We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically designed circuit components, which we refer to as circuit perturbations, acting as a direct representation of the external perturbative force within the quantum circuit in a linear-response setting. The direct mapping between circuit derivatives and the computation of RGFs enables the use of a broad range of differentiation strategies. We provide two such examples, including a class of stochastic estimators which do not require extra qubit connectivity with respect to the underlying time-evolution operations. We demonstrate our approach on interacting spin and fermionic models, showing that accurate dynamical correlations can be obtained even under realistic noise assumptions. Finally, we outline how our proposal can be tied to efficient gradient-estimation techniques relevant for the fault-tolerant regime.

Quantum circuits with local unitaries offer a platform to explore many-body quantum dynamics in discrete time. Their locality makes them suitable for current processors, but verification at scale is difficult for non-integrable systems. Here we study dual-unitary circuits, which are maximally chaotic yet permit exact analytical solutions for certain correlation functions. Using improved noise-learning and error-mitigation methods, we show that a superconducting quantum processor with 91 qubits is able to accurately simulate these correlators. We then perturb the circuits away from the dual-unitary point and benchmark the dynamics against tensor-network simulations. These results establish error-mitigated digital quantum simulation on pre-fault-tolerant processors as a reliable tool to explore emergent quantum many-body phases. Studying many-body quantum chaos on current quantum hardware is hindered by noise and limited scalability. Now it is shown that a superconducting processor, combined with error mitigation, can accurately simulate dual-unitary circuit dynamics.

The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.

Stereoisomers of C13Cl2 exhibiting helical orbitals around a ring of carbon atoms were synthesized by atom manipulation on NaCl surfaces. We resolved the enantiomeric geometries of the singlet states by atomic force microscopy and mapped their helical orbital densities by scanning tunneling microscopy. A π-orbital basis of the helical, nonplanar singlets that twists by 90° in one circulation is consistent with a half-Möbius topology. In such a topology, the π-orbital basis changes sign with respect to two circumnavigations and is periodic with respect to four circumnavigations. A quasiparticle on a ring with this boundary condition could be interpreted as carrying a Berry phase of π/2. We demonstrate reversible switching of the topology between the two singlets of oppositely threaded half-Möbius topology and the planar, topologically trivial triplet state. Multireference calculations, including large-scale, sample-based ab initio calculations executed on quantum hardware, revealed that the switching is associated with a helical pseudo-Jahn-Teller effect.

Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization of the quantum component of the tensor network. In this work, we introduce an alternative strategy that combines a non-parametric quantum state prepared through quantum annealing and a classical isometric tensor network. The latter is variationally optimized while the former is used as a fixed, boundary tensor resource in the form of classical shadows. We demonstrate the feasibility of this approach through extensive numerical simulations on the transverse-field Ising model, showing that the optimization procedure remains robust under statistical and hardware noise. Moreover, our results indicate that our newly proposed setup improves the accuracy of the obtained ground state approximation compared to the original quantum simulation, without increasing the depth of the applied quantum circuits. Therefore, this setup offers a practical route to scale variational quantum algorithms towards the quantum utility scale.

We report quantum chemistry calculations performed on superconducting quantum processors for a molecule exhibiting the half-Möbius electronic topology originally introduced by Rončević et al. Using SqDRIFT, a randomized sample-based Krylov quantum diagonalization algorithm, we achieve reliable quantum simulations on active spaces corresponding to 36 orbitals (72 qubits) and extend previous studies up to 50 orbitals (100 qubits). We demonstrate that a systematic increase of active space sizes, which has a concrete impact on the accuracy of the electronic structure description, is achievable with state-of-the-art quantum processors, thus offering a promising path towards practically relevant quantum-assisted electronic-structure calculations.

Molecular rings of N carbon atoms, that is, cyclo[N]carbons, or C_N, can be formed by tip-induced chemistry [1-7]. Because of their monocyclic geometry, cyclocarbons are fundamentally important for testing theoretical models of aromaticity [8-11]. Here, we synthesized large cyclo[N]carbons, with N up to 88, by tip-induced chemistry on a NaCl surface and studied their aromaticity by measuring their transport gaps by scanning tunnelling spectroscopy. We first generated C_20 and C_22, and then fused multiple cyclocarbons [5-7] by means of atom manipulation, obtaining C_42, C_44, C_46, C_66 and C_88. In agreement with predictions obtained using a finely tuned density functional [12-15] and large active space approximate configuration interaction calculations executed on quantum hardware [16, 17], we observe a substantially smaller transport gap for C_20 (N = 4n) compared to C_22 (4n+2), and for C_44 (4n) relative to C_42 (4n+2). In larger cyclocarbons, the oscillation of the transport gap between anti-aromatic N = 4n and aromatic N = 4n+2 cyclocarbons becomes smaller, and is expected to eventually vanish with increasing N, indicating non-aromaticity. Our experimental results show that aromaticity persists at N = 42, and theory predicts ring currents comparable in magnitude to that of benzene in cyclocarbons of this size. In the future, such large cyclocarbons could be used to study conductance, quantum interference, and the effects of aromaticity in single atomic carbon wires and circuits.

We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, allowing longer evolution times to be evaluated with higher fidelity on contemporary quantum processors. Utilizing zero-noise extrapolation in combination with Pauli twirling, on quantum hardware we accurately simulate the full scattering dynamics on 40 qubits, and further demonstrate the tensor networks compressed state preparation on 80 qubits.

The dynamical evolution of neutrino flavor in supernovae can be modeled by an all-to-all spin Hamiltonian with random couplings. Simulating such two-local Hamiltonian dynamics remains a major challenge, as methods with controllable accuracy require circuit depths that increase at least linearly with system size, thereby exceeding the capabilities of current quantum devices. The eigenstate thermalization hypothesis predicts that these systems should thermalize, a behavior confirmed in small-scale classical simulations. Here we investigate flavor thermalization in much larger systems using random quantum circuits as an empirical tool to emulate the non-local dynamics, and demonstrate that thermal behavior can be reproduced using a depth independent of system size. By simulating systems of over one hundred qubits, we find that the thermalization time grows approximately as the square root of the system size, consistent with predictions from semi-classical methods. Our study also illustrates that near-term quantum devices are useful tools to test and validate empirical classical methods, and highlights an application of random circuits in physics.

Gauge invariance is central to modern physics and underpins quantum simulations of lattice gauge theories (LGTs). Existing quantum simulation approaches employ Gauss's law either to energetically suppress gauge-violating processes in analog platforms or to detect and discard gauge-violating outcomes in digital devices. Here we introduce a third paradigm, in which Gauss's law is used to dynamically generate the gauge theory itself from a substantially simpler Hamiltonian. Starting from a readily programmable three-body XXX model, we employ experimentally efficient single-qubit U(1) gauge symmetry-generator terms that induce the dynamics of a U(1) LGT. We implement this approach using 101 qubits on a 156-qubit IBM quantum processor and observe real-time dynamics in quantitative agreement with the target LGT while reducing the entangling-gate depth per Trotter step by a factor of five compared with a direct implementation. Our results establish gauge protection as a resource for Hamiltonian engineering rather than merely symmetry preservation, opening a scalable resource-efficient route towards digital quantum simulations of increasingly complex gauge theories in higher spatial dimensions.

Proton transfer reactions are central to chemical and biological systems, where quantum effects-such as tunneling, delocalization, and zero-point motion-critically influence reaction kinetics. Classical methods that capture these phenomena scale poorly with system size, limiting their applicability. Here, we extend and benchmark a quantum computing framework based on the Nuclear-Electronic Orbital formalism, treating the transferring proton quantum mechanically, to assess the feasibility of computing accurate energy barriers on current quantum devices. Using malonaldehyde as a prototypical system, we construct deep initial circuits via ADAPT-VQE combined with the frozen natural orbital approximation and apply adaptive approximate quantum compiling to balance circuit depth and fidelity. Transpiling these circuits for the ibm_pittsburgh device and simulating with realistic noise models, we compute barrier heights and delocalized proton densities along the reaction pathway. Circuit refinement and compression yield compact representations that preserve essential quantum features of the transfer process. Notably, our shallowest circuits (AQC-low) reproduce key qualitative features, such as proton density localization, and are near the frontier of feasibility for current hardware. In contrast, deeper circuits (AQC-high) retain higher fidelity to reference barrier height, reducing the error to 1.6 mHa (13%) while still yielding a 98% underestimation of the rate constant at 120 K.

Our work integrates an Evolutionary Algorithm (EA) with the Quantum Approximate Optimization Algorithm (QAOA) to optimize ansatz parameters in place of traditional gradient-based methods. We benchmark this Evolutionary-QAOA (E-QAOA) approach on the Max-Cut problem for d-3 regular graphs of 4 to 26 nodes, demonstrating equal or higher accuracy and reduced variance compared to COBYLA-based QAOA, especially when using Conditional Value at Risk (CVaR) for fitness evaluations. Additionally, we propose a novel distributed multi-population EA strategy, executing parallel, independent populations on two quantum processing units (QPUs) with classical communication of 'elite' solutions. Experiments on quantum simulators and IBM hardware validate the approach. We also discuss potential extensions of our method and outline promising future directions in scalable, distributed quantum optimization on hybrid quantum-classical infrastructures.

Use of light in healthcare is evolving with increasing applications of photodynamic therapy (PDT) for treating various cancers. PDT utilizes light-activated molecules called photosensitizers (PSs) that generate reactive oxygen species (ROSs) to induce tumor cell apoptosis and necrosis. However, the use of PDT is limited by the availability of PSs that can be activated by deep tissue-penetrating near-infrared light, exhibit low dark toxicity, and produce ROSs efficiently. Here we review the different categories of PS currently used in clinical or preclinical trials and highlight the significance of advanced computational methods, including density functional and wave function-based quantum chemistry, for understanding the molecular mechanisms involved in PS activation. Despite advancements in classical computational techniques, the complexities of excited state dynamics in highly correlated molecular systems demand innovative simulation approaches such as quantum computing. We propose that quantum computing holds promise for accurately modeling the excited-state properties of PSs to optimize their design and broaden clinical applications.

Quantum subspace expansion (QSE) offers promising avenues to perform spectral calculations on quantum processors but comes with a large measurement overhead. Informationally complete (IC) measurements, such as classical shadows, were recently proposed to overcome this bottleneck. Here, we report the first large-scale implementation of QSE with IC measurements. In particular, we probe the quantum phase transition of a spin model with three-body interactions, for which we observe accurate ground state energy recovery and mitigation of local order parameters across system sizes of up to 80 qubits. We achieve this by reformulating QSE as a constrained optimization problem, obtaining rigorous statistical error estimates and avoiding numerical ill-conditioning. With over 3 × 10^4 measurement basis randomizations per circuit and the evaluation of O(10^14) Pauli traces, this represents one of the most significant experimental realizations of classical shadows to date.

We investigate the performance and accuracy of digital quantum algorithms for the study of static and dynamic properties of the fermionic Hubbard model at half-filling with next-nearest neighbour hopping terms. We provide quantum circuits to perform ground and excited states calculations, via the Variational Quantum Eigensolver (VQE) and the Quantum Equation of Motion (qEOM) approach respectively, as well as product formulas decompositions for time evolution. We benchmark our approach on a chain with L=6 sites and periodic boundary conditions, computing the charge and spin gaps, the spectral function and spin-spin dynamic correlations. Our results for the ground state phase diagram are in qualitative agreement with known results in the thermodynamic limit. Finally, we provide concrete scalings for the number of gates needed to implement our protocols on a qubit register with all-to-all connectivities and on a heavy hexagonal coupling map.

Quantum computing provides a novel avenue towards simulating dynamical phenomena, and, in particular, scattering processes relevant for exploring the structure of matter. However, preparing and evolving particle wave packets on a quantum device is a nontrivial task. In this work, we propose a method to prepare Gaussian wave packets with momentum on top of the interacting ground state of a fermionic Hamiltonian. Using Givens rotation, we show how to efficiently obtain expectation values of observables throughout the evolution of the wave packets on digital quantum computers. We demonstrate our technique by applying it to the staggered lattice formulation of the Thirring model and studying the scattering of two wave packets. Monitoring the particle density and the entropy produced during the scattering process, we characterize the phenomenon and provide a first step towards studying more complicated collision processes on digital quantum computers. In addition, we perform a small-scale demonstration on IBM's quantum hardware, showing that our method is suitable for current and near-term quantum devices.

Quantum computers (QC) could harbor the potential to significantly advance materials simulations, particularly at the atomistic scale involving strongly correlated fermionic systems, where an accurate description of quantum many-body effects scales unfavorably with size. While a full-scale treatment of condensed matter systems with currently available noisy quantum computers remains elusive, quantum embedding schemes like dynamical mean-field theory (DMFT) allow the mapping of an effective, reduced subspace Hamiltonian to available devices to improve the accuracy of ab initio calculations such as density functional theory (DFT). Here, we report on the development of a hybrid quantum-classical DFT + DMFT simulation framework which relies on a quantum impurity solver based on the Lehmann representation of the impurity Green’s function. Hardware experiments with up to 14 qubits on the IBM Quantum system are conducted, using advanced error mitigation methods and a novel calibration scheme for an improved zero-noise extrapolation to effectively reduce adverse effects from inherent noise on current quantum devices. We showcase the utility of our quantum DFT + DMFT workflow by assessing the correlation effects on the electronic structure of a real material, Ca2CuO2Cl2, which is mapped to an effective single-band Hubbard Hamiltonian and the subsequently derived Anderson impurity model solved with up to 6 bath sites on available quantum hardware. Further, we carefully benchmark our quantum results with respect to exact reference solutions and experimental spectroscopy measurements. While challenges remain to scale our approach to larger, multi-orbital and multi-site systems with more bath sites, the present work marks an important milestone towards achieving utility-scale quantum computation in materials simulation.

Recent innovations in quantum computing hardware and algorithms have raised expectations that practical, real-world applications are within reach. In this context, we explore the potential impact of quantum computing on the drug discovery and development pipeline. Specifically, we discuss use cases from our research programs and outline approaches for prioritizing them based on our assessment of potential benefit from quantum computation. We identify and discuss specific classes of quantum chemistry problems that present challenges for classical computing methods, and where we have made initial efforts to develop and apply quantum computing algorithms. Finally, we offer a perspective on opportunities that will become available as we enter the early-fault tolerant era.

Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many operational aspects of hTN-based algorithms, like the optimization of hTNs, the generalization of standard contraction rules to an hybrid setting, and the design of application-oriented architectures have not been thoroughly investigated yet. In this work, we introduce a novel algorithm to perform ground state optimizations with hybrid Tree Tensor Networks (hTTNs), discussing its advantages and roadblocks, and identifying a set of promising applications. We benchmark our approach on two paradigmatic models, namely the Ising model at the critical point and the Toric code Hamiltonian. In both cases, we successfully demonstrate that hTTNs can improve upon classical equivalents with equal bond dimension in the classical part.

In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine theoretical no-go results and their implications, addressing misconceptions about the practicality of quantum error mitigation techniques and variational quantum algorithms. By emphasizing the nuances of error scaling, circuit depth, and algorithmic feasibility, we highlight viable near-term applications and synergies between error mitigation and early fault-tolerant architectures. Our discussion explores strategies for addressing current challenges, such as barren plateaus in variational circuits and the integration of quantum error mitigation and quantum error correction techniques. We aim to underscore the importance of continued innovation in hardware and algorithmic design to bridge the gap between theoretical potential and practical utility, paving the way for meaningful quantum advantage in the era of late noisy intermediate scale and early fault-tolerant quantum devices.