arXiv subjects

Gonzalo Garcia

Publications and source records attributed to Gonzalo Garcia.

12 recordsLinked to original sources

arXiv2026

Multifractal and Glassy Signatures of Non-Ergodic 2D Quantum Dynamics

The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.

quant-ph↗

arXiv2026

Prescribed Mean Curvature on the ball via a sign change in the derivative

We consider the problem of finding a conformal metric on the $n$-dimensional Euclidean ball $B^n$, $n\geq 3$, with zero scalar curvature in the interior and prescribed mean curvature $H$ on the boundary $\partial B^n = S^{n-1}$. For rotationally symmetric $H=H(r)$ satisfying a flatness condition of order $α\in(n-2,\,n-1)$ at each of its finitely many critical points in the region where $H>0$, we prove that the sign-change of $H'(r)$ in that region is sufficient for existence. Combined with the necessary condition of Liu and Wang, this yields a characterization: in this class, the problem is solvable if and only if $H$ is not monotone where it is positive. Along the way we prove that the single blow-up point of the subcritical approximation must be a local maximum of $H$, the boundary-trace analogue of a lemma used by Chen and Li on the sphere, and, under a separation condition on the values of the local maxima, we obtain multiple solutions. Our approach adapts the variational scheme of Chen and Li for the sphere to the boundary-trace setting, using subcritical approximation and the blow-up analysis of Escobar and García.

math.DG↗

arXiv2026

Reinforcement Learning Control of Quantum Error Correction

Quantum error correction (QEC) is the primary strategy for protecting a quantum computer from the environment. Its prerequisite is that errors must remain sufficiently rare, which requires perpetually adapting the computer's control parameters to the drifting environment conditions. The current solution to this problem is to terminate the entire quantum computation for recalibration, but it is incompatible with the long runtimes of future quantum algorithms. We address this challenge by unifying calibration with computation. We grant the QEC process a dual role: its error detection events are not only used to correct the logical quantum state, but are also repurposed as a learning signal, teaching a reinforcement learning (RL) agent to continuously steer the control parameters and stabilize the quantum system during computation. We experimentally demonstrate this framework on a Willow superconducting processor, improving the logical stability of the surface code 3.5-fold against injected drift. By synthesizing our full suite of technological advances, we achieve record performance of the surface and color codes, with average logical error per cycle of $7.72(9)\times10^{-4}$ and $8.19(14)\times10^{-3}$ respectively. Numerical simulations of large codes with tens of thousands of control parameters confirm the scalability of our RL framework, revealing an optimization speed that is independent of system size. This work thus enables a new paradigm: a quantum computer that learns from its errors and never stops computing.

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arXiv2026

Observation of disorder-induced superfluidity

The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity.

quant-ph↗

arXiv2025

Magic state cultivation on a superconducting quantum processor

Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient alternative to resource-intensive distillation protocols; however, testing the proposal's assumptions represents a challenging departure from quantum memory experiments. We present an experimental study of magic state cultivation on a superconducting quantum processor. We implement cultivation, including code-switching into a surface code, and develop a fault-tolerant measurement protocol to bound the magic state fidelity. Cultivation reduces the error by a factor of 40, with a state fidelity of 0.9999(1) (retaining 8% of attempts). Our results experimentally establish magic state cultivation as a viable solution to one of quantum computing's most significant challenges.

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arXiv2025

Quantum-Classical Separation in Bounded-Resource Tasks Arising from Measurement Contextuality

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

quant-ph↗

arXiv2025

Demonstrating dynamic surface codes

A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome checks, permitting correction of logical information. Recently, the development of time-dynamic approaches to error correction has uncovered new codes and new code implementations. In this work, we experimentally demonstrate three time-dynamic implementations of the surface code, each offering a unique solution to hardware design challenges and introducing flexibility in surface code realization. First, we embed the surface code on a hexagonal lattice, reducing the necessary couplings per qubit from four to three. Second, we walk a surface code, swapping the role of data and measure qubits each round, achieving error correction with built-in removal of accumulated non-computational errors. Finally, we realize the surface code using iSWAP gates instead of the traditional CNOT, extending the set of viable gates for error correction without additional overhead. We measure the error suppression factor when scaling from distance-3 to distance-5 codes of $Λ_{35,\text{hex}} = 2.15(2)$, $Λ_{35,\text{walk}} = 1.69(6)$, and $Λ_{35,\text{iSWAP}} = 1.56(2)$, achieving state-of-the-art error suppression for each. With detailed error budgeting, we explore their performance trade-offs and implications for hardware design. This work demonstrates that dynamic circuit approaches satisfy the demands for fault-tolerance and opens new alternative avenues for scalable hardware design.

quant-ph↗

arXiv2025

Constructive interference at the edge of quantum ergodic dynamics

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.

quant-ph↗

arXiv2024

Scaling and logic in the color code on a superconducting quantum processor

Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors have focused primarily on the surface code, which offers a high error threshold but poses limitations for logical operations. In contrast, the color code enables much more efficient logic, although it requires more complex stabilizer measurements and decoding techniques. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and so far, realizations of color codes have not addressed performance scaling with code size on any platform. Here, we present a comprehensive demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. Scaling the code distance from three to five suppresses logical errors by a factor of $Λ_{3/5}$ = 1.56(4). Simulations indicate this performance is below the threshold of the color code, and furthermore that the color code may be more efficient than the surface code with modest device improvements. Using logical randomized benchmarking, we find that transversal Clifford gates add an error of only 0.0027(3), which is substantially less than the error of an idling error correction cycle. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection (retaining about 75% of the data). Finally, we successfully teleport logical states between distance-three color codes using lattice surgery, with teleported state fidelities between 86.5(1)% and 90.7(1)%. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.

quant-ph↗

arXiv2024

Quantum error correction below the surface code threshold

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $Λ$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $μ$s at distance-5 up to a million cycles, with a cycle time of 1.1 $μ$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.

quant-ph↗

arXiv2024

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

quant-ph↗

arXiv2022

Overcoming leakage in scalable quantum error correction

Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC). In a QEC circuit, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of logical error with scale, challenging the feasibility of QEC as a path towards fault-tolerant quantum computation. Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 \times 10^{-3}$ throughout the entire device. The leakage removal process itself efficiently returns leakage population back to the computational basis, and adding it to a code circuit prevents leakage from inducing correlated error across cycles, restoring a fundamental assumption of QEC. With this demonstration that leakage can be contained, we resolve a key challenge for practical QEC at scale.

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