We study the mixing time of a recently proposed efficiently implementable Lindbladian designed to prepare the Gibbs states in the setting of weakly interacting fermionic systems. We show that at any temperature, the Lindbladian spectral gap for even parity observables is lower bounded by a constant $\mathrm{\Delta }$, when the interaction strength (e.g., the on-site interaction strength for the Fermi-Hubbard model) is below a constant threshold $U_{\beta }$. Both $\mathrm{\Delta }$ and $U_{\beta }$ are independent of the system size. This leads to a mixing time estimate that is at most linear in the system size, thus showing that the corresponding Gibbs states can be prepared efficiently on quantum computers. Our result also implies exponential decay of correlation in these Gibbs states and efficient learnability of their properties.

While experimental measurements of photon correlations have become routine in laboratories, theoretical access to these quantities for the light generated in complex nanophotonic devices remains a major challenge. Current methods are limited to specific simplified cases and lack generality. Here we present a novel method that provides access to photon statistics resolved in space and frequency in arbitrary electromagnetic environments. Within the macroscopic QED framework, we develop a practical tool to compute electric field correlations for complex quantum systems by including lossy two-level systems that act as field detectors within the system. To make the implementation feasible, we use a recently developed multiemitter few-mode quantization method to correctly account for fully retarded light propagation to the detectors. We demonstrate the effectiveness and robustness of the proposed technique by studying the photon correlations of one and two emitters in close proximity to a plasmonic nanoparticle. The simulations show that even in these relatively simple configurations, the light statistics exhibit a strong angular dependence. These results highlight the importance of going beyond conventional quantum optical approaches to fully capture the analyzed physical effects and enable the study of the quantum light generation in realistic nanophotonic devices.

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We introduce a novel algorithm that combines tensor networks and quantum computation to produce results that are more accurate than what could be achieved by either method used in isolation. Our algorithm is based on multiproduct formulas (MPFs)—a technique that linearly combines Trotter product formulas to reduce algorithmic error. It uses a quantum computer to calculate the expectation values and tensor networks to calculate the coefficients used in the linear combination. We present a detailed error analysis of the algorithm and demonstrate the full workflow on a one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum computers, ibm_torino and ibm_kyiv.

The robustness of topological properties, such as quantized currents, generally depends on the existence of gaps surrounding the relevant energy levels or on symmetry-forbidden transitions. Here, we observe quantized currents that survive the addition of bounded local disorder beyond the closing of the relevant instantaneous energy gaps in a driven Aubry-André-Harper chain, a prototypical model of quasiperiodic systems. We explain the robustness using a local picture in configuration space based on Landau-Zener transitions, which rests on the Anderson localization of the eigenstates. Moreover, we propose a protocol, directly realizable in, for instance, cold atoms or photonic experiments, that leverages this stability to prepare topological many-body states with high Chern numbers and opens new experimental avenues for the study of both the integer and fractional quantum Hall effects.

We develop double microwave shielding, which has recently enabled evaporative cooling to the first Bose-Einstein condensate of polar molecules [Bigagli et al., Nature 631, 289 (2024)]. Two microwave fields of different frequency and polarization are employed to effectively shield polar molecules from inelastic collisions and three-body recombination. Here, we describe in detail the theory of double microwave shielding. We demonstrate that double microwave shielding effectively suppresses two- and three-body losses. Simultaneously, dipolar interactions and the scattering length can be flexibly tuned, enabling comprehensive control over interactions in ultracold gases of polar molecules. We show that this approach works universally for a wide range of molecules. This opens the door to studying many-body physics with strongly interacting dipolar quantum matter.

The Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation. However, direct methods to increase its logical dimensions, such as lattice surgery or introducing punctures, often incur prohibitive overheads. In this work, we introduce a ring-theoretic approach for efficiently analyzing topological CSS codes in two dimensions, enabling the exploration of generalized toric codes with larger logical dimensions on twisted tori. Using Gröbner bases, we simplify stabilizer syndromes to efficiently identify anyon excitations and their geometric periodicities, even under twisted periodic boundary conditions. Since the properties of the codes are determined by the anyons, this approach allows us to directly compute the logical dimensions without constructing large parity-check matrices. Our approach provides a unified method for finding new quantum error-correcting codes and exhibiting their underlying topological orders via the Laurent polynomial ring. This framework naturally applies to bivariate bicycle codes. For example, we construct optimal weight-6 generalized toric codes on twisted tori with parameters $[[n,k,d]]$ for $n\le 400$, yielding novel codes such as $[[120,8,12]]$, $[[186,10,14]]$, $[[210,10,16]]$, $[[248,10,18]]$, $[[254,14,16]]$, $[[294,10,20]]$, $[[310,10,\le 22]]$, and $[[340,16,18]]$. Moreover, we present a new realization of the $[[360,12,\le 24]]$ quantum code using the $(3,3)$-bivariate bicycle code on a twisted torus defined by the basis vectors $(0,30)$ and $(6,6)$, improving stabilizer locality relative to the previous construction. These results highlight the power of the topological order perspective in advancing the design and theoretical understanding of quantum low-density parity-check (LDPC) codes.

Magic state distillation (MSD) is an essential element for universal fault-tolerant quantum computing, which distills a high-fidelity magic state from noisy magic states using ideal (error-corrected) Clifford operations. For ideal Clifford operations, it needs to be performed on the logical qubits and hence incurs a large spatiotemporal overhead, which is one of the major bottlenecks for the realization of fault-tolerant quantum computers (FTQCs). Here we propose zero-level distillation, which prepares a high-fidelity logical magic state at the physical level, namely zero level, using physical qubits and nearest-neighbor two-qubit gates on a square lattice. We develop a zero-level distillation circuit and show that distillation can be made even more efficient than the conventional sophisticated approaches with logical level distillations. The key idea involves the Knill et al.-type distillation using the Steane code and its careful mapping to the square-lattice architecture with error detection. The distilled magic state on the Steane-code state is then teleported or converted to surface codes. We numerically find that the error rate of the logical magic state scales as approximately $100\times p^2$ in terms of the physical error rate $p$. For example, with a physical error rate of $p={10}^{-4}$ (${10}^{-3}$), the logical error rate is reduced to $p_L={10}^{-6}$ (${10}^{-4}$), resulting in an improvement of 2 (1) orders of magnitude. This contributes to reducing both space and time overhead for early FTQC as well as full-fledged FTQC combined with conventional multilevel distillation protocols.

Quantum measurement is performed by coupling a quantity $\hat{A}$ of a system to a “meter” and reading the meter. In the regime of strong measurement, the possible outcomes and the final state are entirely defined by $\hat{A}$, with probabilities dictated by the initial state. In this work, we will be interested in the regime in which a strong self-Hamiltonian, and not the coupling, defines the measurement outcomes and the final state. In this regime, the expectation value of any arbitrary set of observables can be measured in a quantum nondemolition (QND) way without reset or repreparation of the state. We discuss applications that include single-shot measurement of the expectation value of all noncommuting observables from a single copy of the state, without any statistics or ensembles, and the decoding of dephasing errors in a Schrödinger-cat qubit quantum error-correction (QEC) code. In the latter, the error syndrome is obtained from single-shot QND measurements of the mean photon number of the cat, even if neither the cat code words nor the stabilizing Hamiltonian commute with the photon-number operator.

The performance of quantum computers is hindered by decoherence and crosstalk, which cause errors and limit the ability to perform long computations. Dynamical decoupling is a technique that alleviates these issues by applying carefully timed pulses to individual qubits, effectively suppressing unwanted interactions. However, as quantum devices grow in size, it becomes increasingly important to minimize the time required to implement dynamical decoupling across the entire system. Here, we present “chromatic Hadamard dynamical decoupling” (CHaDD), an approach that efficiently schedules dynamical decoupling pulses for quantum devices with arbitrary qubit connectivity. By leveraging Hadamard matrices, CHaDD achieves a circuit depth that scales linearly with the chromatic number of the connectivity graph for general two-qubit interactions, assuming instantaneous pulses. This includes $ZZ$ crosstalk, which is prevalent in superconducting quantum processing units (QPUs). The scaling of CHaDD represents an exponential improvement over all previous multiqubit decoupling schemes for devices with connectivity graphs the chromatic number of which grows at most polylogarithmically with the number of qubits. For graphs with a constant chromatic number, the scaling of CHaDD is independent of the number of qubits. We report on experiments we have conducted using IBM QPUs that confirm the advantage conferred by CHaDD. Our results suggest that CHaDD can become a useful tool for enhancing the performance and scalability of quantum computers by efficiently suppressing decoherence and crosstalk across large qubit arrays.

A catalyst is a substance that enables otherwise impossible transformations between states of a system, without being consumed in the process. In this work, we apply the notion of catalysts to many-body quantum physics. In particular, we construct catalysts that enable transformations between different symmetry-protected topological (SPT) phases of matter using symmetric finite-depth quantum circuits. We discover a wide variety of catalysts, including GHZ-like states that spontaneously break the symmetry, gapless states with critical correlations, topological orders with symmetry fractionalization, and spin-glass states. These catalysts are all united under a single framework that has close connections to the theory of quantum anomalies, and we use this connection to put strong constraints on possible pure- and mixed-state catalysts. We also show how the catalyst approach leads to new insights into the structure of certain phases of matter, and to new methods to efficiently prepare SPT phases with long-range interactions or projective measurements.

We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium-87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum simulation experiments with $\mathfrak{s}\mathrm{u}(N)$-symmetric matter. By controlling the resonance conditions of Raman transitions with a tensor light shift, we can perform rotations within a restricted Hilbert space of two isolated spin states among the $2F+1=10$ possible states. These manipulations correspond to engineering unitary operations derived from generators of the $\mathfrak{s}\mathrm{u}(N)$ algebra beyond what can be done by simple spin precession. We present Ramsey interferometers involving an isolated pair of Zeeman states with no measurable decoherence after 3 s. We also demonstrate that one can harness the large spin degrees of freedom as a qudit resource by implementing two interferometer schemes over four states. The first scheme senses in parallel multiple external fields acting on the atoms, and the second scheme simultaneously measures multiple observables of a collective atomic state—including noncommuting ones. Engineering unitary transformations of the large spin driven by other generators than the usual spin-$F$ representation of the $\mathfrak{s}\mathrm{u}(2)$ group offers new possibilities from the point of view of quantum metrology and quantum many-body physics, notably for the quantum simulation of large-spin $\mathfrak{s}\mathrm{u}(N)$-symmetric quantum magnetism with fermionic alkaline-earth atoms.

Quantum entanglement and coherence often allow for protocols that outperform classical ones in estimating a system’s parameter. When using infinite-dimensional probes (such as a bosonic mode), one could, in principle, obtain infinite precision in a finite time for both classical and quantum protocols, which makes it hard to quantify potential quantum advantage. However, such a situation is unphysical, as it would require infinite resources, so one needs to impose some additional constraint: typically the average energy employed by the probe is finite. Here we treat both energy and time as a resource, showing that, in the presence of noise, there is a nontrivial interplay between the average energy and the time devoted to the estimation. Our results are valid for the most general metrological schemes (e.g., adaptive schemes, which may involve entanglement with external ancillae or any kind of continuous measurement). We apply recently derived precision bounds for all parameters characterizing the paradigmatic case of a bosonic mode, subject to Lindbladian noise. We show how the time employed in the estimation should be partitioned in order to achieve the best possible precision. In most cases, the optimal performance may be obtained without the necessity of adaptivity or entanglement with ancilla. We compare results with classical strategies. Interestingly, for temperature estimation, applying a fast-prepare-and-measure protocol with Fock states provides better scaling with the number of photons than any classical strategy.

We simulate the Lipkin-Meshkov-Glick model using the variational-quantum-eigensolver algorithm on a neutral atom quantum computer. We test the ground-state energy of spin systems with up to 15 spins. Two different encoding schemes are used: an individual spin encoding where each spin is represented by one qubit, and an efficient Gray code encoding scheme that only requires a number of qubits that scales with the logarithm of the number of spins. This more efficient encoding, together with zero-noise extrapolation techniques, is shown to improve the fidelity of the simulated energies with respect to exact solutions.

Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2.

The virtual-$Z$ (vz) gate has been established as an important tool for performing quantum gates on various platforms, including but not limited to superconducting systems. Many such platforms offer a limited set of calibrated gates and compile all other gates using combinations of $X$-type and vz gates. Here, we show that the method of compilation has important consequences in an open quantum system setting. Specifically, we experimentally demonstrate that it is crucial to choose a compilation that is symmetric with respect to vz rotations. An important example is dynamical-decoupling (DD) sequences, where improper gate decomposition can result in unintended effects such as the implementation of the wrong sequence. Our findings indicate that in many cases the performance of DD is adversely affected by the incorrect use of vz gates, compounding other coherent pulse errors. This holds even for DD sequences designed to be robust against systematic control errors. In addition, we identify another source of coherent errors: interference between consecutive pulses that follow each other too closely. This work provides insights into improving general quantum gate performance and optimizing DD sequences in particular.

Scaling up a superconducting quantum computer will likely require quantum communication between remote chips, which can be implemented using an itinerant microwave photon in a transmission line. To realize high-fidelity communication, it is essential to control the frequency and temporal shape of the microwave photon. In this work, we demonstrate the generation of frequency-tunable shaped microwave photons without resorting to any frequency-tunable circuit element. We develop a framework that treats a microwave resonator as a band-pass filter mediating the interaction between a superconducting qubit and the modes in the transmission line. This interpretation allows us to stimulate the photon emission by an off-resonant drive signal. We characterize how the frequency and temporal shape of the generated photon depends on the frequency and amplitude of the drive signal. By modulating the drive amplitude and frequency, we achieve a frequency tunability of 40 MHz while maintaining the photon mode shape time symmetric. Through measurements of the quadrature amplitudes of the emitted photons, we demonstrate a consistently high state and process fidelities around 95% across the tunable frequency range. Our hardware-efficient approach eliminates the need for additional biasing lines typically required for frequency tuning, offering a simplified architecture for scalable quantum communication.

Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum states that are being prepared in practice often involve families of quantum states characterized by continuous parameters, such as the time evolution of a quantum state. In this work, we extend the foundations of quantum state tomography to parametrized quantum states. We introduce a framework that unifies different notions of tomography and use it to establish a natural figure of merit for tomography of parametrized quantum states. Building on this, we provide an explicit algorithm that combines signal processing techniques with a tomography scheme to recover an approximation to the parametrized quantum state equipped with explicit guarantees. Our algorithm uses techniques from compressed sensing to exploit structure in the parameter dependence and operates with a “plug-and-play” nature, using the underlying tomography scheme as a black box. In an analogous fashion, we derive a figure of merit that applies to parametrized quantum channels. Substituting the state tomography scheme with a scheme for process tomography in our algorithm, we then obtain a protocol for tomography of parametrized quantum channels. We showcase our algorithm with two examples of shadow tomography of states time evolved under an NMR Hamiltonian and a free-fermionic Hamiltonian.

Fast and accurate qubit measurement remains a critical challenge on the path to fault-tolerant quantum computing. In superconducting quantum circuits, fast qubit measurement has been achieved using a dispersively coupled resonator with a large externally limited linewidth. This necessitates the use of a Purcell filter that protects the qubit from relaxation through the readout channel. Here, we show that a readout resonator and filter resonator, coupled to each other both capacitively and inductively via a multiconductor transmission line, can produce a compact notch-filter circuit that effectively eliminates the Purcell decay channel through destructive interference. By utilizing linewidths as large as 42 MHz, we perform simultaneous readout of four qubits using a 56-ns integration window and benchmark an average assignment fidelity of 99.77%, with the highest qubit assignment fidelity exceeding 99.9%. Including the simulated readout ring-down time, the total readout duration was between 115 and 215 ns for the four qubits, which we anticipate can be reduced to around 100 ns with active ring-down pulse shaping. These results demonstrate a significant advancement in speed and fidelity for multiplexed superconducting-qubit readout.

Echo-based spectroscopy of the superhyperfine interaction of an electronic spin with nuclear spins in its surroundings enables detailed insights into the microscopic magnetic environment of spins in solids. Still, it is an outstanding challenge to resolve individual nuclear spins in a dense bath, in which many of them exhibit a comparable coupling strength. This simultaneously requires a high spectral resolution and a large signal-to-noise ratio. However, when probing spin ensembles, dipolar interactions between the dopants can lead to a concentration-dependent trade-off between resolution and signal. Here, we fully eliminate this limitation of previous optical-echo-envelope-modulation spectroscopy experiments by integrating the emitters into a high-finesse resonator, which allows for strong optical echoes even at very low concentrations. To demonstrate its potential, the technique is applied to erbium dopants in yttrium orthosilicate ($\mathrm{Er}$:$\mathrm{YSO}$). Achieving an unprecedented spectral resolution enables precise measurements of the superhyperfine interaction with four of the Y nuclear spins densely surrounding each emitter. The achieved boost of the signal, enabled by the resonator, allows for extending the approach to the lowest concentration possible—to the level of single dopants, thereby providing a tool for detecting and studying individual nuclear spins. Thus, our technique paves the way for an improved understanding of dense nuclear-spin baths in solids.