In advanced quantum processors, quantum operations are increasingly processed along multiple in-sequence measurements that result in classical data and affect the rest of the computation. Because of the information gain of classical measurements, nonunitary dynamical processes can affect the system, which common quantum channel descriptions fail to describe faithfully. Quantum measurements are correctly treated by so-called quantum instruments, capturing both classical outputs and postmeasurement quantum states. Here we present a general recipe for characterizing quantum instruments and demonstrate its experimental implementation and analysis. Thereby the full dynamics of a quantum instrument can be captured, exhibiting details of the quantum dynamics that would be overlooked with standard techniques. For illustration, we apply our characterization technique to a quantum instrument used for the detection of qubit loss and leakage, which was recently implemented as a building block in a quantum error-correction (QEC) experiment [Nature 585, 207 (2020)]. Our analysis reveals unexpected and in-depth information about the failure modes of the implementation of the quantum instrument. We then numerically study the implications of these experimental failure modes on QEC performance, when the instrument is employed as a building block in QEC protocols on a logical qubit. Our results highlight the importance of careful characterization and modeling of failure modes in quantum instruments, as compared to simplistic hardware-agnostic phenomenological noise models, which fail to predict the undesired behavior of faulty quantum instruments. The presented methods and results are directly applicable to generic quantum instruments and will be beneficial to many complex and high-precision applications.

We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix-product-state (QMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground states, known as fermionic Gaussian matrix-product states (GMPSs), with a polynomial reduction in qubit and (in select cases gate) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique, which we denote GMPS+X. We demonstrate this approach on Quantinuum’s System Model H1 trapped-ion quantum processor for one-dimensional (1D) models of correlated metal and Mott-insulating states. Focusing on the 1D Fermi-Hubbard chain as a benchmark, we show that GMPS+X methods faithfully capture the physics of correlated electron states, including Mott insulators and correlated Luttinger liquid metals, using considerably fewer parameters than problem-agnostic variational circuits.

Optical metasurfaces of subwavelength pillars have provided new capabilities for the versatile definition of the amplitude, phase, and polarization of light. In this work, we demonstrate that an efficient dielectric metasurface lens can be used to trap and image single neutral atoms with a long working distance from the lens of 3 mm. We characterize the high-numerical-aperture optical tweezers using the trapped atoms and compare with numerical computations of the metasurface-lens performance. We predict that future metasurfaces for atom trapping will be able to leverage multiple ongoing developments in metasurface design and enable multifunctional control in complex quantum information experiments with neutral-atom arrays.

We study quantum conditional entropy production, which quantifies the irreversibility of system-environment evolution from the perspective of a third system, called the reference. The reference is initially correlated with the system. We show that quantum unconditional entropy production with respect to the system is less than conditional entropy production with respect to the reference, where the latter includes reference-induced dissipative information. Dissipative information pinpoints the distributive correlation established between the environment and the reference, even though they do not interact directly. When reaching thermal equilibrium, the system-environment evolution has a zero unconditional entropy production. However, one can still have a nonzero conditional entropy production with respect to the reference, which characterizes the informational nonequilibrium of the system-environment evolution from the viewpoint of the reference. The additional contribution to conditional entropy production, dissipative information, characterizes a minimal thermodynamic cost that the system pays to maintain correlation with the reference. Positive dissipative information also characterizes potential work waste. We prove that both types of entropy production and dissipative information follow quantum fluctuation theorems when a two-point measurement is applied. We verify the quantum fluctuation theorem for dissipative information experimentally on IBM quantum computers. We also present examples based on the qubit collisional model and demonstrate universal nonzero dissipative information in the qubit Maxwell’s demon protocol.

We demonstrate a cavity-based solution to scale up experiments with ultracold atoms in optical lattices by an order of magnitude over state-of-the-art free-space lattices. Our two-dimensional (2D) optical lattices are created by power-enhancement cavities with large mode waists of $489(8)\mu \mathrm{m}$ and allow us to trap ultracold strontium atoms at a lattice depth of $60\mu \mathrm{K}$ by using only $80\mathrm{mW}$ of input light per cavity axis. We characterize these lattices using high-resolution clock spectroscopy and resolve carrier transitions between different vibrational levels. With these spectral features, we locally measure the lattice potential envelope and the sample temperature with a spatial resolution limited only by the optical resolution of the imaging system. The measured ground-band and trap lifetimes are $18(3)\mathrm{s}$ and $59(2)\mathrm{s}$, respectively, and the lattice frequency (depth) is long-term stable on the megahertz (0.1%) level. Our results show that large, deep, and stable 2D cavity-enhanced lattices can be created at any wavelength and can significantly increase the qubit number for neutral-atom-based quantum simulators, quantum computers, sensors, and optical-lattice clocks.

Deriving effective Hamiltonian models plays an essential role in quantum theory, with particular emphasis in recent years on control and engineering problems. In this work, we present two symbolic methods for computing effective Hamiltonian models: the nonperturbative analytical diagonalization (NPAD) and the recursive Schrieffer-Wolff transformation (RSWT). NPAD makes use of the Jacobi iteration and works without the assumptions of perturbation theory while retaining convergence, allowing us to treat a very wide range of models. In the perturbation regime, it reduces to RSWT, which takes advantage of an in-built recursive structure where, remarkably, the number of terms increases only linearly with the perturbation order, exponentially decreasing the number of terms compared to the ubiquitous Schrieffer-Wolff method. In this regime, NPAD further gives an exponential reduction in terms, i.e., superexponential compared to the Schrieffer-Wolff transformation, relevant to high-precision expansions. Both methods consist of algebraic expressions and can be easily automated for symbolic computation. To demonstrate the application of the methods, we study the $ZZ$ and cross-resonance interactions of superconducting qubit systems. We investigate both suppressing and engineering the coupling in near-resonant and quasidispersive regimes. With the proposed methods, the coupling strength in the effective Hamiltonians can be estimated with high precision comparable to numerical results.

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that, while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction of replicas, which requires an effort exponential in the number of replicas and which is costly in terms of memory. In contrast, our method requires the stochastic sampling of matrix elements of the classically represented reduced states with respect to random states drawn from simple product probability measures constituting frames. Even though not corresponding to physical operations, such matrix elements are straightforward to calculate for tensor network states, and their moments provide the Rényi entropies and negativities as well as their symmetry-resolved components. We test our method on the one-dimensional critical XX chain and the two-dimensional toric code in a checkerboard geometry. Although the cost is exponential in the subsystem size, it is sufficiently moderate so that—in contrast with other approaches—accurate results can be obtained on a personal computer for relatively large subsystem sizes.

We realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by a gate-defined quantum dot in an $\mathrm{In}\mathrm{As}$-$\mathrm{Al}$ nanowire. Microwave spectroscopy of the transition spectrum of the transmon allows us to probe the ground-state parity of the quantum dot as a function of the gate voltages, the external magnetic flux, and the magnetic field applied parallel to the nanowire. The measured parity phase diagram is in agreement with that predicted by a single-impurity Anderson model with superconducting leads. Through continuous-time monitoring of the circuit, we furthermore resolve the quasiparticle dynamics of the quantum dot Josephson junction across the phase boundaries. Our results can facilitate the realization of semiconductor-based $0$-$\pi$ qubits and Andreev qubits.

Geometric quantum gates are often expected to be more resilient than dynamical gates against certain types of error, which would make them ideal for robust quantum computing. However, this is still up for debate due to seemingly conflicting results in the literature. Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate. For any control Hamiltonian that produces a geometric gate, we find that, under certain common conditions, one can construct another control Hamiltonian that produces an equivalent dynamical gate with identical noise sensitivity (as characterized by the filter function). Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant single-qubit scenarios and providing explicit examples of equivalent geometric and dynamical gates.

Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches, and on-off detectors. We concatenate the topological quantum error-correction code with three-qubit repetition codes and estimate that our architecture can tolerate a remarkably high photon-loss rate of 11.5%; this makes a drastic change that is at least an order higher than those of known proposals. Furthermore, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of ${10}^{-6}({10}^{-15})$ to be $2.07\times {10}^6(5.03\times {10}^7)$. Compared to other all-photonic schemes, our architecture is also resource efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon-loss threshold and the recent progress in generating multiphoton entanglement, our scheme moves scalable photonic quantum computing a step closer to reality.

Quantum many-body systems are characterized by their correlations. While equal-time correlators and unequal-time commutators between operators are standard observables, the direct access to unequal-time anticommutators poses a formidable experimental challenge. Here, we propose a general technique for measuring unequal-time anticommutators using the linear response of a system to a non-Hermitian perturbation. We illustrate the protocol at the example of a Bose-Hubbard model, where the approach to thermal equilibrium in a closed quantum system can be tracked by measuring both sides of the fluctuation-dissipation relation. We relate the scheme to the quantum Zeno effect and weak measurements, and illustrate possible implementations at the example of a cold-atom system. Our proposal provides a way of characterizing dynamical correlations in quantum many-body systems with potential applications in understanding strongly correlated matter as well as for novel quantum technologies.

Machine learning is frequently listed among the most promising applications for quantum computing. This is in fact a curious choice: the machine-learning algorithms of today are notoriously powerful in practice but remain theoretically difficult to study. Quantum computing, in contrast, does not offer practical benchmarks on realistic scales and theory is the main tool we have to judge whether it could become relevant for a problem. In this perspective, we explain why it is so difficult to say something about the practical power of quantum computers for machine learning with the tools we are currently using. We argue that these challenges call for a critical debate on whether quantum advantage and that the narrative of “beating” classical machine learning should continue to dominate the literature in the way it does, and highlight examples for how other perspectives in existing research provide an important alternative to the focus on advantage.

Transmon qubits fabricated with tantalum metal have been shown to possess energy relaxation times greater than $400\mu \mathrm{s}$ and, as such, present an attractive platform for high precision, correlated noise studies across multiple higher-energy transitions. Tracking the multilevel fluctuating qudit frequencies with a precision enabled by the high coherence of the device allows us to extract the charge offset and quasiparticle dynamics. We observe qualitatively different charge-offset behavior in the tantalum device than those measured in previous low-frequency charge-noise studies. In particular, we find the charge-offset dynamics are dominated by rare, discrete jumps between a finite number of quasistationary charge configurations, a previously unobserved charge-noise process in superconducting qubits.

Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple characterizations of rank-$1$ projective measurements, mutually unbiased measurements, and symmetric informationally complete measurements. Notably, our conclusions do not rely on any assumption on the rank, purity, or the number of measurement outcomes, and we do not need bases to start with. Our work demonstrates that all these elementary quantum measurements are uniquely determined by their information-extraction capabilities, which are not even anticipated before. In addition, we offer a new perspective for understanding noncommutativity and incompatibility from tomographic performances, which also leads to a universal criterion for detecting quantum incompatibility. Furthermore, we show that the estimation fidelity can be used to distinguish inequivalent mutually unbiased bases and symmetric informationally complete measurements. In the course of study, we introduce the concept of (weighted complex projective) $1/2$-designs and show that all $1/2$-designs are tied to symmetric informationally complete measurements, and vice versa.

We present Rydberg-atom-array experiments performed to find the maximum independent sets of Platonic graphs. Three Platonic graphs—the tetrahedron, cube, and octahedron of Platonic solids—are constructed with atoms and Rydberg interatomic interactions, representing, respectively, the vertices and edges of the graphs. In particular, the three-dimensional Platonic graph structures are transformed onto the two-dimensional plane by using Rydberg quantum wires that couple otherwise uncoupled long-distance atoms. The maximum independent sets of the graphs correspond to the antiferrolike many-body ground-state spin configurations of the as-constructed Rydberg-atom arrays, which are successfully probed by quasiadiabatic control of the Rydberg-atom arrays from the paramagnetic phase to their antiferrolike phases. Our small-scale quantum simulations using fewer than 18 atoms are limited by experimental imperfections, which can be easily improved upon by the state-of-the-art Rydberg-atom technologies for scales of more than 1000 atoms. Our quantum-wire approach is expected to pave a new route toward large-scale quantum simulations.

The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert space with constraints on a planar lattice. Applying the quantum approximate optimization algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, we show that the implicit approach exhibits better QAOA performance. We propose a generalization of the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. Furthermore, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective $\cos 2\varphi$ elements that exchange “pairs of Cooper pairs” between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum. This protection window broadens upon increasing the number of interferometers if the individual elements are balanced. We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.

We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the $\nu =1/2$ bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.