Erasure qubits offer a promising avenue toward reducing the overhead of quantum error correction (QEC) protocols. However, they require additional operations, such as erasure checks, that may add extra noise and increase the run-time of QEC protocols. To assess the benefits provided by erasure qubits, we focus on the performance of the surface code as a quantum memory. In particular, we analyze various erasure check schedules, find the correctable regions in the phase space of error parameters, and probe the subthreshold scaling of the logical error rate. We then consider a realization of erasure qubits in the superconducting hardware architectures via dual-rail qubits. We use the standard transmon-based implementation of the surface code as the performance benchmark. Our results indicate that QEC protocols with erasure qubits can outperform the ones with state-of-the-art transmons, even in the absence of precise information about the locations of erasure errors.

Quantum error correction is pivotal in advancing toward large-scale quantum computation, and efficient verification is crucial for ensuring the high fidelity of code states. Traditional methodologies, such as state tomography, direct fidelity estimation, and state verification, either fall short in measurement efficiency, especially for large-scale systems, or are restricted to some specific states. In this work, we introduce a general framework for quantum subspace verification, enabling efficient and measurement-noise-robust fidelity estimation between a given state and the target subspace with a specified confidence level. By integrating the proposed subspace verification with direct fidelity estimation, we develop a composite protocol that significantly improves the efficiency of verifying the fidelity of general magic logical states, as demonstrated by intuitive numerical results. This improvement stems from the use of subspace verification, which leverages the knowledge of code subspaces to significantly reduce measurement costs. Additionally, we detail the construction of verification operators for typical error correction codes, including general stabilizer codes and quantum low-density parity-check codes, enabling their efficient implementation using practical local measurements. Notably, for certain codes, such as the Calderbank-Shor-Steane codes and quantum low-density parity-check stabilizer codes, we reduce the number of required measurement settings and sample complexity to a constant level using graphical methods. Our approach facilitates efficient and feasible verification of error correction codes and generic magic logical states, advancing their practical implementations on quantum platforms.

The full characterization of a continuous-variable quantum system is a challenging problem. For the trapped-ion system, a number of methods of measuring the quantum states have been developed, including the measurement of the $Q$ quasiprobability function and the density-matrix elements in the Fock basis, but these approaches are often slow and difficult to scale to multimode states. Here, we demonstrate a novel and powerful scheme for measuring a continuous-variable quantum state that uses the direct single-shot measurement of the joint parity of the phonon states of a trapped ion. We drive a spin-dependent bichromatic beam-splitter interaction that coherently exchanges phonons between different harmonic oscillator modes of the ion. This interaction encodes the joint-parity information into the relative phase between the two spin states, enabling measurement of the combined phonon-number parity across multiple modes in a single shot. Leveraging this capability, we directly measure multimode Wigner quasiprobability distributions to perform quantum state tomography of an entangled coherent state, and calculate various quantum informational quantities with a model-based estimation of the density matrix. We further show that the single-shot joint-parity measurement can be used to detect parity-flip errors in real time. By postselecting the parity-measurement outcomes, we experimentally demonstrate the partial recovery of coherence, effectively implementing an error-mitigation technique. Lastly, we identify the various sources of error affecting the fidelity of the spin-dependent beam-splitter operation and study the feasibility of high-fidelity operations. The interaction studied in this work can be extended to more than two modes, and is highly relevant to continuous-variable quantum computing and quantum metrology.

Photon recoil is one of the fundamental limitations for high-fidelity control of trapped-atom qubits such as neutral atoms and trapped ions. In this work, we derive an analytical model for efficiently evaluating the motion-induced infidelity in remote entanglement generation protocols. Our model is applicable for various photonic qubit encodings, such as polarization, time-bin, and frequency encodings, and with arbitrary initial motional states, thus providing a crucial theoretical tool for realizing high-fidelity quantum networking. For the case of tweezer-trapped neutral atoms, our results indicate that operation in the bad-cavity regime with cavity decay rate exceeding the atom-photon coupling rate and near-ground-state cooling with motional quanta below 1 are desired to suppress the motion-induced infidelity sufficiently below the 1% level required for efficient quantum networking. Finite-temperature effects can be mitigated efficiently by detection time filtering at the moderate cost of success probability and network speed. These results extend the understanding of infidelity sources in remote entanglement generation protocols, establishing a concrete path toward fault-tolerant quantum networking with scalable trapped-atom qubit systems.

We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and developing a phenomenological field theory, focusing on the most general single-qubit $X$-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; for this they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large-scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.

In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased. The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli-$Z$ errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error-correction scheme.

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended $t$-$J$ model where the background spins form a ${\mathbb{Z}}_2$ quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.

Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit $\pi$ or $\pi /2$ pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

Graph states are fundamental objects in the theory of quantum information due to their simple classical description and rich entanglement structure. They are also intimately related to instantaneous quantum polynomial-time (IQP) circuits, which have applications in quantum pseudorandomness and quantum advantage. For us, they are a toy model to understand the relation between circuit connectivity, entanglement structure, and computational complexity. In the worst case, a strict dichotomy in the computational universality of such graph states appears as a function of the degree $d$ of a regular graph state [Ghosh et al., Phys. Rev. Lett. 131, 030601 (2023)]. In this paper, we study the average-case complexity of simulating random graph states of varying degree when measured in random product bases and give distinct evidence that a similar complexity-theoretic dichotomy exists in the average case. Specifically, we consider random $d$-regular graph states and prove three distinct results: First, we show two families of IQP circuits of depth $d$ and show that they anticoncentrate for any $2<d=o(n^{1/2})$ when measured in a random $X$-$Y$ plane product basis. This implies anticoncentration for random constant-regular graph states. Second, in the regime $d=\mathrm{\Theta }(n^c)$ with $c\in (0,1)$, we prove that random $d$-regular graph states contain polynomially large grid graphs as induced subgraphs with high probability. This implies that they are universal resource states for measurement-based computation. Third, in the regime of high degree ($d\sim n/2$), we show that random graph states are not sufficiently entangled to be trivially classically simulable, unlike Haar-random states. Proving the three results requires different techniques—the analysis of a classical statistical-mechanics model using Krawtchouck polynomials, graph-theoretic analysis using the switching method, and analysis of the ranks of submatrices of random adjacency matrices, respectively.

We present the fundamental limits to the precision of estimating parameters of a quantum matter system probed by light, even when some of the light is lost. This practically inevitable scenario leads to a tripartite quantum system of matter, and light—detected and lost. Evaluating fundamental information theoretic quantities such as the quantum Fisher information of only the detected light was heretofore impossible. We succeed by expressing the final quantum state of the detected light as a matrix product operator. We apply our method to resonance fluorescence and pulsed spectroscopy. For both, we quantify the sub-optimality of continuous homodyning and photo-counting measurements in parameter estimation. For the latter, we find that single-photon Fock state pulses allow higher precision per photon than pulses of coherent states. Our method should be valuable in studies of quantum light-matter interactions, quantum light spectroscopy, quantum stochastic thermodynamics, and quantum clocks.

The Gottesman-Kitaev-Preskill (GKP) codes are known to achieve optimal rates under displacement noise and pure-loss channels, which establishes theoretical foundations for its optimality. However, such optimal rates are only known to be achieved at a discrete set of noise strengths with the current self-dual symplectic lattice construction. In this work, we develop a new coding strategy using concatenated continuous variable-discrete variable encodings to go beyond past results and establish GKP’s optimal rate over all noise strengths. In particular, for displacement noise, the rate is obtained through a constructive approach by concatenating GKP codes with a quantum polar code and analog decoding. For a pure-loss channel, we prove the existence of capacity-achieving GKP codes through a random coding approach. These results highlight the capability of concatenation-based GKP codes and provides new methods for constructing good GKP lattices.

Transversal gates on quantum error correction codes have been a promising approach for fault-tolerant quantum computing, but are limited by the Eastin-Knill no-go theorem. Existing solutions such as gate teleportation and magic state distillation are resource-intensive. We present a measurement-free code-switching protocol for universal quantum computation, switching between a stabilizer code for transversal Clifford gates and a permutation-invariant (PI) code for transversal non-Clifford gates that are logical $Z$ rotations for any rational multiple of $\pi$. The novel non-Clifford gates enabled by this code-switching protocol provide for a lower gate count implementation of a universal gate set relative to the Clifford + $T$ gate set. To achieve this, we present a protocol for performing controlled-not gates between the codes using near-term quantum control operations that employ a catalytic bosonic mode. We also present a new class of PI codes with tunable code distance, supporting transversal non-Clifford gates, and demonstrate their reduced gate count overhead relative to a comparable stabilizer code to stabilizer code-switching scheme.

Increasing coherent interrogation times is central to advancing the precision of optical clocks. Synchronous differential optical clock comparisons have now demonstrated atomic coherence times that far exceed the coherence time of the clock laser. While atom coherence times are then primarily limited by errors induced by lattice Raman scattering, excited clock state radiative decay, and broadening from two-body collisions, many of these errors take the atoms out of the clock transition subspace, and can therefore be converted into “erasure” errors if the appropriate readout scheme is employed. Here we experimentally demonstrate a hyperfine-resolved readout technique for ${}^{87}\mathrm{Sr}$ optical lattice clocks that mitigates decoherence from Raman scattering induced by the lattice as well as radiative decay. By employing hyperfine-resolved readout in synchronous differential comparisons between ${}^{87}\mathrm{Sr}$ ensembles with both Ramsey and spin-echo spectroscopy sequences, we achieve enhanced atomic coherence times exceeding 100 and 150 s, respectively, enabling longer coherent measurements without a reduction in performance. We anticipate that this hyperfine-resolved readout technique will benefit applications of state-of-the-art optical lattice clock comparisons in which the coherence times are constrained by Raman scattering or radiative decay.

Low-noise and tunable single-photon sources are essential components of photonic quantum technologies. However, in ${\mathrm{WSe}}_2$ quantum emitters, charge noise from fluctuations in their local electrostatic environment remains a major obstacle to achieving transform-limited single-photon emission and high photon indistinguishability. Here, we systematically investigate two noise mitigation strategies in hexagonal boron nitride ($h$-$\mathrm{BN}$): encapsulation and electrostatic biasing. We demonstrate that $h$-$\mathrm{BN}$ encapsulation alone suppresses spectral wandering (from $\sim 170\text{μ}\mathrm{eV}$ to $\sim 40\text{μ}\mathrm{eV}$) and narrows emission linewidths (from $\sim 524\text{μ}\mathrm{eV}$ to $\sim 120\text{μ}\mathrm{eV}$), while applied bias enables stable Stark tuning over a $280\text{μ}\mathrm{eV}$ range and further linewidth narrowing down to $\sim 100\text{μ}\mathrm{eV}$, reaching the resolution-limited regime. Time-resolved and second-order correlation measurements confirm stable monoexponential decay and high single-photon purity [$g^{(2)}(0)\sim 0.01$] with no observable blinking. To quantify progress toward the transform limit, we define two figures of merit—the linewidth ratio $R=W_{\exp }/W_{\mathrm{dec}}$ and total broadening $\mathrm{\Delta }W=W_{\exp }-W_{\mathrm{dec}}$—with both being reduced more than fivefold in optimized devices. These results provide a robust framework for developing and evaluating low-noise, tunable ${\mathrm{WSe}}_2$ quantum emitters, potentially realizing electrically controllable sources of indistinguishable single photons for future photonic quantum technologies.

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPSs) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPSs, as well as further relevant examples of MPSs including the $W$ state and the Dicke states in an approximate sense. Our findings motivate the usage of Ansätze simpler than tensor networks in systems whose structure is invariant under permutations.

We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical CCZ gate. Combined with a fold-transversal logical Hadamard gate, this enables a universal set of fault-tolerant operations using only transversal gates and qubit permutations. For the purpose of benchmarking under circuit-level noise, we develop an efficient method to simulate non-Clifford circuits with a small number of Hadamard gates. Separately, we demonstrate that certain CSS codes can be concatenated without measurements or having to rely on a universal logical gate set. This is made possible by means of a resource-efficient gadget—termed the “disposable Toffoli gadget”—that realizes the error-correcting feedback. Then, under concatenation of the Bacon-Shor code, we observe a fault-tolerance threshold at a circuit-level depolarizing noise rate of approximately $0.12\mathrm{\%}$. Together, the deformation and concatenation protocols outline a blueprint for a fully fault-tolerant architecture without any feed-forward operation, particularly suited to state-of-the-art neutral-atom platforms.

Optical quantum computing is a promising approach for achieving large-scale quantum computation. While Gaussian operations have been successfully scaled, the inherently weak nonlinearity in optics makes generating highly non-Gaussian states a critical challenge for universality and fault tolerance. Here, we propose and experimentally demonstrate a scalable method to generate optical non-Gaussian states with a resonator-based quantum memory that supports continuous-time storage and retrieval, in contrast to conventional loop-based memories. We introduce a dual-mode operation of the memory, enabling both storage and entangling functionalities within a single device. By employing a time-domain-multiplexed approach, we successfully demonstrate both cat and Gottesman-Kitaev-Preskill breeding protocols in a scalable fashion, marking a key step toward quantum error correction. Our experiment also marks the first full demonstration of an optical resonator memory performing writing, storage, and readout operations. We validate the memory by storing squeezed single-photon states with up to 93% total efficiency, and measure an energy relaxation time $T_1=2.3\text{μ}\mathrm{s}$ and dephasing time $T_{\varphi }=0.96\text{μ}\mathrm{s}$. These results establish a scalable pathway to generating complex non-Gaussian states required for fault-tolerant optical quantum computing. Beyond computation, our techniques provide new tools for enhancing quantum communication, sensing, and metrology.

The implementation of a quantum router capable of performing both quantum signal routing and quantum addressing (a ${\mathrm{Q}}^2$-router) represents a key step toward building quantum networks and quantum random access memories. We realize a ${\mathrm{Q}}^2$-router that uses fixed-frequency transmon qubits to implement a routing protocol based on two native controlled-$i$swap gates. These gates leverage a large $ZZ$ interaction to selectively route information according to a quantum address. We find an estimated average routing fidelity of $95.3\mathrm{\%}$, with errors arising primarily from decoherence or state preparation and measurement. We present a comprehensive calibration and characterization of both the c-$i$swap gates and the overall routing protocol through randomized benchmarking techniques and state tomography.