We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than ${10}^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.

Quantum embedding methods have become powerful tools to overcome the deficiencies of traditional quantum modeling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to achieve rigorous convergence and often necessary to employ empirical parameters. Here, we formulate a quantum embedding theory, building on the methods of density-matrix embedding theory combined with local correlation approaches from quantum chemistry, to ensure the ability to systematically converge properties of real materials with accurate correlated wave-function methods controlled by a single, rapidly convergent parameter. By expanding supercell size, basis set, and the resolution of the fluctuation space of an embedded fragment, we show that the systematic improvability of the approach yields accurate structural and electronic properties of realistic solids without empirical parameters, even across changes in geometry. The results are presented in insulating, semimetallic, and more strongly correlated regimes, finding state-of-the-art agreement with experimental data.

The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling, $S(\ell )\sim {\ell }^{\alpha }$ with tunable $0<\alpha <1$ for subsystems of size $\ell$ in one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive firing. In networks of neurons with current-based synapses, the balanced state emerges dynamically if coupling is strong, i.e., if the mean number of synapses per neuron $K$ is large and synaptic efficacy is of the order of $1/\sqrt{K}$. When synapses are conductance-based, current fluctuations are suppressed when coupling is strong, questioning the applicability of the balanced state idea to biological neural networks. We analyze networks of strongly coupled conductance-based neurons and show that asynchronous irregular activity and broad distributions of rates emerge if synaptic efficacy is of the order of $1/\log (K)$. In such networks, unlike in the standard balanced state model, current fluctuations are small and firing is maintained by a drift-diffusion balance. This balance emerges dynamically, without fine-tuning, if inputs are smaller than a critical value, which depends on synaptic time constants and coupling strength, and is significantly more robust to connection heterogeneities than the classical balanced state model. Our analysis makes experimentally testable predictions of how the network response properties should evolve as input increases.

Many two-dimensional physical systems ranging from atomic-molecular condensates to low-dimensional superconductors and liquid-crystal films are described by coupled XY models. The interplay of topology and competing interactions in these XY systems drives new kinds of emergent behavior relevant in both quantum and classical settings. Such coupled U(1) systems further introduce rich physics, bringing topology into contact with fractionalization and deconfinement. Motivated by a hidden-order phase transition in isotropic liquid-crystal 54COOBC films, we study the finite-temperature phase diagram of a minimalist hexatic-nematic XY model. We identify a small region of composite Potts order above the vortex-binding transition; this phase is characterized by relative hexatic-nematic ordering though both variables are disordered. We propose that the Potts order results from a confinement of fractional vortices into extended nematic defects and discuss the broader implications of fractional vortices and composite ordering in the wider class of coupled XY condensates.

From enzyme binding to robot grasping, the function of many mechanical systems depends upon large, coordinated motions of their components. Such motions arise from a network of physical interactions in the form of links (edges) that transmit forces between constituent elements (nodes) and have been fruitfully modeled in known networks. However, the principled design of precise motions in novel networks is made difficult by the number and nonlinearity of interactions. Here, we formulate a simple but powerful framework for designing fully nonlinear motions using concepts from dynamical systems theory. We demonstrate that a small network unit acts as a one-dimensional map between the distances across pairs of nodes, and we represent the act of combining units as an iteration of this map. By tying the map’s attractors and their stability to the shape and folding sequence in a network of combined units, we program the precise coordinated motion between arbitrarily complex macroscopic shapes, the exact folding sequence between the shapes, and exotic network behaviors such as a mechanical and gate and a period-doubling route to chaos. Further, we construct a unit with a 3-cycle that combines to form a lattice with any positive integer period as a result of Sharkovskii’s theorem. Finally, we construct physical networks and analyze the effect of bond elasticity to demonstrate the framework’s potential and versatility. The precise design of shape change and folding sequence makes this framework ideal as a starting minimal model for many applications, such as robotics, providing a promising direction for future work in metamaterials.

Ultracold atomic gas provides a useful tool to explore many-body physics. One of the recent additions to this experimental toolbox is Floquet engineering, where periodic modulation of the Hamiltonian allows the creation of effective potentials that do not exist otherwise. When subject to external modulations, however, generic interacting many-body systems absorb energy, thus posing a heating problem that may impair the usefulness of this method. For discrete systems with bounded local energy, an exponentially suppressed heating rate with driving frequency has been observed previously, leaving the system in a prethermal state for exceedingly long durations. However, for systems in continuous space, the situation remains unclear. Here, we show that Floquet engineering can be applied to a strongly interacting degenerate Fermi gas held in a flat boxlike potential without inducing excessive heating on experimentally relevant timescales. The driving eliminates the effect of a spin-dependent potential originating from the simultaneous magnetic levitation of two different spin states. We calculate the heating rate and obtain a power-law suppression with the drive frequency. To further test the many-body behavior of the driven gas, we measure both the pair-condensation fraction at unitarity and the contact parameter across the BEC-BCS crossover. At low driving frequencies, the condensate fraction is reduced by the time-dependent force, but at higher frequencies, it revives and attains an even higher value than without driving. Our results are promising for future exploration of exotic many-body phases of a bulk strongly interacting Fermi gas with dynamically engineered Hamiltonians.

Quantum processing architectures that include multiple qubit modalities offer compelling strategies for high-fidelity operations and readout, quantum error correction, and a path for scaling to large system sizes. Such hybrid architectures have been realized for leading platforms, including superconducting circuits and trapped ions. Recently, a new approach for constructing large, coherent quantum processors has emerged based on arrays of individually trapped neutral atoms. However, these demonstrations have been limited to arrays of a single atomic element where the identical nature of the atoms makes crosstalk-free control and nondemolition readout of a large number of atomic qubits challenging. Here we introduce a dual-element atom array with individual control of single rubidium and cesium atoms. We demonstrate their independent placement in arrays with up to 512 trapping sites and observe negligible crosstalk between the two elements. Furthermore, by continuously reloading one atomic element while maintaining an array of the other, we demonstrate a new continuous operation mode for atom arrays without any off-time. Our results enable avenues for auxiliary-qubit-assisted quantum protocols such as quantum nondemolition measurements and quantum error correction, as well as continuously operating quantum processors and sensors.

We derive fundamental bounds on the maximal achievable precision in multiparameter noisy quantum metrology, valid under the most general entanglement-assisted adaptive strategy, which are tighter than the bounds obtained by a direct use of single-parameter results. This allows us to study the issue of the optimal probe incompatibility in the simultaneous estimation of multiple parameters in generic noisy channels, while so far the issue has been studied mostly in effectively noiseless scenarios (where the Heisenberg scaling is possible). We apply our results to the estimation of both unitary and noise parameters and indicate models where the fundamental probe incompatibility is present. In particular, we show that in lossy multiple-arm interferometry the probe incompatibility is as strong as in the noiseless scenario, reducing the potential advantage of simultaneous estimation to a constant factor. Finally, going beyond the multiparameter estimation paradigm, we introduce the concept of random quantum sensing and show how the tools developed may be applied to multiple-channel discrimination problems. As an illustration, we provide a simple proof of the loss of the quadratic advantage of the time-continuous Grover algorithm in the presence of dephasing or erasure noise.

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

We report measurements of the Seebeck effect in both the $ab$ plane ($S_a$) and along the $c$ axis ($S_c$) of the cuprate superconductor ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (Nd-LSCO), performed in magnetic fields large enough to suppress superconductivity down to low temperature. We use the Seebeck coefficient as a probe of the particle-hole asymmetry of the electronic structure across the pseudogap critical doping $p^{\star }=0.23$. Outside the pseudogap phase, at $p=0.24>p^{\star }$, we observe a positive and essentially isotropic Seebeck coefficient as $T\to 0$. That $S>0$ at $p=0.24$ is at odds with expectations given the electronic band structure of Nd-LSCO above $p^{\star }$ and its known electronlike Fermi surface. We can reconcile this observation by invoking an energy-dependent scattering rate with a particle-hole asymmetry, possibly rooted in the non-Fermi-liquid nature of cuprates just above $p^{\star }$. Inside the pseudogap phase, for $p<p^{\star }$, $S_a$ is seen to rise at low temperature as previously reported, consistent with the drop in carrier density $n$ from $n\simeq 1+p$ to $n\simeq p$ across $p^{\star }$ as inferred from other transport properties. In stark contrast, $S_c$ at low temperature becomes negative below $p^{\star }$, a novel signature of the pseudogap phase. The sudden drop in $S_c$ reveals a change in the electronic structure of Nd-LSCO upon crossing $p^{\star }$. We can exclude a profound change of the scattering across $p^{\star }$ and conclude that the change in the out-of-plane Seebeck coefficient originates from a transformation of the Fermi surface.

The interaction of ultraintense laser pulses with an underdense plasma is used in laser-plasma acceleration to create compact sources of ultrashort pulses of relativistic electrons and x rays. The accelerating structure is a plasma wave, or wakefield, that is excited by the laser ponderomotive force, a force that is usually assumed to depend solely on the laser envelope and not on its exact waveform. Here, we use near-single-cycle laser pulses with a controlled carrier-envelope phase to show that the actual waveform of the laser field has a clear impact on the plasma response. The beam pointing of our relativistic electron beam oscillates in phase with the carrier-envelope phase of the laser, at an amplitude of 15 mrad, or 30% of the beam divergence. Numerical simulations explain this observation through asymmetries in the injection and acceleration of the electron beam, which are locked to the carrier-envelope phase. These results imply that we achieve waveform control of relativistic electron dynamics. Our results pave the way to high-precision, subcycle control of electron injection in plasma accelerators, enabling the production of attosecond relativistic electron bunches and x rays.

A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there. Despite the central role played by Anderson localization in the modern understanding of condensed matter, this “quantum boomerang” effect, an essential feature of the localized state, was only recently theoretically predicted. We report the experimental observation of the quantum boomerang effect. Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries. Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears. Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics. These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

Recent theoretical studies inspired by experiments on the Kitaev magnet $\alpha \text{−}{\mathrm{RuCl}}_3$ highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here, we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent region with quantized or negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and, most interestingly, (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

Topological materials have drawn increasing attention owing to their rich quantum properties, as highlighted by a large intrinsic anomalous Hall effect (AHE) in Weyl and nodal-line semimetals. However, the practical applications for topological electronics have been hampered by the difficulty in the external control of their band topology. Here, we demonstrate a magnetic-field-induced switching of band topology in $\alpha \text{−}{\mathrm{EuP}}_3$, a magnetic semimetal with a layered crystal structure derived from black phosphorus. When the magnetic field is applied perpendicular to the single mirror plane of the monoclinic structure, a giant AHE signal abruptly emerges at a certain threshold magnetization value, giving rise to a prominently large anomalous Hall angle of $|{\mathrm{\Theta }}_{\mathrm{AHE}}|\sim 20°$. On the other hand, when the magnetic field is applied along the interlayer direction, which breaks the mirror symmetry, the system shows a pronounced negative longitudinal magnetoresistance. Based on first-principles calculations and group-theoretic analysis, we show that such nontrivial anomalies in the magnetotransport properties are manifestations of two distinct topological phases: topological nodal-line and Weyl semimetals, respectively. Notably, the nodal-line structure is composed of bands with the same spin character and spans a wide energy range around the Fermi level. These topological phases are stabilized via the exchange coupling between localized $\mathrm{Eu}\text{−}4f$ moments and mobile carriers conducting through the phosphorus layers. Our findings provide a realistic solution for external manipulation of band topology, enriching the functional aspects of topological materials.

Quantum error correction requires the detection of errors via reliable measurements of multiqubit correlation operators. As these operations are inherently faulty, fault-tolerant schemes for realizing quantum error correction are required. Recently, a paradigm requiring only minimal resource overhead in the form of “flag” qubits to detect and correct errors has been proposed. We experimentally demonstrate a fault-tolerant weight-4 parity-check measurement scheme, where one additional flag qubit serves to detect errors, which would otherwise proliferate into uncorrectable weight-2 errors onto the qubit register. We achieve a parity measurement fidelity of 92.3(2)%, which increases to 93.2(2)% upon conditioning to the flag readout result, which shows that the measurement scheme intercepts intrinsic errors occurring throughout the sequence. We show that the protocol is capable of reliably intercepting faults by deliberately injecting bit- and phase-flip errors. For holistic benchmarking of the parity measurement scheme, we use an entanglement witnessing scheme requiring a minimal number of measurements to verify genuine six-qubit multipartite entanglement. The demonstrated fault-tolerant parity measurement scheme constitutes the key building block in a broad class of resource-efficient flag-based quantum error correction protocols including topological color codes. Our hardware platform is based on atomic ions stored in a microchip ion trap. The qubit register is dynamically reconfigured via shuttling operations enabling effective full connectivity without operational cross talk, thereby providing key prerequisites underlying fault-tolerant circuit design. These architectural features in combination with the demonstrated approach to flag-based fault-tolerant quantum error correction open up a route toward scalable fault-tolerant quantum computing.

We experimentally study the emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\mathcal{H}$ and angular momentum $\mathcal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\widehat{\beta }$ and rotation frequency $\widehat{\omega }$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies, the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.