Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS) approximations and by more efficient filtering of the prepared state to find the ground-state energy. We show how to achieve unitary synthesis with a Toffoli complexity about $7\times$ lower than that in prior work and use that to derive a more efficient MPS-preparation method. For filtering, we present two different approaches: sampling and binary search. For both, we use the theory of window functions to avoid large phase errors and minimize the complexity. We find that the binary-search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about $0.003$. Finally, we estimate the total resources to perform ground-state energy estimation of $\mathrm{Fe}$-$\mathrm{S}$ cluster systems, including the $\mathrm{Fe}\mathrm{Mo}$ cofactor by estimating the overlap of different MPS initial states with potential ground states of the $\mathrm{Fe}\mathrm{Mo}$ cofactor using an extrapolation procedure. With a modest MPS bond dimension of $4000$, our procedure produces an estimate of approximately $0.9$ overlap squared with a candidate ground state of the $\mathrm{Fe}\mathrm{Mo}$ cofactor, producing a total resource estimate of $7.3\times {10}^{10}$ Toffoli gates; neglecting the search over candidates and assuming the accuracy of the extrapolation, this validates prior estimates that have used perfect ground-state overlap. This presents an example of a practical path to prepare states of high overlap in a challenging-to-compute chemical system.

Recent experimental advances have made it possible to implement logical multiqubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-not (tcnot) gate on two surface codes introduces correlated errors across the code blocks and thus requires modified decoding compared to established methods of decoding surface-code quantum memory (SCQM) or lattice-surgery operations. In this work, we examine and benchmark the performance of three different decoding strategies for the tcnot for scalable fault-tolerant quantum computation. In particular, we present a low-complexity decoder based on minimum-weight perfect matching (MWPM) that achieves the same threshold as the SCQM MWPM decoder. We extend our analysis with a study of tailored decoding of a transversal-teleportation circuit, along with a comparison between the performance of lattice-surgery and transversal operations under Pauli- and erasure-noise models. Our investigation builds toward systematic estimation of the cost of implementing large-scale quantum algorithms based on transversal gates in the surface code.

Quantum error mitigation is a key approach for extracting target state properties on state-of-the-art noisy machines and early fault-tolerant devices. Using the ideas from flag fault tolerance and virtual state purification, we develop the virtual-channel-purification (VCP) protocol, which consumes similar qubit and gate resources as virtual state purification but offers stronger error suppression with increased system size and more noisy operation copies. The application of VCP does not require specific knowledge about the target quantum state, the target problem and the gate noise model in the target circuit, and can still offer rigorous performance guarantees for practical noise regimes as long as the noise is incoherent. Further connections are made between VCP and quantum error correction to produce the virtual error-correction (VEC) protocol, one of the first protocols that combine quantum error correction (QEC) and quantum error mitigation beyond directly applying error-mitigation protocols on top of logical qubits. Assuming perfect syndrome extraction, VEC can virtually remove all correctable noise in the channel while paying only the same sampling cost as low-order purification. It can achieve QEC-level protection on an unencoded register when transmitting it through a noisy channel, removing the associated encoding qubit overhead. Another variant of VEC can mimic the error-suppression power of the surface code by inputting only a bit-flip and a phase-flip code. Our protocol can also be adapted to key tasks in quantum networks like channel capacity activation and entanglement distribution.

Entanglement serves as a foundational pillar in quantum information theory, delineating the boundary between what is classical and what is quantum. The common assumption is that a higher degree of entanglement corresponds to a greater degree of “quantumness.” However, this folk belief is challenged by the fact that classically simulable operations, such as Clifford circuits, can create highly entangled states. The simulability of these states raises the question: What are the differences between “low-magic” entanglement and “high-magic” entanglement? To understand this interplay between entanglement and magic, we take an operational approach by studying tasks such as entanglement estimation, distillation, and dilution. We uncover a separation of Hilbert space into two distinct regimes: the entanglement-dominated (ED) phase, where entanglement surpasses magic, and the magic-dominated (MD) phase, where magic dominates entanglement. This separation induces a computational phase transition: entanglement-related tasks are efficiently solvable in the ED phase, but become intractable in the MD phase. Our results find applications in diverse areas such as quantum error correction, many-body physics, and the study of quantum chaos, providing a unifying framework for understanding the behavior of quantum systems. We also offer theoretical explanations for previous numerical observations, highlighting the broad implications of the ED-MD distinction across various subfields of physics.

In this work, we consider one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating eigenvalues of an $n$-qubit Pauli noise channel. Prior work [Chen et al., Phys. Rev. A 105, 032435 (2022)] has proved no-go theorems for this task in the practical regime in which one has a limited amount of quantum memory; i.e., any protocol with $\le 0.99n$ ancilla qubits of quantum memory must make exponentially many measurements, provided that it is non-concatenating. Such protocols can only interact with the channel by repeatedly preparing a state, passing it through the channel, and measuring immediately afterward. Surprisingly, in this work we show that concatenating protocols with an extremely small amount of quantum memory achieve an exponential advantage for this task. We give a protocol that can estimate any prescribed set of eigenvalues $A$ of a Pauli channel to error $\epsilon$ using only $O(\log \log (|A|)/{\epsilon }^2)$ ancilla qubits, $\tilde{O}(n^2/{\epsilon }^2)$ measurements, and $O(n^2|A|/{\epsilon }^2)$ queries to the Pauli channel. In contrast, we show that any protocol with zero ancilla—even a concatenating one—must make $\mathrm{\Omega }(2^n/{\epsilon }^2)$ measurements. We also prove that the number of queries cannot be improved significantly: with $k$ ancilla qubits, $\mathrm{\Omega }(2^{(n-k)/3})$ queries to the channel are necessary to learn all eigenvalues, even for concatenating protocols.

Pseudorandom states (PRSs) are state ensembles that cannot be efficiently distinguished from Haar-random states. However, the definition of PRSs has been limited to pure states and lacks robustness against noise. In this work, we introduce pseudorandom density matrices (PRDMs), ensembles of $n$-qubit states that are computationally indistinguishable from the generalized Hilbert-Schmidt ensemble (GHSE), which is constructed from $(n+m)$-qubit Haar random states with $m$ qubits traced out. For $m=0$, PRDMs are equivalent to PRSs, whereas for $m=\omega (\log n)$, PRDMs are computationally indistinguishable from the maximally mixed state. PRDMs with $m=\omega (\log n)$ are robust to unital noise channels and separated in terms of security from PRS. PRDMs can disguise valuable quantum resources as trivial states. In particular, we construct pseudoresource state ensembles, which possess near-maximal entanglement, magic and coherence, but are computationally indistinguishable from resource-free states. PRDMs exhibit a pseudoresource gap of $\mathrm{\Theta }(n)$ vs 0, surpassing previously found gaps. We also render EFI pairs, a fundamental cryptographic primitive, robust to strong mixed unitary noise. Our work has major implications on quantum resource theory. We show that entanglement, magic, and coherence cannot be efficiently tested, and that black-box resource distillation requires a superpolynomial number of copies. We also establish lower bounds on the purity needed for efficient testing and black-box distillation. Finally, we introduce memoryless PRSs, a noise-robust notion of PRS, which are indistinguishable to Haar random states for efficient algorithms without quantum memory, as well as noise-robust quantum money. Our work provides a comprehensive framework of pseudorandomness for mixed states, which yields powerful quantum cryptographic primitives and fundamental bounds on quantum resource theories.

The realization of synthetic gauge fields for charge neutral ultracold atoms and the simulation of quantum Hall physics have witnessed remarkable experimental progress. Here, we establish key signatures of fractional quantum Hall systems in their nonequilibrium quantum dynamics. We show that in the lowest Landau level the system generically relaxes subdiffusively. The slow relaxation is understood from emergent conservation laws of the total charge and the associated dipole moment that arises from the effective Hamiltonian projected onto the lowest Landau level, leading to subdiffusive fracton hydrodynamics. We discuss the prospect of rotating quantum gases as well as ultracold atoms in optical lattices for observing this unconventional relaxation dynamics.

Advancing quantum sensing tools for investigating atomic and nanoscale systems is crucial for the progress of quantum technologies. While many protocols use quantum probes to extract information from stationary or weakly coupled environments, challenges intensify at the atomic scale and the nanoscale, where the environment is inherently out of equilibrium and/or strongly coupled with the sensor. In this work, we demonstrate that time-reversal symmetry in the control dynamics of a quantum sensor is broken when the qubit sensor interacts with environments that are out of equilibrium (with nonstationary fluctuations), contain quantum non-Gaussian correlations, or exhibit intrinsic time-reversal symmetry breaking. Leveraging this phenomenon, we introduce a quantum sensing paradigm based on time-asymmetric dynamical control sequences, enabling the probing of the distance of an environment from equilibrium, its time-reversal symmetry-breaking behavior, or its quantum non-Gaussian nature. Additionally, we propose sensing strategies to distinguish between these different sources of symmetry breaking. We validate our approach through proof-of-principle experimental quantum simulations using solid-state nuclear magnetic resonance, where we drive the environment of a qubit sensor out of equilibrium and use our protocol to quantify the nonstationary characteristics of the generated states. Our findings highlight the potential of this framework for quantifying nonstationary behavior, designing tailored pump-probe experiments (including measurements of quantum information scrambling), and detecting quantum states that exhibit time-reversal symmetry breaking, time-crystal structures, or quantum non-Gaussian fluctuations. Overall, this work constitutes a step forward in designing quantum devices for atomic scale and nanoscale sensing, broadening their applicability to complex and dynamic quantum environments.

The quantum simulation of real molecules and materials is one of the most highly anticipated applications of quantum computing. Algorithms for simulating electronic structure using a first-quantized plane-wave representation are especially promising due to their asymptotic efficiency. However, previous proposals for preparing initial states for these simulation algorithms scale poorly with the size of the basis set. We address this shortcoming by showing how to efficiently map states defined in a Gaussian-type orbital basis to a plane-wave basis with a scaling that is logarithmic in the number of plane waves. Our key technical result is a proof that molecular orbitals constructed from Gaussian-type basis functions can be compactly represented in a plane-wave basis using matrix product states. While we expect that other approaches could achieve the same logarithmic scaling with respect to basis-set size, our proposed state-preparation technique is also highly efficient in practice. For example, in a series of numerical experiments on small molecules, we find that our approach allows us to prepare an approximation to the Hartree-Fock state using orders of magnitude fewer non-Clifford gates than a naive approach. By resolving the issue of state preparation, our work allows for the first quantum simulation of molecular systems the end-to-end complexity of which is truly sublinear in the basis-set size.

Quantum computation with bosonic modes presents a powerful paradigm for harnessing the principles of quantum mechanics to perform complex information processing tasks. In constructing a bosonic qubit with superconducting circuits, nonlinearity is typically introduced to a cavity mode through an ancillary two-level qubit. However, the spurious heating of the ancilla has impeded progress toward fully fault-tolerant bosonic qubits. The ability to in situ decouple the ancilla when not in use would be beneficial but has so far only been realized with tunable couplers or additional parametric drives. This work presents a novel architecture for quantum information processing, comprising a three-dimensional post cavity coupled to a fluxonium ancilla via a readout resonator. The intricate energy-level structure of this system results in a complex landscape of interactions, the sign of which can be tuned in situ by the magnetic field threading the fluxonium loop without the need for additional elements. Our results could significantly advance the lifetime and controllability of bosonic qubits.

Measurement correlations in quantum systems can exhibit nonlocal behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, it is in general not known which states are local and which ones are not. In particular, it remains an outstanding challenge to explicitly construct local hidden-variable (LHV) models for arbitrary multipartite entangled states. To address this, we use gradient-descent algorithms from machine learning to find LHV models that reproduce the statistics of arbitrary measurements for quantum many-body states. In contrast to previous approaches, our method employs a general ansatz, enabling it to discover LHV models for all local states. Therefore, it for example provides actual estimates for the critical noise levels at which two-qubit Werner states and three-qubit Greenberger-Horne-Zeilinger and $W$ states become local. Furthermore, we find evidence suggesting that two-spin subsystems in the ground states of translationally invariant Hamiltonians are genuinely local, while bigger subsystems are in general not. Our method now offers a quantitative tool for determining the regimes of nonlocality in any given physical context, such as nonequilibrium, decoherence, or disorder.

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.

Sampling problems demonstrating beyond classical computing power with noisy intermediate-scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the claimed sampling problems is usually limited to simulations of smaller-scale instances and is, therefore, indirect. The problem of verifiable quantum advantage aims to resolve this critical issue and provides us with greater confidence in a claimed advantage. Instantaneous quantum polynomial-time (IQP) sampling has been proposed to achieve beyond classical capabilities with a verifiable scheme based on quadratic-residue codes (QRC). Unfortunately, this verification scheme was recently broken by an attack proposed by Kahanamoku-Meyer. In this work, we revive IQP-based verifiable quantum advantage by making two major contributions. Firstly, we introduce a family of IQP sampling protocols called the stabilizer scheme, which builds on results linking IQP circuits, the stabilizer formalism, coding theory, and an efficient characterization of IQP-circuit correlation functions. This construction extends the scope of existing IQP-based schemes while maintaining their simplicity and verifiability. Secondly, we introduce the hidden structured code (HSC) problem as a well-defined mathematical challenge that underlies the stabilizer scheme. To assess classical security, we explore a class of attacks based on secret extraction, including Kahanamoku-Meyer’s attack as a special case. We provide evidence of the security of the stabilizer scheme, assuming the hardness of the HSC problem. We also point out that the vulnerability observed in the original QRC scheme is primarily attributed to inappropriate parameter choices, which can be naturally rectified with proper parameter settings.

Quantum computing devices can now perform sampling tasks that, according to complexity-theoretic and numerical evidence, are beyond the reach of classical computers. This raises the question of how one can efficiently verify that a quantum computer operating in this regime works as intended. In 2008, Shepherd and Bremner proposed a protocol in which a verifier constructs a unitary from the comparatively easy-to-implement family of so-called IQP circuits and challenges a prover to execute it on a quantum computer. The challenge problem is designed to contain an obfuscated secret, which can be turned into a statistical test that accepts samples from a correct quantum implementation. It was conjectured that extracting the secret from the challenge problem is NP-hard, so that the ability to pass the test constitutes strong evidence that the prover possesses a quantum device and that it works as claimed. Unfortunately, about a decade later, Kahanamoku-Meyer found an efficient classical secret-extraction attack. Bremner, Cheng, and Ji very recently followed up by constructing a wide-ranging generalization of the original protocol. Their IQP Stabilizer Scheme has been explicitly designed to circumvent the known weakness. They also suggested that the original construction can be made secure by adjusting the problem parameters. In this work, we develop a number of secret-extraction attacks that are effective against both new approaches in a wide range of problem parameters. In particular, we find multiple ways to recover the $300$-bit secret hidden in a challenge data set published by Bremner, Cheng, and Ji. The important problem of finding an efficient and reliable verification protocol for sampling-based proofs of quantum advantage thus remains open.

The exploration of the concept of nonlocality beyond standard Bell scenarios in quantum network architectures unveils fundamentally new forms of correlations that hold a strong potential for future applications of quantum communication networks. To materialize this potential, it is necessary to adapt theoretical advances to realistic configurations. Here, we consider a quantum triangle network, for which is has been shown in theory that, remarkably, quantum nonlocality without inputs can be demonstrated for sources with an arbitrarily small level of independence. We realize such correlated sources experimentally by carefully engineering the output state of a single $\mathrm{Al}\mathrm{Ga}\mathrm{As}$ multiplexed entangled-photon source, exploiting energy-matched channels cut in its broad spectrum. This simulated triangle network, based on standard fiber telecom components, is then used to violate experimentally a Bell-like inequality that we derive to capture the effect of noise in the correlations present in our system. We also rigorously validate our findings by analyzing the mutual information between the generated states. Our results allow us to deepen our understanding of network nonlocality while also pushing its practical relevance for quantum communication networks.

Chiral quantum optics is a growing field of research in which light-matter interactions become asymmetrically dependent on momentum and spin, offering novel control over photonic and electronic degrees of freedom. Recently, the platforms for investigating chiral light-matter interactions have expanded from laser-cooled atoms and quantum dots to various solid-state systems, such as microcavity polaritons and two-dimensional layered materials, integrated into photonic structures such as waveguides, cavities, and ring resonators. In this Perspective, we begin by establishing the foundation for understanding and engineering these chiral light-matter regimes. We review the cutting-edge platforms that have enabled their successful realization in recent years, focusing on solid-state platforms, and discuss the most relevant experimental challenges to fully harness their potential. Finally, we explore the vast opportunities that these chiral light-matter interfaces present, particularly their ability to reveal exotic quantum many-body phenomena, such as chiral many-body superradiance and fractional quantum Hall physics.

Finding the ground energy of a quantum system is a fundamental problem in condensed-matter physics and quantum chemistry. Existing classical algorithms for tackling this problem often assume that the ground state has a succinct classical description, i.e., a poly-size classical circuit for computing the amplitude. Notable examples of succinct states encompass matrix product states, contractible projected-entangled-pair states, and states that can be represented by classical neural networks. We study the complexity of the local Hamiltonian problem (LHP) with a succinct ground state. We prove that this problem is $\mathbf{\text{MA}}$-$\mathbf{\text{complete}}$. The Hamiltonian that we consider is general and might not be stoquastic. The $\mathbf{\text{MA}}$ verification protocol is based on the fixed-node quantum Monte Carlo method, particularly the variant of the continuous-time Markov chain introduced by Bravyi, Carleo, Gosset, and Liu. Based on our work, we also introduce a notion of strong guided states and conjecture that the LHP with a strong guided state is $\mathbf{\text{MA}}$-$\mathbf{\text{complete}}$, which will be in contrast with the $\mathbf{\text{QCMA}}$-$\mathbf{\text{complete}}$ result of the LHP with standard guided states.

Photon losses are the main obstacle to fully photonic implementations of device-independent quantum key distribution (DIQKD). Motivated by recent work showing that routed Bell scenarios offer increased robustness to detection inefficiencies for the certification of long-range quantum correlations, we investigate DIQKD protocols based on a routed setup. In these protocols, in some of the test rounds, photons from the source are routed by an actively controlled switch to a nearby test device instead of the distant one. We show how to analyze the security of these protocols and compute lower bounds on the key rates using noncommutative polynomial optimization and the Brown-Fawzi-Fawzi method. We determine lower bounds on the asymptotic key rates of several simple two-qubit routed DIQKD protocols based on CHSH or BB84 correlations and compare their performance to standard protocols. For high-quality short-path tests, we find that routed DIQKD protocols are significantly more robust to losses, showing an improvement of approximately $30\mathrm{\%}$ in the detection efficiency compared to their nonrouted counterparts. This translates to a large improvement in the distance over which nonzero key can be distilled in optical setups with near-perfect single-photon detectors, where the main source of loss in the setup is due to transmission in the fiber. Notably, the routed BB84 protocol achieves a positive key rate with a detection efficiency as low as $50\mathrm{\%}$ for the distant device, the minimal threshold for any QKD protocol featuring two untrusted measurements. However, the advantages we find are highly sensitive to noise and losses affecting the short-range correlations involving the additional test device.