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Quantum error correction 1 , 2 , 3 – 4 provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, in which 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. Here we present two below-threshold surface code memories on our newest generation of superconducting processors, Willow: 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 ± 0.02 when increasing the code distance by 2, culminating in a 101-qubit distance-7 code with 0.143% ± 0.003 per cent error per cycle of error correction. This logical memory is also beyond breakeven, exceeding the lifetime of its best physical qubit by a factor of 2.4 ± 0.3. Our system maintains below-threshold performance when decoding in real time, achieving an average decoder latency of 63 microseconds at distance 5 up to a million cycles, with a cycle time of 1.1 microseconds. We also 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 × 10 9 cycles. Our results indicate device performance that, if scaled, could realize the operational requirements of large-scale fault-tolerant quantum algorithms. Two below-threshold surface code memories on superconducting processors markedly reduce logical error rates, achieving high efficiency and real-time decoding, indicating potential for practical large-scale fault-tolerant quantum algorithms.

secretes a functional amyloid called curli during biofilm formation. Curli fibers are composed of polymers of the CsgA protein, which adopts a beta-sheet rich fold upon fibrillization. A chaperone-like protein called CsgC inhibits CsgA amyloid formation. Like other amyloidogenic proteins, CsgA undergoes a 3-stage aggregation process: an initial lag phase where a beta-rich nucleus forms, an exponential elongation phase, and a plateau phase. It is currently not known if CsgC inhibits amyloid formation by inhibiting formation of the pre-fibril nucleus, or rather, if CsgC inhibits a later stage of amyloid formation by blocking monomer addition to a growing fiber. Here, CsgC homologs from , , and were purified and characterized for their ability to interrogate CsgA amyloid formation. Each of the CsgC homologs prolonged the lag phase of CsgA amyloid formation in a similar fashion as CsgC. Additionally, we found that CsgC interacted transiently and weakly with a monomeric, pre-nucleus species of CsgA and that this interaction delayed amyloid formation. A transient CsgC-CsgA heterodimer was observed using ion mobility-mass spectrometry. When CsgC was added to actively polymerizing CsgA, exponential growth commonly associated with nucleation-dependent amyloid formation was lost. However, the addition of preformed CsgA seeds did not rescue exponential growth indicating that CsgC also has inhibitory activity during fibril elongation. Indeed, CsgC interacted strongly with CsgA fibers, suggesting that the interaction between CsgC and CsgA fibers can slow new fiber growth. CsgC displays a unique inhibitory activity at multiple stages of amyloid formation. CsgC acts as an energy-independent chaperone that transiently interacts with prefibrillar CsgA as well as an amyloid fiber.

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. Here, we investigate the dynamics of local excitations in a \\(Z_2\\) LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics via a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent excitations and string dynamics.

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 \\(_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.

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 \\(\\) = 2.14 \\(\\) 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% \\(\\) 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 \\(\\) 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 \\(\\)s at distance-5 up to a million cycles, with a cycle time of 1.1 \\(\\)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 \\(\\) 10\\(^9\\) cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.

Quantum simulation promises to advance materials discovery by accurately simulating complex states of matter, their microscopic excitations, and macroscopic response functions. The central challenge in resolving the underlying interacting dynamics is to combine high-fidelity evolution with the sophisticated control necessary to manipulate individual quasi-particles in quantum many-body states. Here, we report on high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits. By interleaving digital gates with analog evolution precisely characterized via Hamiltonian learning, we selectively excite magnons at tunable energy densities. Measuring first the linear magnon response -- a central probe in neutron-scattering experiments -- we extract temperature-dependent spectra and lifetimes. Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes. Next, we perform a suite of nonlinear measurements, including the study of self-scattering mechanisms, as well as pump-probe spectroscopy to directly characterize the magnon interactions. While matrix-product state simulations capture the dynamics well in either small systems or at low temperatures, their predictions become inaccurate away from these limits. This work demonstrates precise simulation of the interacting dynamics in quantum magnets, and provides key insights into quasi-particles and their microscopic scattering mechanisms.

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)10^-4\\) and \\(8.19(14)10^-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.

Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting qubits, we study an interacting spin model at finite temperature in a disordered landscape, tracking dynamics both in real space and in Hilbert space. Over a broad disorder range, we observe an intermediate non-ergodic regime with glass-like characteristics: physical observables become broadly distributed and some, but not all, degrees of freedom are effectively frozen. The Hilbert-space return probability shows slow power-law decay, consistent with finite-temperature quantum glassiness. In the same regime, we detect the onset of a finite Edwards-Anderson order parameter and the disappearance of spin diffusion. By contrast, at lower disorder, spin transport persists with a nonzero diffusion coefficient. Our results show that there is a transition out of the ergodic phase in two-dimensional systems.

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.

Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting qubits, we study an interacting spin model at finite temperature in a disordered landscape, tracking dynamics both in real space and in Hilbert space. Over a broad disorder range, we observe an intermediate non-ergodic regime with glass-like characteristics: physical observables become broadly distributed and some, but not all, degrees of freedom are effectively frozen. The Hilbert-space return probability shows slow power-law decay, consistent with finite-temperature quantum glassiness. In the same regime, we detect the onset of a finite Edwards-Anderson order parameter and the disappearance of spin diffusion. By contrast, at lower disorder, spin transport persists with a nonzero diffusion coefficient. Our results show that there is a transition out of the ergodic phase in two-dimensional systems.