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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum complexity in gravity, quantum field theory, and quantum information science

Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. Here, we seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.

Baiguera, Stefano [Istituto Nazionale di Fisica Nu↗
DOE OSTI2025

Quantum information meets high-energy physics: input to the update of the European strategy for particle physics

Some of the most astonishing and prominent properties of Quantum Mechanics, such as entanglement and Bell nonlocality, have only been studied extensively in dedicated low-energy laboratory setups. The feasibility of these studies in the high-energy regime explored by particle colliders was only recently shown and has gathered the attention of the scientific community. For the range of particles and fundamental interactions involved, particle colliders provide a novel environment where quantum information theory can be probed, with energies exceeding by about 12 orders of magnitude those employed in dedicated laboratory setups. Furthermore, collider detectors have inherent advantages in performing certain quantum information measurements and allow for the reconstruction of the state of the system under consideration via quantum state tomography. Here, we elaborate on the potential, challenges, and goals of this innovative and rapidly evolving line of research and discuss its expected impact on both quantum information theory and high-energy physics.

Physics↗
DOE OSTI2025

Quantum entanglement correlations in double quark PDFs

Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions x 1 and x 2 . A nonperturbative three quark model light-cone wavefunction predicts significant nonclassical correlations associated with the “entanglement negativity” measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher Q 2 scale, the nonclassical correlations manifest in the dPDF for nearly symmetric momentum fractions.

Entanglement in field theory↗
DOE OSTI2026

Quantum Computing Algorithms and Applications for Coherent and Strongly Correlated Chemical Systems

This project advanced quantum algorithms, quantum information theory, strongly correlated electronic structure methods, molecular quantum materials, and exciton transport imaging in coherent condensed phase systems. Across the award period, the team developed new methods for open-quantum-system simulation, Hamiltonian learning, state tomography, reduced-density-matrix and contracted-quantum eigensolver approaches, and quantum diagnostics for device capability and openness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review

The detection and certification of entanglement and quantum correlations in materials is of fundamental and far-reaching importance, and has seen significant recent progress. It impacts both the understanding of the basic science of quantum many-body phenomena as well as the identification of systems suitable for novel technologies. Frameworks suitable to condensed matter that connect measurements to entanglement and coherence have been developed in the context of quantum information theory. These take the form of entanglement witnesses and quantum correlation measures. Here, the underlying theory of these quantities, their relation to condensed matter experimental techniques, and their application to real materials are comprehensively reviewed. In addition, their usage in, e.g., protocols, the relative advantages and disadvantages of witnesses and measures, and future prospects in, e.g., correlated electrons, entanglement dynamics, and entangled spectroscopic probes, are presented. Consideration is given to the interdisciplinary nature of this emerging research and substantial ongoing progress by providing an accessible and practical treatment from fundamentals to application. Particular emphasis is placed on quantities accessible to collective measurements, including by susceptibility and spectroscopic techniques. This includes the magnetic susceptibility witness, one-tangle, concurrence and two-tangle, two-site quantum discord, and quantum coherence measures such as the quantum Fisher information.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

Anand, Namit [NASA, Ames; Unlisted, US] (ORCID:000↗
DOE OSTI2025

Entanglement Cost for Infinite-Dimensional Physical Systems

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state ρ ΑΒ with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure—the entanglement cost—for all infinite-dimensional physical systems.

Complexity↗
DOE OSTI2025

Real classical shadows

Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis $\mathcal{W}$ after it has evolved under a unitary transformation randomly sampled from a chosen distribution $\mathcal{U}$. In this work we study the case where $\mathcal{U}$ corresponds to either local or global orthogonal Clifford gates, and $\mathcal{W}$ consists of real-valued vectors. Our results show that for various situations of interest, this ‘real’ classical shadow protocol improves the sample complexity over the standard scheme based on general Clifford unitaries. For example, when one is interested in estimating the expectation values of arbitrary real-valued observables, global orthogonal Cliffords typically decrease the required number of samples by a factor of two. More dramatically, for k-local observables composed only of real-valued Pauli operators, sampling local orthogonal Cliffords leads to a reduction by an exponential-in-k factor in the sample complexity over local unitary Cliffords. Finally, we show that by measuring in a basis containing complex-valued vectors, orthogonal shadows can, in the limit of large system size, exactly reproduce the original unitary shadows protocol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Out-of-Distribution Generalization for Learning Quantum Channels with Low-Energy Coherent States

When experimentally learning the action of a continuous-variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is to use low-energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low-energy inputs but very differently for high-energy inputs. They may also act similarly on coherent-state inputs but differently on nonclassical inputs. Extrapolating the behavior of a channel for more general input states from its action on the far more limited set of low-energy coherent states is a case of out-of-distribution generalization. To be sure that such generalization gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low-energy coherent-state inputs, one can bound how different the input-output relations are for any (high-energy or highly nonclassical) input. This proves that out-of-distribution generalization is always possible for learning quantum channels using low-energy coherent states, as long as enough samples are used.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum speed limit for the out-of-time-ordered correlator from an open-system perspective

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time-ordered correlator (OTOC). Employing the OTOC–Renyi-2 entropy theorem, we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the nonintegrable transverse field Ising model. Furthermore, our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter systems, and engineered quantum platforms.

Fermions↗
DOE OSTI2025

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence↗
DOE OSTI2025

Stochastic Waveform Estimation at the Fundamental Quantum Limit

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Axions↗
DOE OSTI2025

Ansatz-Free Hamiltonian Learning with Heisenberg-Limited Scaling

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

machine learning↗
DOE OSTI2026

Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics

We report a phase transition in the projected ensemble—the collection of postmeasurement wave functions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar random), from a phase where it is minimally entropic (“classical bit-string ensemble”). Crucially, this deep thermalization transition is invisible to the subsystem’s density matrix, which always exhibits thermalization to infinite temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗
DOE OSTI2024

Detecting Multipartite Entanglement Patterns Using Single-Particle Green’s Functions

Here, we present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single-particle Green’s functions. To achieve this, we first establish a connection between the quantum Fisher information and single-particle Green’s functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momentum k. We compute the quantum Fisher information for these witness operators and show that for thermal ensembles it can be expressed as an autoconvolution of the single-particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single-particle Green’s function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Mutual information bounded by Fisher information

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the literature (e.g., the van Trees inequality) that are useful also for cases where the latter ones give trivial bounds. We then generalize them to the quantum case, where they bound the Holevo information in terms of the quantum Fisher information. We illustrate the usefulness of our bounds with a case study in quantum phase estimation. Here, they allow us to adapt to mutual information (useful for global strategies where the prior plays an important role), the known and highly nontrivial bounds for the Fisher information in the presence of noise. The results are also useful in the context of quantum communication, both for continuous and discrete alphabets. Published by the American Physical Society 2025

97 MATHEMATICS AND COMPUTING↗