical infrastructure.

The paper concludes that while current examples serve as counterfactual validations for some targets, the approach is robust and offers a compelling path for utilizing future high-fidelity quantum hardware to generate high-dimensional data for the discovery of new physics.