We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e., when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such channels with a logarithmic amount of effort relative to the size of the system, by employing random state preparation and measurements in the Pauli basis. We extend the applicability of the protocol to channels consisting of a layer of quantum gates with a polylogarithmic number of non-Clifford gates, followed by a low-degree noise channel. Rather than inverting the layer of quantum gates on the hardware—which would introduce additional errors—we instead carry out the inversion in classical postprocessing, while adding to the sample complexity a factor at most polynomial in system size. Numerical simulations support our theoretical findings and demonstrate the feasibility of our method.

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number $\kappa$ of the linear system and the target error $ϵ$. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling $O(\kappa \log (1/ϵ))$—an exponential improvement in $ϵ$, and a shaving of a $\log \kappa$ scaling factor in $\kappa$. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is $837\kappa$ at $ϵ={10}^{-10}$ for Hermitian matrices.

In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a $(2+0)$-dimensional nonunitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network/Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly nonmonotonic entanglement growth at the incipient nonunitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (nonquadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.

Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $\mathrm{\Phi }$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $\mathrm{\Phi }$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by ${\mathsf{Q}\mathsf{A}\mathsf{C}}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.

The electronic energy level structure of yttrium monoxide (YO) provides a long-lived, low-lying ${}^2\mathrm{\Delta }$ state ideal for high-precision molecular spectroscopy, narrowline laser cooling at the single photon-recoil limit, and studying dipolar physics with unprecedented interaction strength. High-resolution laser spectroscopy of ultracold laser-cooled YO molecules is used to study the Stark effect in the ${\mathrm{A}}^{\mathrm{\prime }}{}^2{\mathrm{\Delta }}_{3/2}J=3/2$ state. An immediate onset of the linear Stark effect is observed in the presence of weak applied electric fields due to the near-degenerate $\mathrm{\Lambda }$ doublet and the large electric dipole moment. By applying a small electric field the Stark-insensitive state is spectroscopically isolated and the absolute transition frequency to the $\mathrm{X}{}^2{\mathrm{\Sigma }}^{+}$ electronic ground state is determined with a fractional frequency uncertainty of $9\times {10}^{-12}$. This electric field control is necessary to implement a quasi-closed photon-cycling scheme that preserves parity. With this scheme the first narrowline laser cooling of a molecule is demonstrated, reducing the temperature of sub-Doppler cooled YO in two dimensions.

Achieving industrial quantum advantage is unlikely without the use of quantum error correction (QEC). Other QEC codes beyond surface code are being experimentally studied, such as color codes and quantum low-density parity check codes, that could benefit from new quantum processing unit (QPU) architectures. We introduce the six-qubit star lattice architecture that offers parallelism and effective local all-to-all connectivity and thus enables hardware-efficient implementation of certain QEC codes. As a first demonstration of this new architecture, we encode two logical qubits in a six-qubit superconducting QPU with a star topology using the $\text{⟦}4,2,2\text{⟧}$ code and characterize the logical states with the classical shadow framework. Logical lifetime and logical error rate are measured over repeated quantum error detection cycles for various logical states including a logical Bell state. We measure logical state fidelities above 96% for every cardinal logical state, find logical lifetimes above the best physical element, and logical error-per-cycle values ranging from 0.25(2)% to 0.91(3)%. In future, such star units can be tiled into a lattice to enable QEC codes with high-weight and overlapping stabilizers for improved encoding rates.

In the task of unitarily cooling a quantum system with access to a larger quantum system, known as the machine or reservoir, how does the structure of the machine impact an agent’s ability to cool and the complexity of their cooling protocol? Focusing on the task of cooling a single qubit given access to $n$ separable, thermal qubits with arbitrary energy structure, we answer these questions by giving two new perspectives on this task. First, we show that a set of inequalities related to the energetic structure of the $n$-qubit machine determines the protocol which cools the qubit to the coldest reachable state, which parts of the machine contribute to this protocol and give rise to a Carnot-like bound. Second, we show that cooling protocols can be represented as perfect matchings on bipartite graphs enabling the optimization of cost functions, e.g., gate complexity or dissipation. Our results generalize the algorithmic cooling problem, establish new fundamental bounds on quantum cooling and offer a framework for designing novel autonomous thermal machines and cooling algorithms.

The development of levitated optomechanics has enabled precise force sensors that operate in the quantum measurement regime, opening up unique opportunities to search for new physics whose weak interactions may have evaded existing sensors. We demonstrate the detection of impulsive forces acting on optically levitated nanoparticles, where the dominant noise source is provided by measurement backaction. Using these sensors, we search for momentum transfers that may originate from scattering of passing particlelike dark matter. For dark matter that couples to Standard Model neutrons via a generic long-range interaction, this search constrains a range of models in the mass range 1–${10}^7\mathrm{Ge}\mathrm{V}/c^2$, placing upper limits on single neutron coupling strength as low as $\le 1\times {10}^{-7}$ at the 95% confidence level. We also demonstrate the ability of using the inherent directional sensitivity of these sensors to separate possible dark matter signals from backgrounds. Future extensions of the techniques developed here can enable searches for light dark matter and massive neutrinos that can reach sensitivity several orders of magnitude beyond existing searches.

Long-range quantum systems, in which the interactions decay as $1/r^{\alpha }$, are of increasing interest due to the variety of experimental setups in which they naturally appear. Motivated by this, we study fundamental properties of long-range spin systems in thermal equilibrium, focusing on the weak regime of $\alpha >D$. Our main result is a proof of analyticity of their partition functions at high temperatures, which allows us to construct a classical algorithm with subexponential runtime $\exp (\mathcal{O}({\log }^2(N/ϵ)))$ that approximates the log-partition function to small additive error $ϵ$. As by-products, we establish the equivalence of ensembles and the Gaussianity of the density of states, which we verify numerically in both the weak and strong long-range regimes. This also yields constraints on the appearance of various classes of phase transitions, including thermal, dynamical, and excited-state ones. Our main technical contribution is the extension to the quantum long-range regime of the convergence criterion for cluster expansions of Kotecký and Preiss.

Large-scale quantum computers are expected to benefit from modular architectures. Validating the capabilities of modular devices requires benchmarking strategies that assess performance within and between modules. In this work, we evaluate cross-platform verification protocols, which are critical for quantifying how accurately different modules prepare the same quantum state—a key requirement for modular scalability and system-wide consistency. We demonstrate these algorithms using a six-qubit flip-chip superconducting quantum device consisting of two 3-qubit modules on a single carrier chip, with connectivity for intra- and intermodule entanglement. We examine how the resource requirements of protocols relying solely on classical communication between modules scale exponentially with qubit number, and demonstrate that introducing an intermodule two-qubit gate enables subexponential scaling in cross-platform verification. This approach reduces the number of repetitions required by a factor of 4 for three-qubit states, with greater reductions projected for larger and higher-fidelity devices.

Accurate measurement of vector magnetic fields is critical for applications including navigation, geoscience, and space exploration. Nitrogen-vacancy ($\mathrm{N}$$\mathrm{V}$) center spin ensembles offer a promising solution for high-sensitivity vector magnetometry, as their different orientations in the diamond lattice measure different components of the magnetic field. However, the bias magnetic field typically used to separate signals from each $\mathrm{N}$$\mathrm{V}$ orientation introduces inaccuracy from drifts in permanent magnets or coils. Here, we present a novel bias-field-free approach that labels the $\mathrm{N}$$\mathrm{V}$ orientations via the direction of the microwave (MW) field in a variable-pulse-duration Ramsey sequence used to manipulate the spin ensemble. Numerical simulations demonstrate the possibility to isolate each orientation’s signal with subnanotesla accuracy in most terrestrial fields, even without precise MW field calibration, at only a moderate cost to sensitivity. We also provide proof-of-principle experimental validation, observing relevant features that evolve as expected with the applied magnetic field. Looking forward, by removing a key source of drift, the proposed protocol lays the groundwork for future deployment of $\mathrm{N}$$\mathrm{V}$ magnetometers in high-accuracy or long-duration missions.

We explore the universal properties of mixed quantum matter obtained from “single-shot” adaptive evolution, in which a quantum-critical ground-state is manipulated through a single round of local measurements and local unitary operations conditioned on spatially distant measurement outcomes. The resulting mixed quantum states are characterized by altered long-distance correlations between local observables, mixed-state entropy, and entanglement negativity. By invoking a coarse-grained, continuum description of single-shot adaptation in (1+1) dimensions, we find that the extensive mixed-state entropy exhibits a subleading, constant correction ($\gamma$), while the entanglement negativity can grow logarithmically with subregion size, with a coefficient ($\alpha$); both constants can attain universal values which are distinct from the expected behavior in any quantum-critical ground-state. We investigate these properties in single-shot adaptation on (1) the critical point between a one-dimensional $Z_2\times Z_2$ symmetry-protected topological (SPT) order and a symmetry-broken state, and (2) a spinful Tomonaga-Luttinger liquid. In the former case, adaptive evolution that decoheres one sublattice of the SPT can yield a critical mixed-state in which $\alpha$ attains a universal value, which is half of that in the original state. In the latter case, we show how adaptation—involving feedback on the spin degrees of freedom, after measuring the local charge—modifies long-distance correlations, and determine via an exact replica field-theoretic calculation that $\alpha$ and $\gamma$ vary continuously with the strength of feedback. Numerical studies confirm these results.

We present three schemes for constructing a (2,2)-Shor-encoded 6-ring photonic resource state for fusion-based quantum computing, each relying on a different type of photon source. We benchmark these architectures by analyzing their ability to achieve the loss tolerance threshold for fusion-based quantum computation using the target resource state. More precisely, we estimate their minimum hardware requirements for fault-tolerant quantum computation in terms of the number of photon sources to achieve on-demand generation of resource states with a desired generation period. Notably, we find that a group of 12 deterministic single-photon sources containing a single matter qubit degree of freedom can produce the target resource state near-deterministically by exploiting entangling gates that are repeated until success. The approach is fully modular, eliminates the need for lossy large-scale multiplexing, and reduces the overhead for resource-state generation by several orders of magnitude compared to architectures using heralded single-photon sources and probabilistic linear-optical entangling gates. Our work shows that the use of deterministic single-photon sources embedding a qubit substantially shortens the path toward fault-tolerant photonic quantum computation.

We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate. We derive a generic formula for a transversal $T$ gate on color codes defined on general 3-manifolds, which acts as collective non-Clifford logical ccz gates on any triplet of logical qubits with their logical-$X$ membranes having a ${\mathbb{Z}}_2$ triple intersection at a single point. The triple-intersection number is a topological invariant, which also arises in the path integral of the emergent higher symmetry operator in a topological quantum field theory (TQFT): the ${\mathbb{Z}}_2^3$ gauge theory. Moreover, the transversal $S$ gate of the color code corresponds to a higher-form symmetry in TQFT supported on a codimension-1 submanifold, giving rise to exponentially many addressable and parallelizable logical cz gates. A construction of constant-depth circuits of the above logical gates via cup-product cohomology operation is also presented for three copies of identical toric codes on arbitrary 3-manifolds. We have developed a generic formalism to compute the triple-intersection invariants for 3-manifolds, with the structure encoded into an interaction hypergraph which determines the logical gate property and also corresponds to the hypergraph magic state that can be injected into the code without distillation (“magic-state fountain”). We also study the scaling of the Betti number and systoles with volume for various 3-manifolds, which translates to the encoding rate and distance. We further develop three types of LDPC codes supporting such logical gates: (1) A quasi-hyperbolic code from the product of 2D hyperbolic surface and a circle, with almost-constant rate $k/n=O(1/\log (n))$ and $O(\log (n))$ distance; (2) A homological fiber-bundle code from twisting the product by an isometry of the surface based on the construction by Freedman-Meyer-Luo, with $O(1/{\log }^{\frac{1}{2}}(n))$ rate and $O({\log }^{\frac{1}{2}}(n))$ distance; (3) A specific family of 3D hyperbolic codes: the Torelli mapping-torus code, constructed from mapping tori of a pseudo-Anosov element in the Torelli subgroup, which has constant rate while the distance scaling is currently unknown. We then show a generic constant-overhead scheme for applying a parallelizable universal gate set with the aid of logical-$X$ measurements.

We construct a family of infinitely many candidate non-Abelian self-correcting topological quantum memories in $D\ge 5+1$ spacetime dimensions without particle excitations using local commuting non-Pauli stabilizer lattice models and field theories of ${\mathbb{Z}}_2^3$ higher-form gauge fields with nontrivial topological action. We call such non-Pauli stabilizer models magic stabilizer codes. The family of topological orders have Abelian electric excitations and non-Abelian magnetic excitations that obey Ising-like fusion rules and non-Abelian braiding, including Borromean ring type braiding which is a signature of non-Abelian topological order, generalizing the dihedral group ${\mathbb{D}}_8$ gauge theory in $(2+1)\mathrm{D}$. The simplest example includes a non-Abelian self-correcting memory in $(5+1)\mathrm{D}$ with Abelian loop excitations and non-Abelian membrane excitations. We prove the self-correction property and the thermal stability and devise a probabilistic local cellular-automaton decoder. We also construct fault-tolerant non-Clifford CCZ logical gate using constant-depth circuits from higher-cup products in the 5D non-Abelian code. The use of higher-cup products and non-Pauli stabilizers allows us to get an $O(n^{2/5})$ distance overcoming the $O(n^{1/3})$ distance barrier in conventional topological stabilizer codes, including the 3D color code and the 6D self-correcting color code.

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete- or continuous-variable (qubit or qumode) hardware. To illustrate the oracle’s representation-theoretic power and near-term experimental accessibility, we encode a Gaussian imaginary time-evolution spectral filter. As a result, we define a continuous linear combination of unitaries block encoding. Due to the ancillary qumode’s infinite-dimensional nature, continuous-variable qumodes constitute a powerful compilation tool for encoding continuous spectral functions without discretization errors while minimizing resource requirements. We then focus on the ubiquitous task of preparing eigenstates in quantum spin models. For completeness, we provide an end-to-end compilation which expresses high-level oracles in terms of an experimentally realizable instruction set architecture in both 1D and 2D. Finally, we examine the leading-order effects of physical errors and highlight open research directions. Our algorithms scale linearly with the spatial extent of the target system and are applicable to both near-term and large-scale quantum processors.

We extend the symmetry topological field theory (SymTFT) framework to open quantum systems. Using canonical purification, we embed mixed states into a doubled (2+1)-dimensional topological order and employ the slab construction to study (1+1)-dimensional mixed-state phases through condensable algebras in the doubled SymTFT. Hermiticity and positivity of the density matrix impose additional constraints on allowable anyon condensations, enabling a systematic classification of mixed-state phases—including strong-to-weak symmetry breaking (SWSSB) and average symmetry-protected topological (ASPT) phases. We present examples of mixed-state phase transitions involving SWSSB and show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.

In this work, we give a hybrid quantum-classical algorithm for solving electronic structure problems of molecules using only linear quantum optical systems. The variational ansatz we proposed is a hybrid of noninteracting boson dynamics and classical computational chemistry methods, specifically, the Hartree-Fock method and the configuration interaction method. The boson part is built by a linear optical interferometer, which is easier to realize compared with the well-known unitary coupled cluster (UCC) ansatz composed of quantum gates in conventional variational quantum eigensolver, and the classical part is merely classical processing acting on the Hamiltonian. The appearance of permanents in the boson part has its physical intuition to provide different kinds of resources from commonly used single, double, and higher excitations in classical methods and the UCC ansatz to explore chemical quantum states. Such resources can help enhance the accuracy of methods used in the classical parts. We give a scalable hybrid homodyne and photon-number measurement procedure for evaluating the energy value, which has intrinsic abilities to mitigate photon loss errors, and discuss the extra measurement cost induced by the no Pauli exclusion principle for bosons with its solutions. To demonstrate our proposal, we run numerical experiments on several molecules and obtain their potential energy curves reaching chemical accuracy.

Certifying a quantum state in a device-independent (DI) manner, in which no trust is placed on the internal workings of any physical components, is a fundamental task bearing various applications in quantum information theory. The composability of a state-certification protocol is key to its integration as a subroutine within information-theoretic protocols. In this work, we present a composable certification of quantum states in a DI manner under the assumption that a source prepares a finite sequence of independent quantum states that are not necessarily identical. We show that the security relies on the DI analog of the fidelity, called the extractability. We develop methods to compute this quantity under local operations and classical communication in certain Bell scenarios that self-test the singlet state, which may also be of independent interest. Finally, we demonstrate our framework by certifying the singlet state in a composable and DI manner using the Clauser-Horne-Shimony-Holt inequality.

Recently, significant effort has been devoted towards designing erasure qubits in which dominant physical noise excites detectable leakage states that can be returned to the qubit subspace. Interest in these erasure qubits has been driven by studies showing that the requirements for fault-tolerant quantum error correction are significantly relaxed when noise in every gate operation is dominated by erasures. However, these studies assume perfectly accurate erasure checks after every gate operation which generally come with undesirable time and hardware overhead costs. In this work, we investigate the consequences of using an imperfect but overhead-efficient erasure check for fault-tolerant quantum error correction with the surface code. We show that, under physically reasonable assumptions on the imperfect erasure checks, the threshold error rate is still at least over twice that for Pauli noise. We also study the impact of imperfect erasure checks on the effective error distance and find that it degrades the effective distance under a general error model in which a qubit suffers from depolarizing noise when interacting with a leaked qubit. We then identify a more restrictive but realistic noise model for a qubit that interacts with a leaked qubit, under which the effective error distance is twice that for Pauli noise. We apply our analysis to recently proposed superconducting dual-rail erasure qubits and show that achieving good-performance surface code quantum memories with relaxed system requirements is possible.