The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations in which symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. Here, we construct explicit local unitary ensembles that can achieve high-order unitary $k$-designs under transversal continuous symmetry, in the particularly important $\mathrm{SU}(d)$ case. Specifically, we define the convolutional quantum alternating (CQA) group generated by 4-local $\mathrm{SU}(d)$-symmetric Hamiltonians as well as associated 4-local $\mathrm{SU}(d)$-symmetric random unitary circuit ensembles and prove that they form and converge to $\mathrm{SU}(d)$-symmetric $k$-designs, respectively, for all $k<n(n-3)/2$, with $n$ being the number of qudits. A key technique that we employ to obtain the results is the Okounkov-Vershik approach to $S_n$ representation theory. To study the convergence time of the CQA ensemble, we develop a numerical method using the Young orthogonal form and the $S_n$ branching rule. We provide strong evidence for a subconstant spectral gap and certain convergence time scales of various important circuit architectures, which contrast with the symmetry-free case. We also provide comprehensive explanations of the difficulties and limitations in rigorously analyzing the convergence time using methods that have been effective for cases without symmetries, including Knabe’s local gap threshold and Nachtergaele’s martingale methods. This suggests that a novel approach is likely necessary for understanding the convergence time of $\mathrm{SU}(d)$-symmetric local random circuits.

In this work, we show that the kinetically constrained quantum East model lies between a quantum scarred and a many-body localized system featuring an unconventional type of mobility edge in the spectrum. We name this scenario the state-dependent mobility edge: while the system does not exhibit a sharp separation in energy between thermal and nonthermal eigenstates, the abundance of nonthermal eigenstates results in slow entanglement growth for many initial states, such as product states, below a finite energy density. We characterize the state-dependent mobility edge by looking at the complexity of classically simulating dynamics using tensor networks for system sizes well beyond those accessible via exact diagonalization. Focusing on initial product states, we observe a qualitative change in the dynamics of the bond dimension needed as a function of their energy density. Specifically, the bond dimension typically grows polynomially in time up to a certain energy density, where we locate the state-dependent mobility edge, enabling simulations for long times. Above this energy density, the bond dimension typically grows exponentially, making the simulation practically unfeasible beyond short times, as generally expected in interacting theories. We correlate the polynomial growth of the bond dimension to the presence of many nonthermal eigenstates around that energy density, a subset of which we compute via tensor networks. The outreach of our findings encompasses quantum sampling problems and the efficient simulation of quantum circuits beyond Clifford families.

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2), and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as $\mathrm{T}$-gate counts and logical qubit counts for Hamiltonian simulation. We find a reduction of up to 25 orders of magnitude in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods, which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first-principles quantum simulation of chemistry.

We show that combining ideas from the fields of quantum invariants and optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. The states are specified only implicitly in terms of operators to which they are eigenstates. The scaling in numerical effort of the resultant approach is not given by the typically exponentially growing effort required for the specification of a time-evolved quantum state, but it is given by the effort required for the specification of a time-evolved operator. For certain Hamiltonians, this effort can be polynomial in the system size. We describe how control problems for state preparation and the realization of propagators can be formulated in this approach, and we provide explicit control solutions for a spin chain with an extended Ising Hamiltonian. The states considered for state-preparation protocols include eigenstates of Hamiltonians with more than pairwise interactions and these Hamiltonians are also used for the definition of target propagators. The cost of describing suitable time-evolving operators grows only quadratically with the system size, allowing us to construct explicit control solutions for up to $50$ spins. While subexponential scaling is obtained only in special cases, we provide several examples that demonstrate favorable scaling beyond the extended Ising model.

Multimode quantum light is enticing for several applications, spanning imaging, spectroscopy, communication, and more. Parametric nonlinear processes have been vital in realizing squeezed and other quantum states of light. However, most work exploiting these processes has focused on generating multimode squeezed vacua and squeezing in mode superpositions (supermodes). Bright squeezing in multiple discrete frequency modes, if realized, could unlock novel applications in quantum-enhanced spectroscopy and optical quantum computing. Here, we show how dissipation engineering of a multimode nonlinear cavity with cascaded three-wave-mixing processes allows us to shape above-threshold frequency combs that feature strong single-mode output amplitude noise squeezing over 10 dB below the shot-noise limit, tunable across the comb. In addition, we demonstrate squeezing for multiple discrete frequency modes above threshold. This bright squeezing arises from enhancement of the (noiseless) nonlinear rate relative to decay rates in the system due to the cascaded generation of photons in a single idler “bath” mode. A natural consequence of the strong nonlinear coupling in our system is the creation of an effective cavity in the synthetic frequency dimension that sustains Bloch oscillations in the modal energy distribution. Bloch mode engineering could provide an opportunity to better control nonlinear energy flow in the synthetic frequency dimension, with exciting applications in quantum random walks and topological photonics. Lastly, we show evidence of long-range correlations in amplitude noise between discrete frequency modes, enabling long-range entanglement in a synthetic frequency dimension and providing a new resource for quantum communication.

Unitary $t$-designs are distributions on the unitary group whose first $t$ moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate $t$-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate $t$-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.

Atom-loss errors are a major limitation of current state-of-the-art neutral-atom quantum computers and pose a significant challenge for scalable systems. In a quantum processor with cesium atoms, we demonstrate proof-of-principle circuit-based conversion of this form of leakage error to erasure errors via leakage-detection units (LDUs), which nondestructively map information about the presence or absence of the qubit onto the state of an ancilla. We benchmark the performance of the LDU using a three-outcome low-loss state-detection method and find that the LDU detects atom-loss errors with approximately 93.4% accuracy, limited by technical imperfections of our apparatus. We further compile and execute a swap LDU, wherein the roles of the original data atom and ancilla atom are exchanged under the action of the LDU, providing “free refilling” of atoms in the case of atom loss. This circuit-based leakage-to-erasure error conversion is a critical component of a neutral-atom quantum processor where the quantum information may significantly outlive the lifetime of any individual atom in the quantum register. Finally, we demonstrate that LDUs may also be used to handle other forms of leakage errors where population moves to states outside of the computational subspace.

Qubit decoherence unavoidably degrades the fidelity of quantum logic gates. Accordingly, realizing gates that are as fast as possible is a guiding principle for qubit control, necessitating protocols for mitigating error channels that become significant as gate time is decreased. One such error channel arises from the counter-rotating component of strong, linearly polarized drives. This error channel is particularly important when gate times approach the qubit Larmor period and represents the dominant source of infidelity for sufficiently fast single-qubit gates with low-frequency qubits such as fluxonium. In this work, we develop and demonstrate two complementary protocols for mitigating this error channel. The first protocol realizes circularly polarized driving in circuit QED through simultaneous charge and flux control. The second protocol—commensurate pulses—leverages the coherent and periodic nature of counter-rotating fields to regularize their contributions to gates, enabling single-qubit gate fidelities reliably exceeding 99.997%. This protocol is platform independent and requires no additional calibration overhead. This work establishes straightforward strategies for mitigating counter-rotating effects from strong drives in circuit QED and other platforms, which we expect to be helpful in the effort to realize high-fidelity control for fault-tolerant quantum computing.

The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control and optical bilayer capabilities combined with spatially resolved measurements create a versatile toolbox to study fundamental properties of both nickelate and cuprate high-temperature superconductors. On the one hand, we present a scheme to implement a mixed-dimensional (mixD) bilayer model that has been proposed to capture the essential pairing physics of pressurized bilayer nickelates. This allows for the long-sought realization of a state with long-range superconducting order in current lattice quantum simulation machines. In particular, we show how coherent pairing correlations can be accessed in a partially particle-hole transformed and rotated basis. On the other hand, we demonstrate that control of local gates enables the observation of $d$-wave pairing order in the two-dimensional (single-layer) repulsive Fermi-Hubbard model through the simulation of a system with attractive interactions. Lastly, we introduce a scheme to measure momentum-resolved dopant densities, providing access to observables complementary to solid-state experiments—which is of particular interest for future studies of the enigmatic pseudogap phase appearing in cuprates.

Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computation. While conventional methods use a number of extra qubits that are linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a framework to design flag gadgets using classical codes. Using this framework, we show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance using exponentially fewer qubits than conventional methods when qubit measurement and reset are relatively slow compared to a round of error correction. In particular, our method requires only $(2t+1)t\lceil {\log }_2(w)\rceil$ flag qubits to fault-tolerantly measure a weight-$w$ stabilizer. We further take advantage of the saving provided by our construction to fault-tolerantly measure multiple stabilizers using a single gadget and show that it maintains the same exponential advantage when it is used to fault-tolerantly extract the syndromes of quantum low-density parity-check codes. Using the developed framework, we perform computer-assisted search to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers.

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground-state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that prepares and quantifies the quality of initial states, accomplishing the latter with a new metric—the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates: such an improvement can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage.

Experimental advances in cavity QED are raising the prospect of using light to probe quantum materials beyond the linear response regime. The capability to access quantum coherent phenomena would significantly advance the field. However, theoretical work on many-body systems coupled to light in the quantum coherent regime has been select. Here, we investigate the radiative properties of a finite-sized quantum wire in a microwave cavity. Examples of quantum wires include single-walled carbon nanotubes, a key experimental system in the field of nano-optics and plasmonics. We find that, for a variety of excited states, the repeated emission of photons results in the generation of many-body quantum entanglement. This leads to an increase in the rate at which subsequent photons are emitted, an example of Dicke superradiance. On the other hand, Pauli blocking tends to reduce this effect. Bosonization, the description of the excitations of a one-dimensional electron system as a gas of bosons, is found to be a powerful theoretical tool in this context. Its application means that many of our results generalize to wires with strong electron-electron interactions. The quantum wire thus represents a new platform to realize Dicke-model physics that does not rely on the various fine tunings necessary in traditional realizations involving many spatially isolated emitters. More broadly, this work demonstrates how quantum entanglement can be generated and measured in a many-body system.

Bosonic modes are prevalent in all aspects of quantum information processing. However, existing tools for characterizing the quality, stability, and noise properties of bosonic modes are limited, especially in a driven setting. Here, we propose, demonstrate, and analyze a randomized bosonic benchmarking (RBB) protocol that uses randomized displacements of the bosonic modes in phase space to determine their quality. We investigate the impact of common analytical error models, such as heating and dephasing, on the distribution of outcomes over randomized displacement trajectories in phase space. We show that analyzing the distinctive behavior of the mean and variance of this distribution—describable as a gamma distribution—enables identification of error processes, and quantitative extraction of error rates and correlations using a minimal number of measurements. We experimentally validate the analytical models by injecting engineered noise into the motional mode of a trapped-ion system and performing the RBB protocol, showing good agreement between experiment and theory. Finally, we investigate the intrinsic error properties in our system, identifying the presence of highly correlated dephasing noise as the dominant process.

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is “strongly symmetric,” i.e., it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qudits $N$.

Ultracold atomic systems are among the most promising platforms that have the potential to shed light on the complex behavior of many-body quantum systems. One prominent example is the case of a dense ensemble illuminated by a strong coherent drive while interacting via dipole-dipole interactions. Despite being subjected to intense investigations, this system retains many open questions. A recent experiment carried out in a pencil-shaped geometry [Ferioli et al. Nat. Phys. 19, 1345 (2023)] has reported measurements that have seemed consistent with the emergence of strong collective effects in the form of a “superradiant” phase transition in free space, when looking at the light-emission properties in the forward direction. Motivated by the experimental observations, we carry out a systematic theoretical analysis of the steady-state properties of the system as a function of the driving strength and atom number $N$. We observe signatures of collective effects in the weak-driving regime, which disappear with increasing drive strength as the system evolves into a single-particle-like mixed state comprised of randomly aligned dipoles. Although the steady state features some similarities to the reported superradiant-to-normal nonequilibrium transition, also known as cooperative resonance fluorescence, we observe significant qualitative and quantitative differences, including a different scaling of the critical drive parameter (from $N$ to $\sqrt{N}$). We validate the applicability of a mean-field treatment to capture the steady-state dynamics under currently accessible conditions. Furthermore, we develop a simple theoretical model that explains the scaling properties by accounting for interaction-induced inhomogeneous effects and spontaneous emission, which are intrinsic features of interacting disordered arrays in free space.

Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid-state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also further restrict the connectivity, resulting in a relatively sparse graph such as the heavy-hexagonal (“heavy-hex”) architecture of current IBM Quantum devices. In such cases, it is hard to use all qubits to their full potential. Instead, in order to emulate the denser connectivity required to implement well-known quantum error-correcting codes, many qubits remain effectively unused. In this work, we show how this bug can be turned into a feature. By using the unused qubits of one code to execute another, two codes can be implemented on top of each other, allowing easy application of fault-tolerant entangling gates and measurements. We demonstrate this by realizing a surface code and a Bacon-Shor code on a 133-qubit IBM Quantum device. Using transversal controlled-$X$ (cx) gates and lattice surgery, we demonstrate entanglement between these logical qubits with code distance up to $d=4$ and five rounds of stabilizer-measurement cycles. The nonplanar coupling between the qubits allows us to simultaneously measure the logical $XX$, $YY$, and $ZZ$ observables. With this, we verify the violation of Bell’s inequality for both the $d=2$ case with postselection featuring a fidelity of 94% and the $d=3$ instance using only quantum error correction.

Cavity quantum electrodynamics offers the possibility of observing and controlling the motion of a few or individual atoms, enabling the realization of various quantum technological tasks such as quantum enhanced metrology or quantum simulation of strongly correlated matter. A core limitation of these experiments lies in the mode structure of the cavity field, which is hard coded in the shape and geometry of the mirrors. As a result, most applications of cavity QED trade spatial resolution for enhanced sensitivity. Here, we propose and demonstrate a cavity-microscope device capable of controlling in space and time the coupling between atoms and light in a single-mode high-finesse cavity, reaching a spatial resolution an order of magnitude lower than the cavity-mode waist. This is achieved through local Floquet engineering of the atomic level structure, imprinting a corresponding atom-field coupling. We illustrate this capability by engineering micrometer-scale coupling, using cavity-assisted atomic measurements and optimization. Our system forms an optical device with a single optical axis, has the same footprint and complexity as a standard Fabry-Perot cavity or confocal lens pair, and can be used for any atomic species. This technique opens a wide range of perspectives, from ultrafast cavity-enhanced midcircuit readout to the quantum simulation of fully connected models of quantum matter such as the Sachdev-Ye-Kitaev model.

Experimental platforms based on ultracold atomic gases have significantly advanced the quantum simulation of complex systems, yet the exploration of phenomena driven by long-range interactions remains a formidable challenge. Currently available methods utilizing dipolar quantum gases or multimode cavities allow us to implement long-range interactions with a $1/r^3$ character or with a spatial profile fixed by the mode structure of the vacuum electromagnetic field surrounding the atoms, respectively. Here, we propose an experimental scheme employing laser-painted cavity-mediated interactions, which enables the realization of atom-atom interactions that are fully tunable in range, shape, and sign. Our approach combines the versatility of cavity quantum electrodynamics with the precision of laser manipulation, thus providing a highly flexible platform for simulating and understanding long-range interactions in quantum many-body systems. Our analytical predictions are supported by numerical simulations describing the full dynamics of the atoms, the laser, and the cavity. These reveal the self-organization of domains in the density of the atomic cloud, confirming the finite-range nature of the induced interactions. We demonstrate that there is a wide and experimentally accessible parameter regime in which our protocol works robustly, with negligible heating of the quantum gas. The methodology not only paves the way for exploring new territories in quantum simulation but also enhances the understanding of fundamental physics, potentially leading to the discovery of novel quantum states and phases.

Entanglement is a valuable resource in quantum information technologies. The practical implementation of entangled photon sources faces obstacles from imperfections and defects inherent in physical systems, resulting in a loss or degradation of entanglement. The topological photonic insulators, however, have emerged as promising candidates, demonstrating an exceptional capability to resist defect-induced scattering, thus enabling the development of robust entangled sources. Despite their inherent advantages, building programmable topologically protected entangled sources remains challenging due to complex device designs and weak material nonlinearity. Here, we present a development in entangled photon-pair generation achieved through a nonmagnetic and tunable anomalous Floquet insulator, utilizing an optical spontaneous four-wave-mixing process. We verify the nonclassicality and time-energy entanglement of the photons generated by our topological system. Our experiment demonstrates a substantial enhancement in nonclassical photon-pair generation compared to devices reliant only on topological edge states. Our results could lead to the development of resilient quantum sources with potential applications in quantum technology.

Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as ${\mathbb{Z}}_2$, $U(1)$, and $SU(2)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U(1)$ symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality.