In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower bounds on the number of samples required to estimate the parameters of a quantum system within a prescribed small additive error, with high success probability under maximum-likelihood estimation. Notably, both the upper and lower bounds are determined by the supremum of the maximum diagonal entry of the inverse Fisher information matrix, differing only by a logarithmic factor in the number of parameters to be estimated. We then apply the general bounds to Pauli channel learning and Pauli expectation value learning, which serve as representative tasks in quantum channel and state learning, respectively, in the asymptotic small-error regime. Furthermore, we identify the structural origin of exponential sample complexity in Pauli channel learning without entanglement and in Pauli expectation value learning without quantum memory by comparing the quantum Fisher information matrix and the classical Fisher information matrix. We then extend the analysis to an error criterion based on the Euclidean distance between the true parameter values and their estimators, deriving the corresponding upper and lower bounds on the sample complexity, which are likewise characterized by the inverse Fisher information matrix. As an application, we consider Pauli channel learning with entangled probes. We highlight two fundamental contributions to quantum learning theory. First, we establish a systematic framework that determines the task-independent sample complexity under maximum-likelihood estimation. Second, we show that, in the small-error regime, the learning sample complexity is governed by the inverse Fisher information matrix, which is the central quantity in quantum metrology that determines the ultimate achievable mean squared error.

Leakage to non-computational states is a source of correlated errors in both time and space that limits the effectiveness of quantum error correction (QEC) with superconducting circuits. We present and experimentally demonstrate a high-fidelity, hardware-efficient leakage reduction unit (LRU) operating concurrently with transmon measurement without incurring time overhead for 2-level readout (2RO). Adapted from double-drive reset of population (DDROP), the protocol utilizes simultaneous drives on the transmon and its readout resonator, leveraging the dispersive shift to create a directional process that returns the transmon to the computational subspace. The LRU achieves a 98.4% leakage removal fraction without compromising the 2RO assignment fidelity (99.2%) and can also be configured for 3-level readout. We combine LRU-enhanced measurement and leakage-informed neural-network decoding to successfully suppress logical error rates in both memory and stability QEC experiments without any post-selection. Remarkably, the LRU preserves the logical error-suppression rate in stability experiments as injected leakage increases.

Product formula (PF), which approximates the time evolution under a many-body Hamiltonian by the product of local time-evolution operators, is one of the central approaches for simulating quantum dynamics by quantum computers. It has been of great interest whether the errors of PFs can be expressed by commutators among local terms, since it brings the substantial suppression of the computational cost in the system size reflecting the locality of Hamiltonians. Although recent studies have revealed such error bounds for generic time-independent systems, it remains to be a difficult problem for time-dependent Hamiltonians except for low-order PFs. In this paper, we derive an error bound of generic PFs for smooth time-dependent Hamiltonians, which is expressed explicitly by nested commutators and their time derivatives. It indicates the substantial error suppression in the system size for generic local Hamiltonians, thereby giving a much better estimate of gate counts. Our derivation employs Floquet theory originally developed for time-periodic systems, with which we analyze the time-dependent PF errors by mapping them to those for time-independent PFs defined on an infinite-dimensional space. This approach is also applicable to a family of time-dependent PFs, such as the one for non-unitary dynamics. In particular, we clarify the error bound of a time-dependent multi-product formula, with which we can achieve exponentially better scaling with respect to the target accuracy than the PF. Our results will shed light on applications of near-term and future quantum computers, ranging from quantum simulation of nonequilibrium materials to faster algorithms exploiting time-dependent Hamiltonians such as adiabatic state preparation.

Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. The existing proposals for fault-tolerant quantum algorithms for CFD have almost exclusively been based on the Carleman embedding method, used to encode nonlinearities on a quantum computer. Here, we first identify several key challenges that must be addressed in order to establish quantum advantage using this method, including Carleman convergence, time-stepping requirements, condition-number scaling, and data extraction. Building on this analysis, we develop a novel algorithm for the incompressible lattice Boltzmann equation that addresses them and provide a detailed analysis, including all potential sources of algorithmic complexity and gate count estimates. We find that for an end-to-end problem, a modest quantum advantage may be preserved for selected observables in the high-error-tolerance regime. We establish a lower bound for the Reynolds number scaling of our quantum algorithm in dimension $D$ at Kolmogorov microscale resolution with $O({\mathrm{Re}}^{\frac{3}{4}(1+\frac{D}{2})}\times q_M)$, where $q_M$ is a multiplicative overhead for data extraction with $q_M=O({\mathrm{Re}}^{\frac{3}{8}})$ for the drag force. This upper bounds the scaling improvement over classical algorithms by $O({\mathrm{Re}}^{\frac{3D}{8}})$. However, our numerical investigations suggest a lower speedup, with a scaling estimate of $O({\mathrm{Re}}^{1.936}\times q_M)$ for $D=2$. Our results give robust evidence that small, but nontrivial, quantum advantages can be achieved in the context of CFD and motivate the need for additional rigorous end-to-end quantum algorithm development.

Measurement backaction degrades dispersive readout of superconducting qubits even at modest drive strengths, often via the reduction of qubit lifetimes during readout. In this work, we theoretically and experimentally study this degradation and show how it can result from the interplay between detuned two-level systems (TLSs) and a drive-renormalized qubit spectrum. For modest to strong readout, the qubit emission spectrum becomes non-Lorentzian and depends sensitively on the readout drive frequency (even when the measurement rate is fixed). We combine the readout-modified qubit emission spectrum with time-dependent perturbation theory to predict qubit lifetimes in the presence of a TLS bath. Master equation simulations and experimental measurements on a frequency-tunable transmon confirm these predictions quantitatively. In particular, we find that driving at the resonator frequency associated with the qubit ground state yields the narrowest qubit emission spectrum and the least lifetime degradation for a fixed measurement rate, providing a practical guideline for optimizing readout protocols in future quantum processors.

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford + T circuit with T-count $O(2^{4n/3}{n}^{2/3})$ and ancilla-count $O(2^{2n/3}{n}^{1/3})$. The previous best T-count for unitary synthesis was $O(2^{3n/2}n)$ with $O(2^{n/2})$ ancillae by [Low et al., Quantum 8, 1375 (2024)]. There is a fundamental tradeoff between T gates and ancillae, and our algorithm extends the achievable regime of this tradeoff, reducing the exponent in T-count from $3n/2$ to $4n/3$. The best known lower bound remains $\mathrm{\Omega }(2^n)$, so the optimal T-count for general unitary synthesis is still open. Our construction is based on a recursive application of the cosine-sine decomposition, together with a generalization of the optimal diagonal unitary synthesis method by [D. Gosset et al., Quantum 10, 2168 (2026)] to multi-controlled $k$-qubit unitaries.

Quantum batteries, microscopic devices designed to address energy demands in quantum technologies, promise high power during charging and discharging processes. However, their performance depends crucially on reliability, quantified by the inverse of noise-to-signal ratios (NSRs), i.e., normalized fluctuations of work and power. We establish fundamental limits to this reliability: both work and power NSRs are universally bounded from below by a function of charging speed, imposing a reliability limit inherent to any quantum battery. More strikingly, we find that a quantum mechanical uncertainty relation forbids the simultaneous suppression of work and power fluctuations, revealing a fundamental trade-off that also limits the reliability of quantum batteries. We analyze the trade-off and limits, as well as their scaling behavior, across parallel, collective, and hybrid charging schemes for many-body quantum batteries, finding that increasing power by exploiting stronger entanglement comes at the cost of diminished reliability of power. Similar trends are also observed in the charging of quantum batteries utilizing Ising-like interactions. These suggest that achieving both high power and reliability requires neither parallel nor collective charging, but a hybrid charging scheme with an intermediate range of interactions. Therefore, our analysis shapes the practical and efficient design of reliable and high-performance quantum batteries.

Tunnel-coupled optically active quantum dot molecules (QDMs) have the potential to operate as spin-photon interfaces with coupled spins that interact with two different photon frequencies at the same time. A prerequisite is to deterministically prepare two (electron or hole) spins in the QDM and be able to electrically tune the orbital state couplings. Here, we demonstrate the sequential optical charging of a single QDM with two-electron spins while simultaneously maintaining the ability to widely tune orbital couplings using static electric fields and optically drive the system for quantum light generation. We optically prepare one- and two-spin states, initialize via optical pumping and explore orbital and spin relaxation dynamics for one- and two-spin states as a function of the energy detuning and hybridization of orbital states. For two-spin states, remarkably long singlet-triplet relaxation times are observed, extending beyond $\sim 100\mathrm{\mu }\mathrm{s}$ with strong dependence on the relative energy of ground and excited two-spin states. Qualitative agreement is observed with $\mathit{k}·\mathit{p}$ calculations of phonon-mediated spin relaxation. Our results provide new quantitative understanding of the dynamics of one- and two-spin states and address a number of key prerequisites for using QDMs to create multidimensional photonic cluster states.

Benchmarking physical devices and verifying logical algorithms are important tasks for scalable fault-tolerant quantum computing. Numerous protocols exist for benchmarking devices before running actual algorithms. In this work, we show that both physical and logical errors of fault-tolerant circuits can even be characterized in situ using syndrome data. To achieve this, we map general fault-tolerant Clifford circuits to subsystem codes using the spacetime code formalism and develop a scheme for estimating Pauli noise in Clifford circuits using syndrome data. We give necessary and sufficient conditions for the learnability of physical and logical noise from given syndrome data, and show that we can accurately predict logical fidelities from the same data. Importantly, our approach requires only a polynomial sample size, even when the logical error rate is exponentially suppressed by the code distance, and thus gives an exponential advantage against methods that use only logical data such as direct fidelity estimation. We demonstrate the practical applicability of our methods in various scenarios using synthetic data as well as the experimental data from a recent demonstration of fault-tolerant circuits by Bluvstein et al. [Nature 626, 7997 (2024)]. Our methods provide an efficient, in situ way of characterizing a fault-tolerant quantum computer to help gate calibration, improve decoding accuracy, and verify logical circuits.

Extensive theoretical and experimental work has established high-fidelity electron shuttling in Si/SiGe systems, whereas demonstrations in $\text{Si}/{\text{SiO}}_2$, also known as silicon metal-oxide-semiconductor (SiMOS), devices remain at an early stage. To help address this, we perform 3D simulations of conveyor-belt charge shuttling in a realistic SiMOS device, building on earlier 2D modeling. We solve the Poisson and time-dependent Schrödinger equations for varying shuttling speeds and gate voltages, focusing on potential pitfalls of typical SiMOS devices such as oxide-interface roughness, gate fabrication imperfections, and charge defects along the transport path. The simulations reveal that for low clavier-gate voltages, the additional oxide screening in multi-layer gate architectures causes conveyor-belt shuttling to collapse to the bucket-brigade mode, inducing considerable orbital excitation in the process. Increasing the confinement restores conveyor-belt operation, which we find to be robust against interface roughness, gate misalignment, and charge defects buried in the oxide. However, our results indicate that defects located at the $\text{Si}/{\text{SiO}}_2$ interface can induce significant orbital excitation. For lower conveyor gate biases, positive defects in the transport channel can even capture passing electrons. Hence we identify key challenges and find operating regimes for reliable charge transport in SiMOS architectures.

As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification methods. In this work, we introduce logical accreditation, a framework for efficiently certifying the correctness of quantum computations performed on logical qubits. Our protocol is robust against general noise models, far beyond those typically considered in performance analyses of quantum error-correcting codes. Through numerical simulations, we demonstrate that logical accreditation can scalably certify quantum advantage experiments and indicate the crossover point where encoded computations begin to outperform physical computations. The framework also enables evaluation of whether logical error rates are sufficiently low that error mitigation can be efficiently performed, extends entropy benchmarking to the regime of fault-tolerant computation, and upper bounds the infidelity of the logical output state of a computation. Underlying the framework is a novel randomized compilation scheme that converts arbitrary logical circuit noise into stochastic Pauli noise. This scheme includes a method for twirling non-transversal logical gates beyond the standard $T$ gate, resolving an open problem posed by [Piveteau et al. PRL 127, 200505 (2021)]. By bridging fault-tolerant computation and computational certification, logical accreditation offers a scalable, practical means of certifying the accuracy of quantum computations performed using encoded logical qubits.

Quantum phases at zero temperature can be characterized as equivalence classes under local unitary transformations: two ground states within a gapped phase can be transformed into each other via a local unitary circuit. We generalize this circuit-based characterization of phases to systems at finite-temperature thermal equilibrium described by Gibbs states. We construct a channel circuit that approximately transforms one Gibbs state into another provided the two are connected by a path in parameter space along which a certain correlation-decay condition holds. For finite-dimensional systems of linear size $L$ and approximation error $ϵ$, the locality of the circuit is $\text{Polylog}(\text{Poly}(L)/ϵ)$. The correlation-decay condition, which we specify, is expected to be satisfied in the interior of many noncritical thermal phases, including those displaying discrete symmetry breaking and topological order. As an application, we show that any system in the same thermal phase as a zero-temperature topological code coherently preserves quantum information for a macroscopically long time, establishing self-correction as a universal property of thermal phases. As part of the proof, we provide explicit encoding and decoding channel circuits to encode information into, and decode it from, a system in thermal equilibrium.

Finite-size general security proofs for quantum key distribution based on Rényi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has hitherto been tackled using ad hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols and demonstrate a dramatic runtime improvement over the state of the art.

Moments of ensembles of unitaries play a central role in quantum information theory as they capture the statistical properties of dynamics of systems with some form of randomness. Indeed, concepts such as approximate $t$-designs arise when comparing how close an associated moment operator of a given unitary ensemble is to that of another, reference ensemble. Despite the importance of moment operators, their properties have not been as explored for quantum channels. In this work we develop a theoretical framework to compute moment operators for ensembles of quantum channels, for all moment orders $t$, with a special focus on determining ensembles that can be used as points of reference. By deriving hierarchies between ensembles, via inequalities of their moment operator norms, we give them operational meaning and define useful concepts such as that of channel $t$-designs. Finally, we perform theoretical and numerical studies which show that different types of noise can decrease the norm of the moment operators (e.g., depolarizing noise), as well as increase it (e.g., amplitude damping noise), and generalize noise-induced concentration phenomena to channel-design-induced phenomena. Along the way, we find a block-orthogonal basis for permutations, which greatly simplifies our analyses, and may be of independent interest in moment calculations.

Open quantum systems can be described by unraveling their Lindblad master equation into ensembles of quantum trajectories. Here we investigate how the complexity of such trajectories is affected by conservation laws and other dynamical constraints of the underlying Lindblad evolution. We characterize this complexity using a data-driven approach based on the intrinsic dimension, defined as the minimal number of variables required to encode the information contained in a data set. Applying this framework to several systems, including variants of the quantum top and of the XXZ chain, we find that the intrinsic dimension is sensitive to the structure of their dynamics. The Lindblad evolution in these systems is typically chaotic, but additional constraints arise at specific parameter values, where the dynamics becomes integrable, exhibits Hilbert-space fragmentation, or develops a closed BBGKY hierarchy, leading to pronounced minima in the intrinsic dimension. Our approach results in an unsupervised probe of the complexity of dissipative quantum systems that is sensitive to chaos and ergodicity-breaking phenomena beyond the initial transient regime.

Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the system converges to a steady state with a fixed energy density. Classical simulation of the time dependence of such wave functions requires exponential resources. However, typical computations aim to estimate expectation values of local operators and correlation functions to some expected precision. For thermalizing systems at sufficiently high-energy densities, such computations can be done without storing the full wave function by instead simulating the evolution of the local operator, which requires significantly fewer resources. Nonetheless, constructing such resource-efficient classical algorithms remains a challenge for intermediate energy densities, where simulating both the wave function and operator evolution is costly. In this paper, we propose a heuristic approach to accelerate the convergence of matrix product state (MPS) simulations of expectation values, applicable across a broad range of energy densities. We estimate the desired observables by rescaling the MPS results at low bond dimensions with a factor that depends on the fidelity of the MPS wave function. Using this technique, we simulated the dynamics of the two-dimensional transverse-field Ising model (TFIM) on a $7\times 8$ grid with periodic boundary conditions, using a maximum bond dimension of $\chi =4096$ on a single A100 GPU, as well as the dynamics of the two-dimensional XY model on grids of size up to $9\times 9$. We compare our TFIM results to similar simulations on a digital quantum processor [R. Haghshenas et al. Nature (London) 653, 56 (2026)], demonstrating excellent agreement and confirming the predictive power of our method.

Random many-body states and matrices are both a useful tool to model certain physical systems and an important asset for quantum computation. Realizing them, however, generally requires an exponential (in system size) amount of resources. Recent research has presented a way out by showing that one can generate random states and matrices, or more precisely a controlled approximation of them, by applying a quantum circuit built in terms of few-body unitary gates. Most of this research has been focussed on the case of quantum circuits composed by fully random unitary gates. Here we consider what happens for circuits that, instead, involve a minimal degree of randomness. Specifically, we concentrate on two different settings: (a) brickwork quantum circuits with a single one-qudit random matrix at a boundary; (b) brickwork quantum circuits with fixed interactions but random one-qudit gates everywhere. We show that, for any given initial state, (a) and (b) produce a distribution of states approaching the Haar distribution in the limit of large circuit depth. More precisely, we show that the moments of the distribution produced by our circuits can approximate the ones of the Haar distribution in a depth proportional to the system size. Interestingly we find that in both Cases (a) and (b) the relaxation to the Haar distribution occurs in two steps—this is in contrast with what happens in fully random circuits. Moreover, we show that choosing appropriately the fixed interactions, for example taking the local gate to be a dual-unitary gate with high enough entangling power, minimally random circuits produce a Haar random distribution more rapidly than fully random circuits. In particular, dual-unitary circuits with maximal entangling power—i.e. perfect tensors—appear to provide the optimal quantum state design preparation for any design number. Our results also suggest that the minimally random settings (a) and (b) give an optimal framework to prepare unitary designs, i.e., random unitary matrices.

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve logarithmically short circuit depth in terms of accuracy, but they need to coherently encode all possible jump operators with a large ancilla consumption. Minimizing the gate and ancilla counts while achieving such a logarithmic scaling in accuracy remains an important challenge. In this work, we present two randomized quantum algorithms for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation that achieves a circuit depth with not only logarithmic scaling in accuracy but also either partial or complete independence from the parameters specifying the Lindbladian. This is based on a novel random circuit compilation method that leverages dissipative processes with only a single jump operator, leading to the proposed methods using minimal ancilla qubits—$4+\lceil {\log }_{2}M\rceil$ in the first case and seven in the other, where each single jump operator has at most $M$ Pauli strings. In addition, we numerically demonstrate the practical advantage over existing approaches by providing a detailed analysis of the required gate and ancilla counts. This work represents a significant step toward making open quantum system simulations more feasible on early fault-tolerant quantum computing devices.

To successfully perform quantum computations, it is often necessary to first accurately characterize the noise in the underlying hardware. However, it is well known that fundamental limitations prevent the unique identification of the noise model. This raises the question of whether these limitations impact the ability to predict noisy dynamics and mitigate errors. Here, we show, both theoretically and experimentally, that when learnable parameters are self-consistently characterized, the unlearnable (gauge) degrees of freedom do not impact predictions of noisy dynamics or error mitigation. We use the recently introduced framework of gate set Pauli noise learning to efficiently and self-consistently characterize and mitigate noise of a complete gate set, including state preparation, measurements, single-qubit gates and multi-qubit entangling Clifford gates. We validate our approach through experiments with up to 92 qubits and show that, while the gauge choice does not affect error-mitigated observables, optimizing it reduces sampling overhead.

Entanglement purification protocols (EPPs) are essential for generating high-fidelity entangled states in noisy quantum systems, enabling robust quantum networking and computation. Building on the circuit of the foundational recurrence protocol, we generalize two-way EPPs to arbitrary stabilizer codes. Through analytical derivations and noisy-circuit simulations incorporating circuit-level noise, we demonstrate enhanced purification performance, with fidelity improvements and finite distillation rates for distillable input states. We propose efficient circuit designs for EPPs tailored to dual-species Rydberg atom arrays, leveraging species-specific laser control and interspecies Rydberg interactions. Introducing a low-overhead operation set, the dual-species atom convenient operation set, we facilitate straightforward compilation of EPP circuits without the need for ancillary atoms or complex atom rearrangements. Our framework provides practical guidance for near-term implementations on dual-species platforms, advancing toward scalable entanglement distribution in neutral atom systems and paving the way for fault-tolerant quantum technologies.