Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking: the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

Quantum error correction benefits from high-fidelity, noninvasive measurements for fault-tolerant quantum computing. Deviations from ideal quantum nondemolition (QND) measurements can disturb the encoded information. To address this challenge, we develop a readout protocol for a $D$-dimensional system that, after a single positive outcome, switches to probing only the $D-1$ remaining subspace. This adaptive switching strategy minimizes measurement-induced errors by relying on negative-result measurement results that do not perturb the Hamiltonian. We apply the protocol on an eight-dimensional ${}^{123}\mathrm{Sb}$ nuclear qudit in silicon and achieve an increase in the readout fidelity from (98.93±0.07) % to (99.61±0.04) %, while reducing threefold the overall readout time. To highlight the broader relevance of measurement-induced errors, we study a ten-dimensional ${}^{73}\mathrm{Ge}$ nuclear spin read out through Pauli spin blockade, revealing nuclear spin flips arising from hyperfine and quadrupole interactions. We discuss the applicability of our method to other quantum hardware platforms such as color centers in diamond, spins in lithographic quantum dots, clusters of donors in silicon, and dual-species neutral atom arrays. These results unveil the effect of nonideal QND readout across diverse platforms and introduce an efficient readout protocol that can be implemented with minimal field-programmable gate array (FPGA) logic on existing hardware.

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random stabilizer codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher detection threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.

We construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes. Similarly to QHP codes, the proposed codes have highly redundant sets of low-weight stabilizer generators, which improves decoding accuracy in a fault-tolerant regime and gives them single-shot properties. The advantage of the construction is that it gives shorter codes. We derive simple expressions for the dimension of the proposed codes in two important special cases, give bounds on the distances and explicitly construct some relatively short codes. Circuit simulations for codes locally equivalent to four-dimensional toric codes show a (pseudo)threshold close to $1.1\mathrm{\%}$, better than for toric or surface codes with a similar noise model.

Quantum code surgery is a flexible and low-overhead technique for performing logical measurements on quantum error-correcting codes, which generalizes lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit stabilizer low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel. For a collection of logically disjoint Pauli product measurements supported on $t$ logical qubits, our scheme uses $\mathcal{O}(t\omega (\log t+{\log }^3\omega ))$ ancilla qubits, where $\omega \ge d$ is the maximum weight of the single logical Pauli representatives involved in the measurements and $d$ is the code distance. This is all done in time $\mathcal{O}(d)$ independent of $t$. Our proposed scheme preserves both the LDPC property and the fault-distance of the original code, without requiring ancillary logical codeblocks, which may be costly to prepare. This addresses a shortcoming of several recently introduced surgery schemes, which can only be applied to measure a limited number of logical operators in parallel if they overlap on data qubits.

We characterize the coherence of a triangular exchange-only (EO) spin qubit operated at a leakage-protected idle (LPI) point. The triangular geometry enables independent control of all three pairwise exchange interactions, and the LPI condition occurs when these couplings are turned on simultaneously and tuned to equal strength. In this configuration, the exchange interaction induces an energy gap $E_g=3J/2$ that suppresses leakage from the computational subspace while leaving the qubit state unaffected. We develop procedures to calibrate the LPI point and measure $E_g$, and use these to characterize the qubit dephasing time over a broad range of gap energies. While operating with large always-on exchange couplings exposes the qubit to charge noise, we find that ${\tilde{T}}_2^{\ast }$ still exceeds that of conventional exchange-only spin qubits for $E_g/h<60$ MHz. The precise control of simultaneous, all-to-all connected exchange demonstrated here presents a natural path toward improving the performance of EO qubits and also enables alternative qubit encodings.

Multimode multiphoton states are at the center of many photonic quantum technologies, from photonic quantum computing to quantum sensing. In this work, we derive a procedure to generate exactly, and with a predictable number of steps, any such state by using only multiport interferometers, photon number resolving detectors, photon additions, and displacements. We achieve this goal by establishing a connection between photonic quantum state engineering and the algebraic problem of symmetric tensor decomposition. This connection allows us to solve the problem by using corresponding results from algebraic geometry and unveils a mechanism of photon catalysis, where photons are injected and subsequently retrieved in measurements, to generate entanglement that cannot be obtained through Gaussian operations. We also introduce a tensor decomposition, that generalizes our method and allows to construct circuits yielding perfect fidelity, using the minimum number of catalysis photons. As a benchmark, we numerically evaluate our method and compare its performance with state-of-the art results, confirming 100% fidelity on different classes of states.

The process tensor provides a general representation of a quantum system evolving under repeated interventions and is fundamental for numerical simulations of local many-body dynamics. In this work, we introduce the projected process ensemble, an ensemble of pure output states of a process tensor in a given basis of local interventions, and use it to define increasingly more fine-grained probes of quantum chaos. The first moment of this ensemble encapsulates numerous previously studied chaos quantifiers, including the Alicki-Fannes quantum dynamical entropy, butterfly flutter fidelity, and spatiotemporal entanglement. We discover characteristic entanglement structures within the ensemble’s higher moments that can sharply distinguish chaotic from integrable dynamics, overcoming deficiencies of the quantum dynamical and spatiotemporal entropies. These conclusions are supported by extensive numerical simulations of many-body dynamics for a range of spin-chain models, including noninteracting, interacting-integrable, chaotic, and many-body localized regimes. Our work elucidates the fingerprints of chaos on spatiotemporal correlations in quantum stochastic processes and provides a unified framework for analyzing the complexity of unitary and monitored many-body dynamics.

Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits interspersed with $t$ single-qubit non-Clifford gates. We establish rigorous convergence bounds toward unitary $k$-designs, revealing the intrinsic cost in terms of non-Clifford resources in various flavors. First, we analyze the $k\mathrm{th}$ order frame potential, which quantifies how well the ensemble of doped Clifford circuits is spread within the unitary group. We prove that a quadratic doping level, $t=\tilde{\mathrm{\Theta }}(k^2)$, is both necessary and sufficient to approximate the frame potential of the full unitary group. As a consequence, we refine existing upper bounds on the convergence of the ensemble toward state $k$-designs. Second, we derive tight bounds on the convergence of $t$-doped Clifford circuits toward relative-error $k$-designs, showing that $t=\tilde{\mathrm{\Theta }}(nk)$ is both necessary and sufficient for the ensemble to form a relative $\epsilon$-approximate $k$-design. Similarly, $t=\tilde{\mathrm{\Theta }}(n)$ is required to generate pseudorandom unitaries. All these results highlight that generating random unitaries is extremely costly in terms of non-Clifford resources, and that such ensembles fundamentally lie beyond the classical simulability barrier. Additionally, we analyze high-order doped-Clifford-Weingarten functions to derive analytic expressions for the twirling operator over the ensemble of random doped Clifford circuits, and we establish their asymptotic behavior in relevant regimes.

We construct stabilizer states and error-correcting codes on hybrid discrete- and continuous-variable systems, generalizing the Gottesman-Kitaev-Preskill (GKP) lattice formalism. Our framework embeds qudit phase space into a hybrid phase space parameterized by continuous variables, with unit cells that grow with qudit dimension—enabling simultaneous measurement of an arbitrarily large range of noncommuting displacements. Simple hybrid states arise from applying a conditional displacement to a GKP state and a Pauli eigenstate, or by encoding qudits of a stabilizer state into a GKP code; their oscillator-qudit entanglement is non-Gaussian, distinguishing them as a resource beyond tensor products of stabilizer states. Simple hybrid codes are subsystem GKP codes whose gauge factor is entangled with a qudit. Numerical experiments suggest that they can outperform GKP codes against physical noise, with decoders tunable to either qudit or oscillator errors. We also relate stabilizer codes to noncommutative tori, showing that a general construction yields multimode multiqudit GKP extensions. We compute the codes’ logical dimension and operators via Morita equivalence.

We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $\text{⟦}7,1,3\text{⟧}$ color code on Quantinuum H2-2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant techniques for the $\mathrm{Clifford}+R_Z$ (arbitrary-angle single-qubit rotation) gate set and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits’ performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (midcircuit measurements), and $\sim 3900$ ($\sim 760$) total operations are applied on average. The energy $E$ is experimentally estimated to within $E-E_{\mathrm{FCI}}=0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground-state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols toward higher memory noise protection is the most promising avenue to improve our experimental results.

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

Hybrid quantum dot (QD)-superconductor system can be used to realize Majorana zero modes in artificial Kitaev chains. These chains provide a promising platform for the realization of Majorana qubits. Radio-frequency gate reflectometry is a fast, noninvasive, and sensitive technique that can be used to read out such qubits. In this work, we use gate reflectometry to probe two QDs coupled via a semiconductor-superconductor hybrid segment. We demonstrate that gate sensing can resolve charge stability diagrams and clearly distinguish between elastic cotunneling and crossed-Andreev reflection, the two key processes that allow one to form a Kitaev chain. Furthermore, we show that this information is accessible, even when the system is completely decoupled from the normal leads. In this closed regime, we show that the observed quantum-capacitance signal is indicative of parity switching between the even and odd ground states. Our measurements in both open and closed regimes confirm that gate reflectometry captures the essential features of interdot coupling and parity dynamics.

Cooling quantum systems with finite resources is a central task in quantum technologies and has been extensively explored in discrete-variable settings. As continuous-variable (CV) platforms play an increasingly important role in quantum information processing, it becomes crucial to understand the fundamental limitations of cooling bosonic systems. In this work, we develop a general framework for cooling CV systems, identifying both the constraints imposed by Gaussianity and the advantages enabled by non-Gaussian interactions. We derive a reachable bound on the cooling performance of Gaussian operations that applies to arbitrary cooling architectures. By optimizing over all protocols saturating this bound, we further identify the most efficient scheme, which minimizes dissipated energy for a given number of ancilla modes. Beyond Gaussian operations, we show that $p$-excitation exchange exploits non-Gaussian resources to achieve a $p$-fold enhancement of the cooling limit. Our results establish the fundamental limits of CV heat-bath algorithmic cooling and reveal the crucial role of non-Gaussianity in surpassing Gaussian cooling barriers.

Majorana-based quantum computation in nanowires and neutral atoms has gained prominence as a promising platform to encode qubits and protect them against noise. In order to run computations reliably on such devices, a fully fault-tolerant scheme is needed for state preparation, gates, and measurements. However, current fault-tolerant schemes have either been limited to specific code families or have not been developed fully. In this work, we extend the tools of qubit fault tolerance to Majorana codes. We emphasize the division between even and odd Majorana codes and how it manifests when constructing fault-tolerant gadgets for these families. We provide transversal constructions and supplement them with measurements to obtain several examples of fault-tolerant Clifford gadgets. For the case of odd codes, we give a construction for gadgets using quantum reference frames that allows one to implement operations that are forbidden due to parity superselection. We also provide a fault-tolerant measurement scheme for Majorana codes inspired by Steane error correction, enabling state preparation, measurement of logical operations, and error correction. We also point out a construction for odd Majorana codes with transversal T gates. Finally, we construct a high-rate quantum low density parity check codes (LDPC) Majorana code with logical qubits. Our work shows that all necessary elements of fault-tolerant quantum computation can be consistently implemented in fermionic hardware such as Majorana nanowires and fermionic neutral atoms.

The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, provably efficient algorithms for preparing thermal states—crucial for probing equilibrium behavior—became available only recently with breakthrough algorithms based on the simulation of well-designed dissipative processes, a quantum-analog to Markov chain Monte Carlo algorithms. We show a way to implement these algorithms avoiding expensive block encoding and relying only on dense local circuits, akin to Hamiltonian simulation. Specifically, our method leverages spatial truncation and Trotterization of exact quasilocal dissipative processes. We rigorously prove that the approximations we use have little effect on rapid mixing at high temperatures and allow convergence to the thermal state with small bounded error. Moreover, we accompany our analytical results with numerical simulations that show that this method, unlike previously thought, is within the reach of current generation of quantum hardware. These results provide the first provably efficient quantum thermalization protocol implementable on near-term quantum devices, offering a concrete path toward practical simulation of equilibrium quantum phenomena.

We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research demonstrated that some carefully designed quantum circuits affected by non-unital noise cannot be efficiently simulated, we show that this does not apply to average-case circuits, as these can be efficiently simulated using Pauli-path methods. Specifically, we prove that, with high probability over the circuit gates’ choice, Pauli propagation algorithms with tailored truncation strategies achieve an inversely polynomially small simulation error. This result holds for arbitrary circuit topologies and for any local noise, under the assumption that the distribution of each circuit layer is invariant under single-qubit random gates. Under the same minimal assumptions, we also prove that most noisy circuits can be truncated to an effective logarithmic depth for the task of estimating expectation values of observables, thus generalizing prior results to a significantly broader class of circuit ensembles. We further numerically validate our algorithm with simulations on a $6\times 6$ lattice of qubits under the effects of amplitude damping and dephasing noise, as well as real-time dynamics on an $11\times 11$ lattice of qubits affected by amplitude damping.

We study the information transmission capacities of quantum Markov semigroups acting on finite-dimensional quantum systems. We show that, in the limit of infinite time, the capacities can be efficiently computed in terms of the structure of the peripheral space of the semigroup, are strongly additive, and satisfy the strong converse property. We also establish convergence bounds to show that the infinite-time capacities are reached after time scaling quadratically with the system dimension. From a data storage perspective, our analysis provides tight bounds on the number of bits or qubits that can be reliably stored for long times in a quantum memory experiencing Markovian noise. From a practical standpoint, we show that typically, a quantum memory with Markovian noise acting independently and identically on all qubits and a fixed time-independent global error correction mechanism becomes useless for storage after time scaling exponentially with the number of qubits. In contrast, if the error correction is local, the memory becomes useless much more quickly, i.e., after time scaling logarithmically with the number of qubits. In the setting of point-to-point communication between two spatially separated parties, our analysis provides efficiently computable bounds on the optimal rate at which bits or qubits can be reliably transmitted via long Markovian communication channels, both in the finite block-length and asymptotic regimes.