Quantum Control Reveals Hidden Phase Transitions

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Author: Denis Avetisyan

Researchers have experimentally observed and distinguished two distinct types of phase transitions driven by measurement and feedback in a superconducting quantum processor.

A superconducting quantum processor, housing 66 transmon qubits arranged in a $6 \times 11$ lattice-with a focused subset of 30 utilized to minimize interference-facilitates the implementation of an adaptive quantum circuit leveraging alternating layers of two-qubit entanglers and real-time measurement-feedback to navigate non-equilibrium phase transitions, demonstrated by cumulative error rates of 0.07%, 0.7%, and 1.3% for synchronized SQG, iSWAP, and mid-circuit RO operations respectively.
A superconducting quantum processor, housing 66 transmon qubits arranged in a $6 \times 11$ lattice-with a focused subset of 30 utilized to minimize interference-facilitates the implementation of an adaptive quantum circuit leveraging alternating layers of two-qubit entanglers and real-time measurement-feedback to navigate non-equilibrium phase transitions, demonstrated by cumulative error rates of 0.07%, 0.7%, and 1.3% for synchronized SQG, iSWAP, and mid-circuit RO operations respectively.

The study demonstrates measurement-induced entanglement transitions and absorbing-state transitions, confirming theoretical predictions of adaptive quantum dynamics.

Realizing robust quantum computation demands overcoming the limitations of uncontrolled decoherence, prompting exploration of active control strategies. This work, ‘Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor’, reports the experimental observation of both measurement-induced entanglement transitions and absorbing-state transitions within a superconducting quantum processor, demonstrating clear distinctions between these non-equilibrium phenomena. By achieving high-fidelity mid-circuit measurements and rapid feedback, we extract critical exponents consistent with directed percolation at the absorbing-state transition. Do these results pave the way for utilizing adaptive quantum circuits as a novel platform for exploring complex many-body dynamics and ultimately, enhancing quantum information processing?

Whispers of Chaos: Beyond Unitary Evolution

Quantum simulations, at their core, rely on unitary evolution – a deterministic process where the quantum state changes predictably over time, governed by the Schrödinger equation. However, this framework encounters significant limitations when modeling complex many-body systems. The exponential growth of the Hilbert space with increasing particle number quickly overwhelms even the most powerful classical computers used to simulate these quantum dynamics. Moreover, real-world quantum systems are susceptible to decoherence – the loss of quantum information due to interactions with the environment. This introduces errors and destroys the delicate superposition and entanglement crucial for quantum computation. Consequently, traditional unitary simulations struggle to accurately represent the behavior of these systems for any meaningful duration, hindering progress in fields like materials science, drug discovery, and fundamental physics. The very nature of unitary evolution, while mathematically elegant, proves insufficient for tackling the inherent complexities and fragility of quantum phenomena.

The pursuit of truly controllable quantum dynamics requires a paradigm shift from pre-programmed, unitary evolution to systems capable of responding to and correcting errors in real-time. Traditional quantum circuits execute a fixed sequence of gates, vulnerable to environmental noise and imperfections that lead to decoherence and inaccurate results. To overcome these limitations, researchers are exploring methods to incorporate feedback loops, where measurement outcomes influence subsequent gate operations. This adaptive control demands a tight integration of quantum processors with classical computation, allowing for continuous monitoring of the quantum state and dynamic adjustment of control parameters. Such hybrid approaches aim to steer the system towards the desired outcome, effectively mitigating errors and enhancing the fidelity of complex quantum computations, ultimately unlocking the potential of quantum technologies beyond the reach of purely passive circuits.

The limitations of strictly unitary quantum circuits in handling complex systems necessitate a shift towards hybrid quantum-classical computation. Purely passive circuits, while theoretically elegant, are ill-equipped to combat decoherence and the intricacies of many-body interactions. Instead, researchers are exploring architectures where classical computation actively influences and corrects the quantum evolution in real-time. This integration involves utilizing classical processors to measure quantum states, analyze the results, and then dynamically adjust control parameters applied to the quantum system-essentially creating a feedback loop. This capability allows for real-time optimization, error mitigation, and the implementation of complex algorithms that would be difficult or impossible to realize with fixed quantum circuits. The speed and accuracy of this classical-quantum loop are critical for the performance of adaptive quantum algorithms.

Experimental and numerical analysis of an eight-qubit circuit reveals a measurement-induced entanglement transition, identified by a peak in the variance of RĂ©nyi entropy at a measurement rate of approximately 0.20.
Experimental and numerical analysis of an eight-qubit circuit reveals a measurement-induced entanglement transition, identified by a peak in the variance of RĂ©nyi entropy at a measurement rate of approximately 0.20.

The Adaptive Circuit: A Dialogue with Reality

Adaptive quantum circuits utilize mid-circuit measurements to gain information about the state of qubits during computation. These measurements, performed on one or more qubits while the circuit is still executing, project the quantum state and yield classical data. This data doesn’t simply represent the final result; instead, it characterizes the intermediate quantum state, providing insights into the probabilities of different outcomes and the overall evolution of the system. The measurement process itself introduces a probabilistic element, collapsing the superposition and affecting subsequent quantum gates, but this is a controlled aspect of the adaptive approach, allowing for dynamic circuit modification based on observed state information.

Classical feedback in adaptive quantum circuits utilizes the results of mid-circuit measurements to modify the sequence of subsequent quantum gates. This process involves transmitting measurement data to a classical processor, where it is analyzed to determine optimal adjustments to the quantum circuit’s parameters or gate selection. The adjusted control signals are then sent back to the quantum hardware, influencing the state of qubits and directing the computation along a dynamically determined path. This capability allows for real-time optimization, error mitigation, and the implementation of complex algorithms that would be difficult or impossible to realize with fixed quantum circuits.

The integration of classical processing with quantum computation in adaptive quantum circuits enables a synergistic approach to problem-solving. Quantum systems excel at specific tasks like superposition and entanglement, but are limited by coherence times and susceptibility to noise. Classical computation provides the ability to analyze mid-circuit measurement data, perform complex calculations, and dynamically adjust subsequent quantum operations. This hybrid model allows for error mitigation, optimization of quantum algorithms, and the exploration of larger, more complex quantum state spaces than would be feasible with purely quantum methods. The classical component effectively augments the quantum processor, providing control and flexibility beyond the capabilities of fixed quantum circuits.

Adaptive quantum circuits have been experimentally realized using multiple physical platforms, including Rydberg atom arrays, trapped ion systems, and superconducting qubits-specifically, Transmon qubits. Recent implementations have demonstrated high-fidelity performance critical for successful adaptation; mid-circuit measurement fidelity reached 98.7%, indicating accurate state characterization during computation. Furthermore, the fidelity of the subsequent feedback operation-the adjustment of quantum gates based on measurement results-achieved 98.4%. These values confirm the feasibility of dynamically controlling quantum circuits and optimizing performance through classical-quantum interaction.

Numerical simulations and experimental results on a 30-qubit processor demonstrate that adaptive quantum circuits transition to an absorbing state via measurement rate modulation, exhibiting ballistic or sub-ballistic spreading consistent with the dynamic properties of the DP universality class.
Numerical simulations and experimental results on a 30-qubit processor demonstrate that adaptive quantum circuits transition to an absorbing state via measurement rate modulation, exhibiting ballistic or sub-ballistic spreading consistent with the dynamic properties of the DP universality class.

Whispers Crystallize: Unveiling Novel Quantum Phases

Adaptive quantum circuits, through repeated measurement and feedback, can induce phase transitions in quantum many-body systems even without changing the underlying Hamiltonian. These measurement-induced phase transitions fundamentally alter the entanglement structure of the quantum state; specifically, they can drive a system from a volume-law entangled phase to one with area-law entanglement. This transition is not driven by altering the system’s energy landscape but by the information gained through projective measurements. The repeated measurements effectively create an environment that selects for states with reduced entanglement, leading to a qualitative change in the system’s long-range correlations and ultimately defining a new phase of matter.

Measurement-induced phase transitions in adaptive quantum circuits demonstrate behavior consistent with absorbing-state transitions, classifying them within the universality class of Directed Percolation. This means the critical properties of these transitions, such as the divergence of correlation lengths and the associated critical exponents, are predicted to match those observed in Directed Percolation, a well-studied model of spreading phenomena. Specifically, the probability of an active region vanishing to zero at the critical point follows a power law with an exponent characteristic of the Directed Percolation universality class. This classification allows for the application of theoretical tools and established results from the study of Directed Percolation to understand and predict the behavior of these quantum systems undergoing measurement-induced transitions.

RĂ©nyi Entropy serves as a quantifiable metric for assessing the purity of a quantum state and characterizing phase transitions induced by measurements. Experimental determination of critical points reveals the measurement-induced entanglement transition occurs at $p_{cMIPT} = 0.20$, while the transition to the absorbing state is observed at $p_{cabs} = 0.35$. These values define the thresholds at which significant changes in quantum state purity and entanglement properties are detected, providing precise parameters for understanding measurement-induced phase transitions.

Time-dependent Density Matrix Renormalization Group (tDMRG) simulations were employed to corroborate the experimentally determined critical points for measurement-induced phase transitions. These simulations accurately reproduced the critical point for the entanglement transition, $p_{cMIPT} = 0.20$, and the absorbing-state transition, $p_{cabs} = 0.35$. The tDMRG method provides a numerical verification of the theoretical predictions regarding the location of these phase boundaries and confirms the observed behavior of the system under measurement feedback. The agreement between experimental findings and tDMRG simulations strengthens the understanding of measurement-induced phenomena and validates the analytical framework used to describe them.

Numerical simulations of 30-qubit circuits reveal that the von Neumann and second RĂ©nyi entanglement entropies exhibit area-law scaling even before the absorbing-state transition, with results converging for bond dimensions of 64 and 128.
Numerical simulations of 30-qubit circuits reveal that the von Neumann and second RĂ©nyi entanglement entropies exhibit area-law scaling even before the absorbing-state transition, with results converging for bond dimensions of 64 and 128.

The Flow of Chaos: Implications for Quantum Information

Adaptive quantum circuits represent a powerful mechanism for achieving rapid quantum information scrambling within complex, many-body systems. Unlike traditional fixed-depth circuits, these circuits dynamically adjust their operations based on the evolving quantum state, effectively ‘reshuffling’ information across the system’s constituent qubits. This dynamic adaptation allows for the efficient exploration of the Hilbert space and facilitates the propagation of local perturbations throughout the entire system – a process analogous to the rapid spreading of information in a chaotic system. The resulting scrambled state exhibits strong correlations between qubits, even those initially distant, and is characterized by a loss of local information, replaced by a globally distributed quantum state. This ability to efficiently scramble information is crucial not only for understanding fundamental aspects of quantum chaos but also for enhancing the performance of quantum algorithms and simulations that rely on the rapid and uniform distribution of quantum information.

The rapid spread of quantum information, facilitated by adaptive quantum circuits, isn’t merely a dispersal – it’s deeply connected to the principles of hydrodynamic transport. This link reveals that the many-body quantum system begins to behave collectively, exhibiting characteristics remarkably similar to those observed in classical fluids. Instead of individual particles acting independently, the quantum information effectively flows and diffuses, driven by gradients in quantum entanglement. This collective behavior isn’t just an analogy; the mathematical descriptions of fluid dynamics can be applied to model the spread of quantum information, suggesting a fundamental connection between seemingly disparate areas of physics and potentially unlocking novel methods for controlling and manipulating complex quantum states. The emergence of these fluid-like dynamics offers a powerful new lens through which to understand and harness the behavior of entangled quantum systems.

The emergent dynamics fostered by adaptive quantum circuits hold significant promise for accelerating quantum computation. By facilitating rapid information dispersal – a process akin to scrambling – these circuits can dramatically reduce the time required for quantum algorithms to converge on solutions. Simulations, particularly those involving complex many-body systems, often suffer from exponential scaling in computational cost; however, the enhanced transport properties achieved through this method offer a pathway towards mitigating this challenge. The ability to efficiently explore the Hilbert space allows for more accurate and faster calculations in areas such as materials science, drug discovery, and fundamental physics, potentially unlocking solutions currently intractable for even the most powerful classical computers.

The advancement of adaptive quantum circuits provides researchers with unprecedented tools for investigating and manipulating the behavior of complex quantum systems. Recent experiments demonstrate a high degree of control, evidenced by a measured single-qubit gate error of $7 \times 10^{-4}$ and a two-qubit iSWAP gate error of $7 \times 10^{-3}$. These low error rates are critical, enabling the exploration of many-body quantum dynamics with increased precision and scalability. This level of control not only facilitates fundamental studies of quantum chaos and information scrambling, but also paves the way for developing novel quantum technologies, including more efficient quantum algorithms and improved simulations of complex physical phenomena, pushing the boundaries of what is achievable in quantum information science.

Time-dependent measurements reveal that repeated feedback operations induce a uniform decay of qubit occupation from a fully occupied initial state, contrasting with spatial spreading observed with single-site initialization and demonstrating global relaxation as confirmed by both numerical simulations and experimental results on a 30-qubit processor.
Time-dependent measurements reveal that repeated feedback operations induce a uniform decay of qubit occupation from a fully occupied initial state, contrasting with spatial spreading observed with single-site initialization and demonstrating global relaxation as confirmed by both numerical simulations and experimental results on a 30-qubit processor.

The pursuit within this research-observing measurement-induced phase transitions and absorbing-state transitions-echoes a deeper truth about coaxing order from chaos. It isn’t about controlling the quantum system, but rather about subtly influencing its tendencies, understanding where its inherent instability lies. As Niels Bohr once observed, “Everything we call ‘reality’ is made of patterns, not substances.” The researchers didn’t impose a state, they navigated the probabilistic landscape, carefully applying measurement and feedback to nudge the system towards revealing its underlying structure. The distinction between entanglement transitions and absorbing-state transitions isn’t a separation of phenomena, but facets of the same dance – a testament to the fact that even the most rigorous observation only reveals a chosen slice of an infinite possibility.

The Road Ahead

The observation of both measurement-driven entanglement transitions and absorbing-state transitions on solid-state hardware is, predictably, not a destination. It’s a calibration. The neat distinction demonstrated here-that these are, in fact, separable phenomena-begs the question of how robust that separation remains when subjected to the insistent noise of larger, more complex systems. These transitions, after all, aren’t obeying a law; they’re responding to a persuasion-the persistent gaze of measurement.

Future work will inevitably push toward harnessing this responsiveness. The potential for adaptive quantum dynamics, where measurement isn’t merely observation but active control, is apparent. But control is an illusion, of course. The true challenge lies in domesticating the chaos that inevitably arises when scaling these experiments. Predicting where the system will choose to transition, rather than simply observing where it did, demands a deeper understanding of the underlying stochasticity-a better divination of the noise.

One suspects the ultimate limit won’t be coherence time, but the ability to interpret the whispers. Data is always right-until it hits production. The true test will be whether these transitions can be reliably sculpted into useful computation, or whether they remain beautiful, fleeting glimpses into the heart of quantum indeterminacy.

Original article: https://arxiv.org/pdf/2512.07966.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-10 12:24