IBM researchers have demonstrated control of quantum chaos using a superconducting quantum processor with 100 qubits. The team experimentally realized adaptive monitored quantum circuits, incorporating mid-circuit measurements and resets to steer chaotic dynamics toward a fixed point within a quantum version of the Bernoulli map. By successfully applying nearly 5000 entangling gates and 5000 non-unitary operations, the work provides insight into a dynamical phase transition between quantum and classical dynamics and is a signpost on the route towards fault tolerance.
IBM Quantum Processor Demonstrates Control of 100 Qubits
The implementation of mid-circuit resets proved central to stabilizing quantum states during the experiment; these resets, where qubit states are measured and then forced back to a defined value, actively countered the disruptive effects of quantum chaos. This approach, detailed in the work, transforms chaos from a hindrance into a resource for robust quantum control by using ambient instabilities to enhance state stabilization.
This experimental realization of adaptive monitored quantum circuits incorporated conditional feedback into non-unitary evolution, a technique previously challenging to implement at scale. The team’s work demonstrates the ability to apply these circuits on up to 100 qubits, a significant increase in qubit count for experiments exploring quantum chaos and suggesting a move toward practical application of chaos mitigation.
The scrambler operation, denoted , both increases entanglement and randomizes measurement outcomes, while the control operation, , attempts to polarize the system towards a ground state where all qubits are at |0⟩. The experimental design involved applying local quantum operations at each time step, choosing between a scrambling operation and a control operation with defined probabilities. The control operation itself relies on measuring the qubit and applying an X gate if the post-measurement state is |1⟩, a process important for steering the system.
“Order from chaos with adaptive circuits on quantum hardware,” encapsulates the core achievement of the study, which demonstrates a pathway to harness quantum chaos rather than simply being disrupted by it. The work’s findings contribute to the ongoing effort to build more robust quantum computers capable of maintaining coherence in the face of environmental noise and internal system instabilities.
Adaptive Circuits Enable Control of Quantum Chaotic Dynamics
The adaptive Bernoulli circuit model, a stochastic quantum circuit, interleaves dynamics mirroring a chaotic Bernoulli map with control operations designed to drive quantum states toward an unstable fixed point of the classical map. This approach uses random unitary gates interspersed with quantum measurements and resets, scaling with the number of qubits in the system to achieve control.
Theoretical models predict a measurement-induced phase transition (MIPT) between extensive volume-law entanglement and subextensive area-law entanglement, alongside a control-induced phase transition (CIPT) where dynamics settle at the fixed point. Experiments demonstrate that the Lyapunov exponent, a measure of chaotic behavior, transitions from positive to negative at a critical point of p = 0.5, a finding visually represented by a dashed line in accompanying data.
Analysis of von Neumann entanglement entropy reveals a shift in late-time entanglement, moving from a volume law to an area law within the chaotic phase, and ultimately to a nearly unentangled state as control increases. The implementation of these circuits relies on a stochastic process where the location of operations is determined by a random walk biased by the parameter p; if a scrambling operation, denoted , is applied, the process moves to the next qubit, while a control operation, , moves it back.
This adaptive circuit model’s success hinges on a competition between scrambling, which spreads quantum information, and control, which attempts to localize it. Estimates of universal critical properties, essential for characterizing the transition, were obtained with high accuracy. The ability to accurately determine these properties on quantum hardware signifies a step toward realizing fault tolerance in quantum computing systems.
Quantum Bernoulli Map Implementation on Superconducting Qubits
The implementation of adaptive circuits transformed chaos into a resource for quantum control, allowing researchers to stabilize targeted states despite inherent instabilities within the system. This stabilization was achieved using an IBM superconducting quantum processor, a scale that enabled the synthesis of diverse quantum evolutions, including chaotic ones, from random unitary gates. The team’s approach differs from traditional methods by using ambient instabilities, rather than attempting to eliminate them, to enhance the robustness of quantum control.
This work goes beyond conventional averaging techniques, measuring quantum fluctuations arising from the interplay of chaos, measurement and feedback for the first time, revealing critical exponents consistent with theoretical calculations. The experimental data demonstrated critical properties at the control transition with precise universal finite-size scaling behavior in both the dynamics and the long-time steady state of the system.
The success of this implementation relied on overcoming challenges to scale the dynamics and a number of quantum operations that grew quadratically with system size. The ability to access the highly entangled volume-law phase, alongside the more classically tractable area-law phase, and produce quantitatively accurate critical properties marks a step toward understanding and harnessing quantum chaos, and demonstrates coherent control of superconducting qubits in a far-from-equilibrium dynamical phase transition.
Mid-Circuit Measurements and Resets Steer Quantum States
Adaptive circuits now extend beyond simply observing quantum systems. They actively reshape their evolution through mid-circuit measurements and resets, a technique previously limited by hardware scale. This approach allows for steering chaotic quantum dynamics toward stable states, a feat demonstrated using an IBM superconducting quantum processor. Unlike earlier experiments constrained to fewer than 70 qubits, this work uses up to 100 qubits to sample a quantum Bernoulli map, a system designed to scramble information, and then attempts to guide it to a fixed point.
The success hinges on the ability to perform numerous mid-circuit measurements while the quantum computation is underway, an important step toward realizing practical quantum error correction protocols. The implementation of this adaptive control goes beyond merely collapsing the wavefunction locally. It introduces conditional feedback into the non-unitary evolution of the qubits.
This is a departure from previous explorations of measurement-induced phase transitions, which often relied on post-selection of measurement histories or avoided mid-circuit measurements altogether to maintain shallow circuit depths. Researchers found that fluctuations arising from these measurements can be driven to a critical point and observed without needing to select specific measurement outcomes, a significant advantage for complex quantum systems. This capability was previously out of reach due to the extensive number of mid-circuit measurements and resets required for implementation.
Previous experiments examining similar phenomena were limited to tens of qubits, while this work explores more complex dynamics. By successfully applying nearly 5000 entangling gates and 5000 non-unitary mid-circuit operations, this experiment is a signpost on the route towards fault tolerance.
Dynamical Phase Transition Between Quantum and Classical Behavior
The transition from chaotic to controlled quantum dynamics manifests as a change in a key metric, the Lyapunov exponent, shifting from exponentially diverging trajectories to stable ones when the control parameter reaches 0.5. This shift, observed in both classical and quantum versions of the Bernoulli map, accompanies a non-zero fidelity of the quantum wavefunction with a target state, indicating a successful steering of the system.
Researchers found that the implementation of qubit resets during computation drives a phase transition in the entanglement of the late-time wavefunction, a phenomenon not fully captured by standard classical simulations. Classical simulations struggle to accurately model the system’s behavior, particularly in the volume-law phase where entanglement scales with system size, even within areas exhibiting area-law entanglement.
This difficulty arises because individual circuit realizations can produce states challenging for classical computers, while the quantum computer efficiently explores the full phase diagram. This work experimentally demonstrates coherent control of up to 100 superconducting qubits, probing a dynamical quantum phase transition from chaotic to controlled behavior, and from quantum to effectively classical dynamics.
Noisy Simulations Validate Experimental Quantum Control
Experimental data aligns closely with theoretical models, demonstrating the accuracy of simulations used to understand complex quantum behavior. Estimates of the universal critical properties are obtained to high accuracy on the quantum computer thanks to the large number of qubits used in the calculation. This validation is particularly significant given the challenges of modeling such systems classically. The researchers compared the distribution of (Δ M_z)^2 to those generated by both a dephasing model and the matrix product state simulations, finding that the experimental data more closely matched the quantum simulations.
As described in the paper, highlighting the convergence of these approaches. The consistency across these methods strengthens confidence in the ability to accurately predict and control quantum chaotic dynamics.
Universal Critical Properties Estimated with High Accuracy
The precision of estimates for universal critical properties improved significantly through calculations performed on a quantum computer. Analysis of the system’s behavior involved examining circuit diagrams representing three distinct regimes: a chaotic phase, a critical point, and a controlled phase. Time-series data of magnetization density, derived from 500 shots per circuit, revealed characteristics specific to each phase, with standard errors providing a measure of data consistency. These calculations were supported by theoretical approaches including noisy simulations and matrix product states, allowing for comparison with statistical mechanics models.
Quantum Control Leverages Unstable Periodic Orbits
Quantum systems, typically susceptible to disruption from chaotic dynamics, can now be steered toward stability by exploiting inherent instabilities within the chaos itself. This large qubit count enabled the synthesis of complex quantum evolutions, including those mimicking chaotic behavior, through the application of random unitary gates. “This approach uses ambient instabilities to enhance rather than undermine the stabilization of targeted states with control,” the researchers state, highlighting the counterintuitive nature of their method.
The team’s experiments confirm these predictions, revealing a transition where the quantum dynamics “sticks” to the fixed point, effectively taming the chaos. The equivalence of the quantum circuit dynamics to a classical Bernoulli map, a mathematical model of chaos, under specific conditions further solidifies the understanding of this control mechanism, allowing for precise comparisons between quantum and classical behaviors. This work represents a step toward building quantum computers resilient to the inherent instabilities of chaotic systems, potentially unlocking new avenues for quantum computation and simulation.
5000+ Gate Operations Advance Towards Fault Tolerance
Experiments achieved nearly 5000 entangling gates and 5000 non-unitary mid-circuit operations, demonstrating a substantial increase in circuit complexity for controlling quantum dynamics. The ability to maintain coherent control during such lengthy and detailed sequences is critical for realizing complex algorithms and mitigating the effects of environmental noise. The research team implemented a strategy of interleaving quantum gates with mid-circuit resets, a technique where computation pauses for measurement and correction, to actively manage the instabilities inherent in quantum chaotic systems.
Consecutive resets were merged to optimize circuit efficiency, demonstrating a practical approach to managing the overhead associated with error mitigation. The duration of reset operations was found to be substantially longer than that of two-qubit gates, highlighting a potential area for hardware optimization. The success in coordinating unitary gates, measurement, and feedback demonstrates the potential to generate scientifically valuable results with current quantum computers, even before achieving full fault tolerance.
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