We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to postselect on sets of measurement outcomes with Born probabilities that are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential “postselection problem”, is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate classical shadows into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations that both upper and lower bound the measurement-averaged von Neumann entanglement entropy, as well as cross-correlations that lower bound the measurement-averaged purity and entanglement negativity. These bounds show that experiments can be performed to constrain postmeasurement entanglement without the need for postselection. To illustrate our technique, we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory.

We study quantum many-body mixed states with a symmetry from the perspective of separability, i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decohered $p+ip$ superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition.

We study the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up $N-1$ further identical qubits by means of a global unitary operation. A standard back-of-the-envelope high-temperature estimate establishes that the target qubit temperature can be dynamically cooled by at most a factor of $1/\sqrt{N}$. Here we provide the exact expression for the minimum temperature to which the target qubit can be cooled and reveal that there is a crossover from the high initial temperature regime, where the scaling is $1/\sqrt{N}$, to a low initial temperature regime, where a much faster scaling of $1/N$ occurs. This slow, $1/\sqrt{N}$ scaling, which was relevant for early high-temperature NMR quantum computers, is the reason dynamic cooling was dismissed as ineffectual around 20 years ago; the fact that current low-temperature quantum computers fall in the fast, $1/N$ scaling regime, reinstates the appeal of dynamic cooling today. We further show that the associated work cost of cooling is exponentially more advantageous in the low-temperature regime. We discuss the implementation of dynamic cooling in terms of quantum circuits and examine the effects of hardware noise. We successfully demonstrate dynamic cooling in a three-qubit system on a real quantum processor. Since the circuit size grows quickly with $N$, scaling dynamic cooling to larger systems on noisy devices poses a challenge. We therefore propose a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers.

Coupling between a single quantum emitter and an optical cavity presents a key capability for future quantum networking applications. Here, we explore interactions between individual germanium-vacancy ($\mathrm{Ge}$V) defects in diamond and an open microcavity at cryogenic temperatures. Exploiting the tunability of our microcavity system to characterize and select emitters, we observe a Purcell-effect-induced lifetime reduction of up to $4.5\pm 0.3$ and extract coherent-coupling rates up to $360\pm 20$ MHz. Our results indicate that the $\mathrm{Ge}$V defect has favorable optical properties for cavity coupling, with a quantum efficiency of at least $0.34\pm 0.05$ and likely much higher.

Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle, with perfect fidelity. To what extent do correlations and entanglement of a many-body wave function transfer under imperfect teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wave function, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection (i) preserves both the universal long-range entanglement and correlations of the original quantum critical state, (ii) weakly modifies these quantities away from their universal values, and (iii) obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a “built-in” decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors—highlighting a potential practical application of measurement-altered criticality.

In satellite-based quantum-key-distribution (QKD), the number of secret bits that can be generated in a single satellite pass over the ground station is severely restricted by the pass duration and the free-space optical channel loss. High channel loss may decrease the signal-to-noise ratio due to background noise, reduce the number of generated raw key bits, and increase the quantum bit error rate (QBER), all of which have detrimental effects on the output secret key length. Under finite-size security analysis, a higher QBER increases the minimum raw key length necessary for nonzero secret-key-length extraction due to less efficient reconciliation and postprocessing overheads. We show that recent developments in finite-key analysis allow three different small-satellite-based QKD projects, CQT-Sat, the United Kingdom QUARC-ROKS, and QEYSSat, to produce secret keys even under conditions of very high loss, improving on estimates based on previous finite-key bounds. This suggests that satellites in low Earth orbit can satisfy finite-size security requirements but that this remains challenging for satellites further from Earth. We analyze the performance of each mission to provide an informed route toward improving the performance of small-satellite QKD missions. We highlight the short- and long-term perspectives on the challenges and potential future developments in small-satellite-based QKD and quantum networks. In particular, we discuss some of the experimental and theoretical bottlenecks and the improvements necessary to achieve QKD and wider quantum networking capabilities in daylight and at different altitudes.

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions.

Generating indistinguishable photons from independent nodes is an important challenge for the development of quantum networks. In this work, we demonstrate the generation of highly indistinguishable single photons from two dissimilar atomic quantum nodes. One node is based on a fully blockaded cold Rydberg ensemble and generates on-demand single photons. The other node is a quantum repeater node based on a Duan-Lukin-Cirac-Zoller quantum memory and emits heralded single photons after a controllable memory time that is used to synchronize the two sources. We demonstrate an indistinguishability of $94.6\pm 5.2\mathrm{\%}$ for a temporal window including $90\mathrm{\%}$ of the photons. This advancement opens new possibilities for interconnecting quantum repeater and processing nodes with high-fidelity Bell state measurement without sacrificing its efficiency.

Topological order offers possibilities for processing quantum information that can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work, we demonstrate the robustness of certain aspects of $Z_2\times Z_2$ symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional $ZXZ$ cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two nonlocal logical qubits and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized edge qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens up the possibility of engineering entangled states relevant to quantum information processing.

The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This “coherence” is rigorously quantified by resource theories, which aim to understand how such properties may be exploited in quantum technologies. There has been much research on what the resource theory of coherence can reveal about quantum metrology, almost all of which has been from the viewpoint of Fisher information. We prove, however, that the relative entropy of coherence, and its recent generalization to positive operator-valued measures (POVMs), naturally quantify the performance of Bayesian metrology. In particular, we show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence (C) is equal to the difference between the optimal Holevo information (X), and the mutual information attained by a measurement (I). We call this relation the CXI equality. The ensemble coherence lets us visualize how much information is locked away in superposition and hence is inaccessible with a given measurement scheme and quantifies the advantage that would be gained by using a joint measurement on multiple states. Our results hold regardless of how the parameter is encoded in the state, encompassing unitary, dissipative, and discrete settings. We consider both projective measurements and general POVMs. This work suggests new directions for research in coherence, provides a novel operation interpretation for the relative entropy of coherence and its POVM generalization, and introduces a new tool to study the role of quantum features in metrology.

Qubit-specific measurement in a superconducting quantum processor requires physical interconnects that traverse 4 orders of magnitude in temperature from 293 K to 10 mK. Although the quantum processor can be thermalized and shielded from electromagnetic noise, the interconnects themselves introduce an unavoidable remote heat bath that causes decoherence of quantum states. In the present work, we report quantitative and device-independent measurements of the power radiated to the quantum processor from its control lines. Our results have been obtained using a calibrated bolometer that operates within a millikelvin environment with time-resolved measurement capability. In the limit of zero applied power, the noise power emitted to the quantum processor is equivalent to that of a blackbody with temperature 63–71 mK for the prototypical drive lines in the study. Experimentally, we increase the applied power of a simulated control signal to map out the resulting temperature rise and thermal time constant of five prototypical drive-line varieties. We input the data to an open quantum system model to demonstrate the trade-off between dissipated signal power, transmon-qubit lifetime, pure dephasing, gate fidelity, and the implied decoherence rates due to self-heating during microwave operations. Beyond explaining dephasing rates observed in the literature, our work sets the stage for accurate noise modeling in novel quantum computer interfacing methods due to our device-agnostic approach.

Cooling a quantum system to its ground state is important for the characterization of nontrivial interacting systems and in the context of a variety of quantum information platforms. It can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements realized by coupling the system to auxiliary quantum degrees of freedom (“detectors”) are rather costly and protocols in which the number of detectors scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the ultimate dilute limit where the number of detectors is independent of system size. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications of dilute cooling.

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that $|P|\le 1$, a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where $P$ and $Q$ are known. In cases where only $P$ is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding $Q$ for polynomials of degree on the order of ${10}^7$. We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the $ϵ$-approximate fractional query problem that requires $\mathcal{O}((1/\delta )+\log (1/ϵ))$ queries to perform where $\mathcal{O}(1/\delta )$ is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only $\mathcal{O}(d\log N+{\log }^2N)$ 1 and 2-qubit gates for a filter of lengths $d$.

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one’s control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a byproduct, we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies, which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase shifts.

The quantum Zeno effect asserts that quantum measurements inhibit simultaneous unitary dynamics when the “collapse” events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It is possible to implement a dissipative control that is known as “Zeno dragging” by dynamically varying the monitored observable, and hence also the eigenstates, which are attractors under Zeno dynamics. This is similar to adiabatic processes, in that the Zeno-dragging fidelity is highest when the rate of eigenstate change is slow compared to the measurement rate. We demonstrate here two theoretical methods for using such dynamics to achieve control of quantum systems. The first, which we shall refer to as “shortcut to Zeno,” is analogous to the shortcuts to adiabaticity (counterdiabatic driving) that are frequently used to accelerate unitary adiabatic evolution. In the second approach, we apply the Chantasri-Dressel-Jordan stochastic action [PRA 88, 042110 (2013)], and demonstrate that the extremal-probability readout paths derived from this are well suited to setting up a Pontryagin-style optimization of the Zeno-dragging schedule. A fundamental contribution of the latter approach is to show that an action suitable for measurement-driven control optimization can be derived quite generally from statistical arguments. Implementing these methods on the Zeno dragging of a qubit, we find that both approaches yield the same solution, namely, that the optimal control is a unitary that matches the motion of the Zeno-monitored eigenstate. We then show that such a solution can be more robust than a unitary-only operation and we comment on solvable generalizations of our qubit example embedded in larger systems. These methods open up new pathways toward systematically developing dynamic control of Zeno subspaces to realize dissipatively stabilized quantum operations.

Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation through simplifications of computations and topological transformations to optimization and quantum computing. Adiabatic time evolution generally works well for gapped ground states, but not for thermal states in the middle of the spectrum that lack a protecting energy gap. Here we show that quantum many-body scars—a particular type of highly excited states—are suitable for adiabatic time evolution despite the absence of a protecting energy gap. Considering two rather different models, namely a one-dimensional model constructed from tensor networks and a two-dimensional fractional quantum Hall model with anyons, we find that the quantum scars perform similarly to gapped ground states with respect to adiabatic dynamics when the required final adiabatic fidelity is around 0.99. The maximum speed at which the scar state of the one-dimensional model can be adiabatically transformed decreases as a power law with system size, as opposed to exponentially for both generic thermal and disorder-driven localized states. At constant and very low ramp speed, we find that the deviation of the fidelity from unity scales linearly with ramp speed for scar states, but quadratically for gapped ground states. The gapped ground states hence perform better when the required adiabatic fidelities are very high, such as 0.9999 and above. We identify two mechanisms for leakage out of the scar state and use them to explain our results. While manipulating a single, isolated ground state is common in quantum applications, adiabatic evolution of scar states provides the flexibility to manipulate an entire tower of ground-state-like states simultaneously in a single system.

We develop and demonstrate a trainable temporal postprocessor (TPP) harnessing a simple but versatile machine learning algorithm to provide optimal processing of quantum measurement data subject to arbitrary noise processes for the readout of an arbitrary number of quantum states. We demonstrate the TPP on the essential task of qubit state readout, which has historically relied on temporal processing via matched filters in spite of their applicability for only specific noise conditions. Our results show that the TPP can reliably outperform standard filtering approaches under complex readout conditions, such as high-power readout. Using simulations of quantum measurement noise sources, we show that this advantage relies on the TPP’s ability to learn optimal linear filters that account for general quantum noise correlations in data, such as those due to quantum jumps, or correlated noise added by a phase-preserving quantum amplifier. Furthermore, we derive an exact analytic form for the optimal TPP weights: this positions the TPP as a linearly scaling generalization of matched filtering, valid for an arbitrary number of states under the most general readout noise conditions, all while preserving a training complexity that is essentially negligible in comparison with that of training neural networks for processing temporal quantum measurement data. The TPP can be autonomously and reliably trained on measurement data and requires only linear operations, making it ideal for field-programmable gate array implementations in circuit QED for real-time processing of measurement data from general quantum systems.

Quantum links between physically separated modules are important for scaling many quantum computing technologies. The key metrics are the generation rate and fidelity of remote Bell pairs. In this work, we propose an experimental protocol for generating remote entanglement between neutral ytterbium atom qubits using an optical cavity. By loading a large number of atoms into a single cavity, and controlling their coupling using only local light shifts, we amortize the cost of transporting and initializing atoms over many entanglement attempts, maximizing the entanglement generation rate. A twisted ring cavity geometry suppresses many sources of error, allowing high-fidelity entanglement generation. We estimate a spin-photon entanglement rate of $5\times {10}^5{\mathrm{s}}^{-1}$, and a Bell pair rate approaching ${10}^5{\mathrm{s}}^{-1}$, with an average fidelity near $0.999$. Furthermore, we show that the photon detection times provide a significant amount of soft information about the location of errors, which may be used to improve the logical qubit performance. This approach provides a practical path to scalable modular quantum computing using neutral ytterbium atoms.

In recent years, research in quantum computing has largely focused on two approaches: near-term intermediate-scale quantum (NISQ) computing and future fault-tolerant quantum computing (FTQC). A growing body of research into early fault-tolerant quantum computing (EFTQC) is exploring how to utilize quantum computers during the transition between these two eras. However, without agreed-upon characterizations of this transition, it is unclear how best to utilize EFTQC architectures. We argue for the perspective that this transition period will be characterized by a law of diminishing returns in quantum error correction (QEC), where the ability of the architecture to maintain quality operations at scale determines the point of diminishing returns. Two challenges emerge from this picture: how to model this phenomenon of diminishing return of QEC as the performance of devices is continually improving and how to design algorithms to make the most use of these devices. To address these challenges, we present models for the performance of EFTQC architectures, capturing the diminishing returns of QEC. We then use these models to elucidate the regimes in which algorithms suited to such architectures are advantageous. As a concrete example, we show that for the canonical task of phase estimation, in a regime of moderate scalability and using just over one million physical qubits, the “reach” of the quantum computer can be extended (compared to the standard approach) from 90-qubit instances to over 130-qubit instances using a simple early fault-tolerant quantum algorithm, which reduces the number of operations per circuit by a factor of 100 and increases the number of circuit repetitions by a factor of 10 000. This clarifies the role that such algorithms might play in the era of limited-scalability quantum computing.

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground-state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization.