We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently proposed “space-evolving block decimation” (SEBD) [Napp et al, Phys. Rev. X 12, 021021 (2022)] and extends it to the case of noisy circuits. SEBD is based on a mapping of two-dimensional unitary circuits to one-dimensional monitored ones, which feature measurements alongside unitary gates; it exploits the presence of a measurement-induced entanglement phase transition to achieve efficient (approximate) sampling below a finite critical depth $T_c$. Our noisy-SEBD algorithm unravels the action of noise into measurements, further lowering entanglement and enabling efficient classical sampling up to larger circuit depths. We analyze a class of physically relevant noise models (unital qubit channels) within a two-replica statistical mechanics treatment, finding weak measurements to be the optimal (i.e., most disentangling) unraveling. We then locate the noisy-SEBD complexity transition as a function of circuit depth and noise strength in realistic circuit models. As an illustrative example, we show that circuits on heavy-hexagon qubit arrays with noise rates of approximately equal to $2\mathrm{\%}$ per cnot, based on IBM Quantum processors, can be efficiently sampled up to a depth of five $i$swap (or ten cnot) gate layers. Our results help sharpen the requirements for practical hardness of simulation of noisy hardware.

We study quantum interior-point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity and/or depth of non-Clifford $T$ gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant prefactors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.

Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent time evolution and do not explicitly reconstruct the full time-dependent Hamiltonian or interrupt evolution for tomography. Here, we experimentally demonstrate that an a priori unknown, time-dependent Hamiltonian can be reconstructed from continuous weak measurements concurrent with coherent time evolution in a system of two superconducting transmons coupled by a flux-tunable coupler. In contrast to previous work, our technique does not require interruptions, which would distort the recovered Hamiltonian. We introduce an algorithm, which recovers the Hamiltonian and density matrix from an incomplete set of continuous measurements, and demonstrate that it reliably extracts amplitudes of a variety of single-qubit and entangling two-qubit Hamiltonians. We further demonstrate how this technique reveals deviations from a theoretical control Hamiltonian, which would otherwise be missed by conventional techniques. Our work opens up novel applications for continuous weak measurements, such as studying nonidealities in gates, certifying analog quantum simulators, and performing quantum metrology.

$W$ states are a valuable resource for various quantum information tasks, and several protocols to generate them have been proposed and implemented. We introduce a quantum repeater protocol to efficiently distribute three-qubit $W$ states over arbitrary distances in a two-dimensional triangular quantum network with polylogarithmic overhead, thereby enabling these applications between remote parties. The repeater protocol combines two ingredients that we establish: probabilistic entanglement swapping with three copies of three-qubit $W$ states to a single long-distance three-qubit $W$ state, and an improved entanglement purification protocol. The latter not only shows a better performance, but also an enlarged purification regime as compared to previous approaches. We show that the repeater protocol allows one to deal with errors resulting from imperfect channels or state preparation, and noisy operations, and we analyze error thresholds, achievable fidelities, and overheads.

Quantum threshold theorems impose hard limits on the hardware capabilities to process quantum information. We derive tight and fundamental upper bounds to loss-tolerance thresholds in different linear-optical quantum information processing settings through an adversarial framework, taking into account the intrinsically probabilistic nature of linear optical Bell measurements. For logical Bell state measurements—ubiquitous operations in photonic quantum information—we demonstrate analytically that linear optics can achieve the fundamental loss threshold imposed by the no-cloning theorem even though, following the work of Lee et al. [Phys. Rev. A 100, 052303 (2019)] the constraint was widely assumed to be stricter. We spotlight the assumptions of the latter publication and find their bound holds for a logical Bell measurement built from adaptive physical linear-optical Bell measurements. We also give an explicit even stricter bound for nonadaptive Bell measurements.

Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits. A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an $LC$ circuit connecting two qubits. Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself. Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states. Using this method, we experimentally demonstrate a controlled-$Z$ gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of $97.6\mathrm{\%}\pm 0.4\mathrm{\%}$ characterized by cross-entropy benchmarking.

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice and/or Bob’s receiver station. This restriction is modeled by lossy channels between relevant parties, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques. An artifact of such lossy channels is the possibility of having bypass channels, those that are not accessible to Eve but that may not necessarily be characterized by the users either. This creates interesting unexplored scenarios for analyzing QKD security. In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding with direct and reverse reconciliation. We find regimes of operation in which the above restrictions on Eve can considerably improve system performance. We also develop customized bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve. In this case, the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss. In all these cases, the part of the transmitted signal that does not reach Eve can play a nontrivial role in specifying the achievable key rate. Our work opens up new security frameworks for spaceborne quantum communications systems.

In the race to build scalable quantum computers, minimizing the resource consumption of their full stack to achieve a target performance becomes crucial. It mandates a synergy of fundamental physics and engineering: the former for the microscopic aspects of computing performance and the latter for the macroscopic resource consumption. For this, we propose a holistic methodology dubbed metric noise resource (MNR) that is able to quantify and optimize all aspects of the full-stack quantum computer, bringing together concepts from quantum physics (e.g., noise on the qubits), quantum information (e.g., computing architecture and type of error correction), and enabling technologies (e.g., cryogenics, control electronics, and wiring). This holistic approach allows us to define and study resource efficiencies as ratios between performance and resource cost. As a proof of concept, we use MNR to minimize the power consumption of a full-stack quantum computer, performing noisy or fault-tolerant computing with a target performance for the task of interest. Comparing this with a classical processor performing the same task, we identify a quantum energy advantage in regimes of parameters distinct from the commonly considered quantum computational advantage. This provides a previously overlooked practical argument for building quantum computers. While our illustration uses highly idealized parameters inspired by superconducting qubits with concatenated error correction, the methodology is universal—it applies to other qubits and error-correcting codes—and it provides experimenters with guidelines to build energy-efficient quantum computers. In some regimes of high energy consumption, it can reduce this consumption by orders of magnitude. Overall, our methodology lays the theoretical foundation for resource-efficient quantum technologies.

The quantum Fourier transform (QFT) is a key component of many important quantum algorithms, most famously being the essential ingredient in Shor’s algorithm for factoring products of primes. Given its remarkable capability, one would think it can introduce large entanglement to qubit systems and would be difficult to simulate classically. While early results showed the QFT indeed has maximal operator entanglement, we show that this is entirely due to the bit reversal in the QFT. The core part of the QFT has Schmidt coefficients decaying exponentially quickly, and thus it can generate only a constant amount of entanglement regardless of the number of qubits. In addition, we show the entangling power of the QFT is the same as the time evolution of a Hamiltonian with exponentially decaying interactions, and thus a variant of the area law for dynamics can be used to understand the low entanglement intuitively. Using the low entanglement property of the QFT, we show that classical simulations of the QFT on a matrix product state with low bond dimension take time linear in the number of qubits, providing a potential speedup over the classical fast Fourier transform on many classes of functions. We demonstrate this speedup in test calculations on some simple functions. For data vectors of length ${10}^6$–${10}^8$, the speedup can be a few orders of magnitude.

We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables the efficient extraction of the magic contained in the correlations between widely separated subsystems, which characterizes the nonlocality of magic. Our method can be implemented in a variety of situations. We describe an efficient sampling procedure using tree tensor networks, that exploit their hierarchical structure leading to a modest $O(\log N)$ computational scaling with system size. To showcase the applicability and efficiency of our method, we demonstrate the importance of magic in many-body systems via the following discoveries: (a) for one-dimensional systems, we show that long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic; (b) in two-dimensional ${\mathbb{Z}}_2$ lattice gauge theories, we provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes. Finally, we discuss an experimental implementation of the method, which relies only on measurements of Pauli observables.

Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant, and universal quantum computing. However, current gate proposals for such qubits induce substantial noise of the unprotected type, the poor scaling of which with the relevant experimental parameters limits their practical use. In this work, we provide a new perspective on dissipative cat qubits by reconsidering the reservoir mode used to engineer the tailored two-photon dissipation and showing how it can be leveraged to mitigate gate-induced errors. Doing so, we introduce four new designs of high-fidelity and bias-preserving cat-qubit gates and compare them to the prevalent gate methods. These four designs should give a broad overview of gate engineering for dissipative systems with different and complementary ideas. In particular, we propose both already achievable low-error gate designs and longer-term implementations.

Single-qubit sensing protocols can be used to measure qubit-bath coupling parameters. However, for sufficiently large coupling, the sensing protocol itself perturbs the bath, which is predicted to result in a characteristic response in the sensing measurements. Here, we observe this bath perturbation, also known as a quantum quench, by preparing the nuclear spin bath of a nitrogen-vacancy (NV) center in polarized initial states and performing phase-resolved spin-echo measurements on the NV electron spin. These measurements reveal a time-dependent phase determined by the initial state of the bath. We derive the relationship between the sensor phase and the Gaussian spin-bath polarization and apply it to reconstruct both the axial and transverse polarization components. Using this insight, we optimize the transfer efficiency of our dynamic nuclear polarization sequence. This technique for directly measuring bath polarization may assist in preparing high-fidelity quantum memory states, improving nanoscale NMR methods, and investigating non-Gaussian quantum baths.

An understanding of heat transport is relevant to developing efficient strategies for thermal management in areas of study such as microelectronics, as well as for fundamental science purposes. However, the measurement of temperatures in nanostructured environments and in cryogenic conditions remains a challenging task, requiring both high sensitivity and noninvasive approaches. Here, we present a portable nanothermometer based on a molecular two-level quantum system that operates in the (3–20)-K temperature range, with temperatures and spatial resolutions on the order of millikelvins and micrometers, respectively. We validate the performance of this molecular thermometer by estimating the thermal conductivity of a nanopatterned silicon membrane, where we find a quadratic temperature dependence. In addition, we demonstrate two-dimensional temperature mapping via the simultaneous spectroscopy of multiple probes deposited onto such a suspended membrane. Overall, these results demonstrate the unique potential of the proposed molecular thermometer to explore thermal properties with submicron accuracy and unveil related phenomena manifested at cryogenic temperatures.

One of the most formidable challenges of scaling up quantum computers is that of control-signal delivery. Today’s small-scale quantum computers typically connect each qubit to one or more separate external signal sources. This approach is not scalable due to the input/output (I/O) limitations of the qubit chip, necessitating the integration of control electronics. However, it is no small feat to shrink control electronics into a small package that is compatible with qubit-chip fabrication and operational constraints without sacrificing performance. This so-called “wiring challenge” is likely to impact the development of more powerful quantum computers even in the near term. In this paper, we address the wiring challenge of trapped-ion quantum computers. We describe a control architecture called WISE (Wiring using Integrated Switching Electronics), which significantly reduces the I/O requirements of ion-trap quantum computing chips without compromising performance. Our method relies on judiciously integrating simple switching electronics into the ion-trap chip—in a way that is compatible with its fabrication and operation constraints—while the complex electronics remain external. To demonstrate its power, we describe how the WISE architecture can be used to operate a fully connected $1000$-qubit trapped-ion quantum computer using approximately $200$ signal sources at a speed of approximately $40–2600$ quantum gate layers per second.

The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random matrices as an effective measure of quantifying dissipative quantum chaos. By means of Hermitization, we reveal the unique characteristics of the singular-value statistics that distinguish them from the complex-eigenvalue statistics, and establish the comprehensive classification of the singular-value statistics for all the 38-fold symmetry classes of non-Hermitian random matrices. We also analytically derive the singular-value statistics of small random matrices, which well describe those of large random matrices in the similar spirit to the Wigner surmise. Furthermore, we demonstrate that singular values of open quantum many-body systems follow the random-matrix statistics, thereby identifying chaos and nonintegrability in open quantum systems. Our work elucidates that the singular-value statistics serve as a clear indicator of symmetry and lay a foundation for statistical physics of open quantum systems.

Building error-corrected quantum computers relies crucially on measuring and modeling noise on candidate devices. In particular, optimal error correction requires knowing the noise that occurs in the device as it executes the circuits required for error correction. As devices increase in size, we will become more reliant on efficient models of this noise. However, such models must still retain the information required to optimize the algorithms used for error correction. Here, we propose a method of extracting detailed information of the noise in a device running syndrome extraction circuits. We introduce and execute an experiment on a superconducting device using 39 of its qubits in a surface code doing repeated rounds of syndrome extraction but omitting the midcircuit measurement and reset. We show how to extract from the 20 data qubits the information needed to build noise models of various sophistication in the form of graphical models. These models give efficient descriptions of noise in large-scale devices and are designed to illuminate the effectiveness of error correction against correlated noise. Our estimates are furthermore precise: we learn a consistent global distribution where all one- and two-qubit error rates are known to a relative error of 0.1%. By extrapolating our experimentally learned noise models toward lower error rates, we demonstrate that accurate correlated noise models are increasingly important for successfully predicting subthreshold behavior in quantum error-correction experiments.

No quantum system can be considered totally isolated from its environment. In most cases the interaction between the system of interest and the external degrees of freedom deeply changes its dynamics, as described by open quantum system theory. Nevertheless engineered environment can be turned into beneficial effects for some quantum information tasks. Here we demonstrate an optical simulator of a quantum system coupled to an arbitrary and reconfigurable environment built as a complex network of quantum interacting systems. We experimentally retrieve typical features of open quantum system dynamics like the spectral density and quantum non-Markovianity, by exploiting squeezing and entanglement correlation of a continuous-variable optical platform. This opens the way to the experimental tests of open quantum systems in reconfigurable environments that are relevant in, among others, quantum information, quantum thermodynamics, quantum transport, and quantum synchronization.

We explore universality and phases of matter in hybrid quantum dynamics combining chaotic time evolution and projective measurements. We develop a unitary representation of measurements based on the Stinespring theorem, which we crucially identify with the time evolution of the system and measurement apparatus, affording significant technical advantages and conceptual insight into hybrid dynamics. We diagnose spectral properties in the presence of measurements for the first time, along with standard, experimentally tractable probes of phase structure, finding no nontrivial effects due to measurements in the absence of feedback. We also establish that nonlinearity in the density matrix is neither sufficient nor necessary to see a transition, and instead identify utilization of the measurement outcomes (i.e., “feedback”) as the crucial ingredient. After reviewing the definition of a phase of matter, we identify nontrivial orders in adaptive hybrid dynamics—in which measurement outcomes determine future unitary gates—finding a genuine measurement-induced absorbing-state phase transition in an adaptive quantum East model. In general, we find that only deterministic and constrained Haar-random dynamics with active feedback and without continuous symmetries can realize genuine, measurement-induced phases of matter.

Neutral atoms that are optically trapped using the evanescent fields surrounding optical nanofibers are a promising platform for developing quantum technologies and exploring fundamental science, such as quantum networks and many-body physics of interacting photons. Building on the successful advancements with trapped alkali atoms, here we trap strontium-88 atoms, an alkaline-earth element, in a state-insensitive, nanofiber-based optical dipole trap using the evanescent fields of an optical nanofiber. Employing a two-color, double magic-wavelength trapping scheme, we realize state-insensitive trapping of the atoms for the kilohertz-wide $5s^2{}^1{S}_0-5s5p{}^3{P}_{1,|m|=1}$ intercombination transition, which we verify by performing high-resolution spectroscopy for an atom-surface distance of about 300 nm. This allows us to experimentally find and verify the state insensitivity of the trap nearby a theoretically predicted magic wavelength of 435.827(25) nm, a necessary step to confirm precision atomic physics calculations. Alkaline-earth atoms also exhibit nonmagnetic ground states and ultranarrow linewidth transitions making them ideal candidates for atomic clocks and precision metrology applications, especially with state-insensitive traps. Additionally, given the low collisional scattering length specific to strontium-88, this work also lays the foundation for developing versatile and robust matter-wave atomtronic circuits over nanophotonic waveguides.

It is well known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here we study qualitative limitations on causal structures and correlations imposed by local quantum theory. We find a necessary graph-theoretic criterion—the “siblings-on-cycles” property—for a causal structure to be admissible: only such causal structures admit a realization consistent with local quantum theory. We conjecture that this property is moreover sufficient. This conjecture is motivated by an explicit construction of quantum causal models, and is supported by numerical calculations. We show that these causal models, in a restricted setting, are indeed consistent. We identify two sets of causal structures that, in the classical-deterministic case, forbid and give rise to noncausal correlations, respectively.