Papers

Deciding whether the clique complex of a given graph has nontrivial homology in a given dimension, under vertex-product weighting and an inverse-polynomial spectral gap promise on the combinatorial Hodge Laplacian, is known to be $\mathsf{QMA}_1$-hard and contained in $\mathsf{QMA}$ by King and Kohler (FOCS 2024). The vertex weights are essential in the known proof, where they provide the scale separation needed for the spectral gap analysis. We prove that, when every vertex has weight one, the problem remains $\mathsf{QMA}_1^{g_2}$-hard and is contained in $\mathsf{QMA}_1^{g_2}$, where $\mathsf{QMA}_1^{g_2}$ is $\mathsf{QMA}_1$ with the universal gate set $g_2=\{\mathsf{X},\mathsf{CX},\mathsf{CCX},H\otimes H\}$. The construction replaces weight by expansion: each vertex of the weighted complex is blown up into a clique whose size encodes its weight. The block sizes are chosen so that symmetric averages reproduce the weighted Hodge metric. The symmetric sector therefore carries the weighted Laplacian up to a common scalar factor, while a local averaging argument gives a uniform lower bound on the orthogonal complement to the symmetric sector. Hence the weighted gap analysis transfers to an unweighted clique complex without introducing either additional low-energy states or spurious homology. Containment in $\mathsf{QMA}_1^{g_2}$ follows from Rudolph's exact linear combination of unitaries simulation of sparse integer clique Laplacians. The result shows that the gap promise, rather than vertex weighting, is the source of the complexity of gapped clique homology.

Tensor network methods provide powerful analytical and numerical tools for characterizing quantum phases of matter. While the mathematical structure of matrix product states (MPS) is well understood through the MPS fundamental theorem, an analogous understanding for mixed-state tensor networks remains largely absent: if two purification tensors generate the same density matrix, how are they related? In this work, we initiate the study of a fundamental theorem for matrix product locally purifiable density operators (LPDOs) and focus on sequentially generated LPDOs (sLPDOs), a broad subclass admitting an interpretation in terms of successive applications of quantum channels on an initial state. We prove that, under suitable invertibility or cyclic conditions, two sLPDO representations generate the same density matrix for arbitrary system sizes if and only if they are related by a matrix product isometry acting on the purification bonds. Beyond the sLPDO setting, we provide a counterexample that suggests an obstruction to a general fundamental theorem for LPDOs with periodic boundary conditions. Finally, we discuss implications for mixed-state symmetry-protected topological phases, including the possibility of nontrivial phases protected only by weak symmetry conditions.

At large $N$, two coupled Sachdev-Ye-Kitaev models realize an eternal traversable wormhole with a discrete spectrum. We show that at finite $N$ the spectrum organizes into clusters labeled by operator size. Low-size clusters evolve into the conformal towers and define a weak-ergodicity-breaking subspace responsible for the long-lived wormhole revival dynamics. Moreover, the competition between size energy and size entropy provides a microscopic interpretation of the wormhole-black hole transition. These results reveal operator size as the bridge between the finite-$N$ spectrum and the emergent gravitational physics at large $N$.

We develop a unified framework for analyzing the complexity of quantum property testing through functionals of the form $\mathcal{L}_{\phi}(\rho) = \operatorname{tr}(\phi(d\rho))/d$, where $\rho$ is an unknown $d$-dimensional quantum state and $\phi$ is a given function. A master theorem is established that derives sample complexity lower bounds for estimating $\mathcal{L}_\phi(\rho)$ from properties of $\phi$, combining Haar-random moment encoding with moment matching and best polynomial approximation. Corresponding query complexity lower bounds follow from quantum sample-to-query lifting. The framework yields nearly tight bounds for a broad class of problems, including entropy estimation (von Neumann, Rényi, and Tsallis), closeness estimation (trace distance and Uhlmann fidelity), spectrum estimation, rank testing (operator rank, Schmidt rank, and matrix product states). Combined with known upper bounds, these results resolve several open problems and establish the optimality of 31 quantum algorithms since 2015, up to polylogarithmic factors.

We develop an argmax principle for analyzing sum-of-squares relaxations of optimization problems over the unit sphere. Given a feasible pseudo-expectation, we form a polynomial of high-order pseudo-moments, such as $\Phi_k(u)=\widetilde{\mathbb E}\langle x,u\rangle^{2k}$. Our guiding principle is that its maximizers are rounding candidates: their local and global optimality conditions reveal the reweighed pseudo-expectation inequalities governing SoS convergence. This viewpoint unifies several problems previously analyzed by rather different techniques. We obtain three results. First, for Best Separable State, we give a degree-$O(\sqrt{n/\epsilon})$ SoS analysis for approximating $h_{\mathrm{sep}}(P)$ in the perfect-completeness regime, improving and simplifying Barak, Kothari and Steurer (STOC'17). The dependence is essentially tight for inverse-linear gap under the Exponential-Time Hypothesis, matching hardness from $\mathrm{QMA}(2)$ protocols. Second, for the matrix $2\to4$ norm, degree-$O(\sqrt n/\epsilon)$ SoS gives a multiplicative $(1+\epsilon)$ approximation. Barak et al. (STOC'12) previously gave a comparable-time constant-gap decision algorithm; our result gives a multiplicative guarantee and extends to a family of $p\to q$ norms with even $q$. Finally, for degree-$d$ polynomial optimization, we recover the convergence theorem of Bhattiprolu et al. (FOCS'17) with a shorter, more direct proof: degree-$k$ SoS gives approximation ratio $O_d((n/k)^{d/2-1})$. The paper introduces no new relaxation. Instead, the high-moment argmax gives a common way to read an SoS solution, unifying previously separate convergence analyses and yielding sharper bounds or simpler proofs.

We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $\rho_N\in D(\mathrm{Sym}^N(\mathbb C^d))$, there is a probability measure $\nu$ on the unit sphere such that \[ \left\| \rho_N^{(2)}-\int |u\rangle\langle u|^{\otimes 2}\,d\nu(u) \right\|_1 \le \frac{\sqrt{d-1}}{N-1}. \] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchangeable states. These results settle the dimension dependence left open by Christandl, König, Mitchison, and Renner (CMP 2007). The proof casts de Finetti approximation as sum-of-squares rounding and applies the argmax method of Jeronimo, Wu, and Xu (manuscript 2026). More generally, $t$-site marginals satisfy $O(t\sqrt d/N)$ bosonic and $O(td/N)$ permutation-invariant bounds. Our proof formulates de Finetti approximation as the integrality gap of a symmetric-extension semidefinite program and rounds an optimum by the argmax principle. The sharp bounds have several consequences. For every fixed $\varepsilon\in(0,1)$, we construct a channel with input dimension $D=\exp(O_\varepsilon(\sqrt d\log d))=\exp(o(d))$ whose outputs are $\varepsilon$-close to separable states of local dimension $d$ and whose image contains every such separable state, thereby refuting Watrous's disentangler conjecture. We also obtain deterministic $\exp(\widetilde O(\sqrt d/\varepsilon))$-time algorithms for explicit Best Separable State without perfect completeness and for trace-distance separability testing. Finally, spectral truncation gives the first dimension-free bosonic de Finetti theorem in Hilbert–Schmidt distance, with the optimal rate $\Theta(N^{-1/2})$ when the dimension may grow.

The mysterious nature of entanglement, one of the most prominent exquisitely quantum phenomena, is reflected in its intricate operational structure, with a hierarchy of classes of free operations that enable its manipulation at different levels of effectiveness. Here we use the class of 'flower states', parametrised by their (even) local dimension $2k$, to shine light on some aspects of this varied landscape. We compute all the main entanglement measures for flower states, uncovering a large gap between all forms of distillable entanglement, equal to 1 ebit independently of the local dimension, and the entanglement cost under local operations and classical communication (LOCC), known to be equal to $\log\big(2\sqrt{k}\big)$. Even under the strictly more powerful class of non-entangling (NE) operations, we show that their cost is still equal to $\log\big(1+\sqrt{k}\big)$, only about an ebit less than for LOCCs. This result, which we prove by calculating the recently introduced tempered entanglement negativity for these states, demonstrates the largest known 'irreversibility gap', i.e. the difference between distillable entanglement and entanglement cost, under NE operations, equal to $\Theta\big(\frac12 \log d\big)$, with $d$ being the local dimension. A notable consequence is that the celebrated squashed entanglement is not a monotone under NE operations. Finally, we compute the exact cost under LOCC operations for flower states; this is given by the Schmidt number, which turns out to be additive over multiple copies and equal to $\min_{r|k} \log\left( r + \frac{k}{r} \right)$; for prime $k$ this reduces to $\log(k+1)$, about twice the standard LOCC cost. These last results leverage the uncertainty relations over cyclic groups proved by Tao and Meshulam.

We investigate a quantum Otto engine (QOE) constructed from the two-qubit quantum Rabi model, operating within a cavity quantum electrodynamics (QED) architecture. The engine operates with two qubits as the working substance and a single non-Markovian hot thermal bath, modeled via the hierarchical equations of motion (HEOM) formalism. In place of a conventional cold thermal reservoir, the cooling stroke is realized through a projective measurement protocol on the cavity mode, which acts as an ancillary subsystem and effectively mimics a cold bath for the qubit working medium via measurement back-action. A squeezing drive applied to the cavity mode serves as a quantum fuel. We demonstrate that cavity squeezing systematically enhances both the power output and operational efficiency of the engine - the work extracted per unit of heat drawn from the hot bath-driving it above the standard quantum Otto limit. In the limit-cycle regime, the efficiency, while remaining above the Otto bound throughout, asymptotically converges to it from above. This identifies squeezing as a controllable quantum resource for thermodynamic optimization. Our results reveal that the interplay between qubit-cavity coupling, measurement-induced cooling, and non-equilibrium squeezing gives rise to a multi-resource thermodynamic architecture with performance characteristics inaccessible to conventional two-bath quantum Otto engines, thereby providing a concrete route toward experimentally realizable quantum heat engines in cavity QED platforms.

Pseudomode approaches allow for an exact and unapproximated description of a quantum system interacting arbitrarily strongly with a bath. In general, a system coupled to pseudomodes will not thermalize to the system's Gibbs state: This is to be expected when the system-bath coupling is non-perturbative, but conflicts with common thermodynamic intuition when the system-bath coupling is asymptotically weak. We explore under which circumstances pseudomode models satisfy detailed balance (and subsequently thermalize to the system Gibbs state) and how specific choices of parameters can force "weak" detailed balance that is restricted to a limited frequency range. A combination of Hermitian and non-Hermitian pseudomodes that yields a flat effective-temperature profile is also considered. The results and criteria established here are relevant for the construction of pseudomode models in contexts where thermodynamic consistency is required.

We compare two popular models applicable to analyzing heat transport by thermal microwave photons in quantum circuits. The first model is derived from a weak-coupling Lindblad master equation, with transition rates determined by Fermi's golden rule induced by thermal dissipation sources. The second approach employs a circuit model, where thermal Johnson-Nyquist noise generated by dissipative elements introduces currents, and consequently Joule power, in other parts of the circuit. This leads to a Landauer type expression of heat transport where the transmission coefficient is proportional to the transconductance in the circuit. We find that the two models yield identical results in a linear circuit in the weak coupling limit with an analytic expression of power in an archetypal circuit of a cavity mediating heat between two baths. Our analysis yields a quantitative assessment of the range of validity of the weak coupling assumption in a circuit. Due to the correspondence of the two results, we feel confident in applying the weak coupling Lindblad model also for analyzing heat transport in quantum circuits consisting, e.g. of qubits and/or non-linear resonators.

The goal of quantum process tomography is to fully characterize an operation performed on a quantum state. By considering high-dimensional quantum states (qudit), we show that it is possible to fully reconstruct an arbitrary operation without performing any measurement on the transformed qudit. Our method is interferometric and conceptually different from existing techniques of quantum process tomography that must perform a measurement on the transformed qudit.

Tensor-network methods have opened a powerful route for the study of dynamical spectral functions in two-dimensional quantum systems. However, existing approaches within the framework of infinite projected entangled-pair states construct the required renormalization tensors solely from the ground-state environment and can suffer from severe numerical instability. We identify the origin of this instability and introduce an excitation-tailored corner-transfer-matrix renormalization-group (ET-CTMRG) method to resolve it. By incorporating excitation tensors into the renormalization procedure, the method constructs a substantially more accurate effective Hamiltonian matrix and thereby yields reliable and well-converged excitation spectra. For Heisenberg antiferromagnets, it reduces truncation errors by orders of magnitude and for the particularly complex case of the supersolid phase in the triangular-lattice XXZ magnet $\mathrm{K_2Co(SeO_3)_2}$, it achieves excellent quantitative agreement with inelastic neutron-scattering measurements. ET-CTMRG therefore provides a robust framework for investigating the dynamical properties of strongly correlated quantum systems.

Pendulums are attractive for macroscopic quantum control because gravity dilution reduces mechanical loss, while the $1/f$ force-noise spectrum associated with structural damping allows nearly lossless trapping to suppress the thermal noise sampled at an upward-shifted resonance. The same $1/f$ spectrum, however, produces a low-frequency tail that penalizes entanglement. With $10\%$ detection loss, we find that this tail raises the required back-action-to-thermal force-noise ratio by about $50\%$, corresponding to a required suspension gain $G_{\rm req}=1.49$. To overcome this structural-noise penalty, we realize a $7$-mg pendulum suspended by a stepped fused-silica fiber, with an energy-decay rate $\Gamma/2\pi=361(39)$ nHz ($Q\equiv\omega_0/\Gamma=7.3(8)\times10^6$) at $\omega_0/2\pi=2.63$ Hz. The reduction in $\omega_0\Gamma$ yields a measured gain $G_q\simeq2.5$ relative to the previous monolithic device, exceeding the requirement.

We investigate the spread complexity of quantum quenches in generalized and long-range Aubry-Andre-Harper (AAH) models, encompassing regimes with and without mobility edges. In particular, in the generalized AAH models supporting energy-dependent mobility edges, we demonstrate that the long-time averaged spread complexity exhibits nonanalytic behavior when the post-quench quasiperiodic potential crosses the mobility edge associated with the energy of the initial eigenstate, thereby accurately identifying the mobility-edge transition. Such a behavior is supported by the spreading of local density of states. We further derive analytical expressions for the moments and the corresponding Lanczos coefficients for quenches between the limits of vanishing and strong quasiperiodic potentials. The Lanczos coefficients display qualitatively distinct behavior depending on the presence of mobility edges - they exhibit an initial plateau followed by a decay with the Krylov basis index, in contrast to the nearly constant behavior of the conventional AAH model without mobility edges. For LR hopping, the coefficients decay with the Krylov basis index for quenches from the localized to the extended phase, while they coincide with the AAH results for quenches in the opposite direction.

The standard benchmark for high-dimensional entanglement is the number of dimensions in which entanglement must be present in order to generate the state. This is called the Schmidt number and its detection is usually based on implementing an appropriate set of local basis measurements. However, as quantum technology brings increasingly large physical dimensions within reach, the implementation of such measurements typically becomes more costly. Here, we develop a scheme for detecting Schmidt numbers based only on sequences of single-qubit observables. These measurements are simpler to implement as they require only low-depth quantum circuits. Using up to sixteen-dimensional photonic spatial mode entanglement and multi-plane light conversion technology, we demonstrate how it simplifies setup complexity and successfully detects the maximal (or close-to-maximal) Schmidt number. Our results reveal that simple and more scalable measurements are sufficient to detect high-dimensional entanglement properties.

We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.

We report precise measurements of inter-level interactions in a bosonic optical lattice clock based on $^{88}$Sr atoms. We observe a nonlinear density dependence of the clock shift, even without reaching quantum degeneracy. In a 2D lattice, the Rabi line shape exhibits an interaction sideband consistent with a collective spin model, while in a 1D lattice the shift is modified by density-induced dephasing. These findings, combined with a careful choice of interrogation detuning and atomic density, can enable operation at a net-zero systematic density shift in $^{88}$Sr lattice clocks. We discuss the implications of these findings in many-body physics, quantum simulation, and precision isotope shift measurements, which provide a powerful probe for new physics beyond the Standard Model.

Entanglement generation is a fundamental dynamical capability in quantum information science and underpins many quantum advantages. While quantum theory enables it through unitary dynamics, boxworld, a generalized probabilistic theory admitting Popescu–Rohrlich boxes with supraquantum correlations, has no reversible transformation capable of generating entanglement. We show that this no-go picture changes fundamentally once reversibility is relaxed to pure-state preservation. We construct a pure-state-preserving transformation that maps every uncorrelated pure state to a Popescu–Rohrlich box and completely classify all pure-state-preserving entangling transformations in the simplest bipartite boxworld. Our results provide the first explicit mechanism for generating beyond-quantum entanglement without introducing mixing and demonstrate a physical distinction between reversibility and pure-state preservation that is obscured by the structure of quantum theory.

Nitrogen-vacancy (NV) centers in chemical-vapor-deposition (CVD) diamond can form preferentially oriented ensembles with high sensing performance and low densities of lattice defects. Thin films of this material are a cornerstone of various imaging modalities. However, nitrogen injection needed to produce such films can transiently drive growth out of equilibrium, generating interfacial strain and spin defects that degrade NV coherence. Here, we investigate this disorder in $^{12}\text{C}$-enriched, preferentially oriented NV layers grown on (111) diamond using two nitrogen-injection procedures, combined with nanometer-scale selective plasma etching and NV spin-coherence measurements. Pulsed nitrogen injection produces a pronounced nitrogen overshoot within a 60–80 nm interfacial region, generating excessive amounts of defects. By contrast, smooth nitrogen delivery through mass flow controllers substantially suppresses interfacial disorder, yielding coherence properties close to the theoretical limit imposed by spin-bath noise. A 50-nm NV layer is used to demonstrate proton nuclear magnetic resonance detection. This work reveals the role of interfacial disorder associated with the nitrogen-doping procedure and provides a route to growing high-quality, thin NV-doped layers for quantum-sensing applications.

Preserving metrological information under noise is central to quantum sensing, yet finite detectors and memories impose an unavoidable limit on how finely noise trajectories can be resolved. Using exact symmetric-logarithmic-derivative geometry, we determine when a monitored trajectory can be compressed without losing quantum Fisher information. For an explicit faithful monitored qubit family, the complete joint signal-and-noise model is recoverable from only polynomially many type records, requiring $O(\log n)$ terminal memory, whereas deferred recovery of arbitrary $n$-qubit states requires exponentially many trajectories, or $O(n)$ memory. Online correction replaces this terminal storage by an irreducible per-use readout and feedback alphabet. These results establish syndrome information as a task- and timing-dependent resource connecting quantum sensing, statistical sufficiency, and quantum error correction.

Quantum resource theory has sharpened our understanding of the intrinsic complexity of quantum systems, particularly their classical simulability. However, it remains unclear which quantum resource governs the classical learnability of quantum circuits, especially beyond the regime of efficient classical simulation. Here we close this knowledge gap by studying the expectation-value functions of families of tunable quantum circuits, with many applications in digital quantum simulation, quantum metrology, and quantum-system characterization. Specifically, we introduce a new resource measure, the dynamical stabilizer entropy (\DSE), which quantifies how broadly an expectation-value function is distributed across its frequency modes. By relating \DSE to operator stabilizer entropy, we establish a computational phase diagram that compares classical simulators with quantum-data-assisted classical surrogates. We first determine the \DSE-dependent learnability boundary of this diagram by deriving bounds on the sample complexity and runtime of classical surrogates, and by developing a \DSE-guided surrogate. We then complete the diagram by proving, under standard complexity-theoretic assumptions, the existence of circuit families that can be efficiently learned by this surrogate but cannot be efficiently emulated from their circuit descriptions alone. Numerical experiments on random and structured circuits with up to 80 qubits support the predicted \DSE-dependent computational landscape. These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning, motivate resource measures linking quantum resources to learnability, and guide the design of learning-based algorithms for scalable quantum systems beyond the reach of direct classical simulation.

We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of every density-matrix element for an arbitrary time-independent Hamiltonian and show that the Hamiltonian enters the dynamics only through the corresponding Bohr frequencies. This leads to a natural distinction between two classes of quantum systems: gapped and gapless. In gapped systems (systems with a discrete energy spectrum), while the diagonal elements remain unchanged, the off-diagonal elements of the density matrix in the energy eigenbasis decay algebraically with a continuously varying exponent and with an amplitude that oscillates periodically in $\log t$. The system therefore approaches a stationary state that is independent of the resetting rate and retains a strong memory of the initial state. In gapless systems (systems with a continuous energy spectrum), arbitrarily small Bohr frequencies prevent stationarity. Instead, the position distribution spreads on the universal (ultra-slow) scale $\log(rt)/r$, independently of the initial state and of the details of the Hamiltonian. We illustrate these results with a two-level system, a harmonic oscillator, and a free quantum particle, and contrast them with their classical counterparts.

Two-dimensional (2D) spectroscopy is a powerful pump-pump-probe technique for revealing couplings between quantum states and disentangling the different contributions to the optical response of a system. We present an efficient method for 2D spectroscopy simulations in the Markovian limit for the environment, capable of handling arbitrary pulse shapes and reproducing time-ordering and overlapping pulse effects, while maintaining a computational cost that scales linearly with the number of sampling points. We leverage this framework to investigate how 2D spectra are affected by spectral phase distortions and highly non-Gaussian pulse shapes, such as those produced experimentally by hollow-core fibers or non-collinear optical amplifiers. We show that realistic pulses can induce the appearance of additional spectral features, lineshape distortions and oscillating contributions in the system's dynamics. Notably, even weak temporal pulse tails arising from uncorrected high-order spectral phase terms cause visible changes in the 2D spectra. We also find that homodyne detection schemes employed in experiments can mitigate the presence of such pulse effects. These results emphasize the importance of including realistic pulses in 2D spectroscopy simulations to identify pulse-induced effects and minimize ambiguities in the interpretation of experimental data.

Phase fluctuations between optical inputs limit programmable photonic processors because their output powers depend on coherent interference. We study the phase-drift penalty that arises when sine and cosine quadratures are measured sequentially rather than simultaneously. The analysis is motivated by measurements from an eight-mode programmable photonic processor, including 35 free-running recordings of 300 s acquired at approximately 125 samples per second per channel. These recordings provide an empirical route for estimating the phase-increment variance at a selected reconfiguration interval. The estimate is defined at the time of the second measurement. For fixed quadrature order, perturbation of the atan2 reconstruction gives $e_{C\to S}=-\delta_\tau\sin^2\phi_0+O(\delta_\tau^2)$ and $e_{S\to C}=-\delta_\tau\cos^2\phi_0+O(\delta_\tau^2)$. Writing $Q_\tau=\operatorname{Var}(\delta_\tau)$, uniform phase averaging gives the first-order drift mean-square error $3Q_\tau/8$. A phase-predicted ordering rule measures the locally less informative quadrature first and the more informative quadrature second. Its uniform first-order penalty is $(3/8-1/\pi)Q_\tau$, which is 84.9 percent below the fixed-order value. We also derive an increment-aware estimator from a local state-space model. Marginalizing the unknown phase increment increases the variance of a stale phase observation by $Q_\tau$, reducing its Fisher information from $I$ to $I/(1+IQ_\tau)$. For ideal balanced Poisson detection, the Fisher information of each quadrature equals its detected signal-photon number. This yields dimensionless architecture boundaries in spatial information and phase-increment variance. Nonlinear Monte Carlo simulations validate the perturbative laws, quantify robustness to prediction error, and compare simultaneous, fixed-order, increment-aware, and adaptive receivers under a common noise model.

Many-body localization (MBL) is a dynamical phenomenon that describes the non-ergodicity of isolated quantum many-body systems. In contrast to thermalization, this phenomenon leads to a long-lived memory of initial states of local systems and slow growth of entanglement. In this work, we study Stark MBL in a 12-qubit correlated fermionic system described by the one-dimensional Fermi-Hubbard model using Hamiltonian simulation on an IBM superconducting qubit quantum computer. To enable such a computation on current-day noisy hardware, we combine a series of compilation steps, including the use of the spin-resolved Jordan-Wigner transformation, employing SWAP networks, and integrating a tensor-network-based quantum circuit optimization routine on top of a standard circuit optimization pipeline. As a result, there is approximately an 88$\%$ and 87$\%$ reduction in two-qubit gate count and circuit depth, respectively. Through such simulations of the real-time dynamics using Trotterized quantum circuits, we exhibit a crossover from thermalizing dynamics of the system at a weak tilt of the field to a strongly localized behavior at large tilt with short evolution times. We also benchmark our obtained results with respect to those from exact simulations.

Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.

Most recently proposed quantum algorithms for solving linear and nonlinear partial differential equations rely on non-unitary operations. These operations are typically implemented probabilistically, requiring postselection and thus increasing the computational cost. We show that quantum lattice gas algorithms enable unconditionally successful quantum simulation of nonlinearities, yielding, to our knowledge, the first quantum algorithm for Burgers equation whose time steps can be concatenated without probabilistic failure. The key idea is to exploit the correspondence between the stochasticity of quantum measurement in the linear combination of unitaries framework and the intrinsic randomness of the classical lattice gas algorithm. In doing so, we identify general properties that characterize probabilistic classical algorithms amenable to this time-marching formulation, and illustrate the approach with an additional application.

In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.

The Aharonov–Bohm (AB) effect is usually read out through phase differences associated with spatially distinct electron paths. We show that confined orbital modes provide a same-path alternative: a core-confined magnetic flux writes opposite propagation phases on the co-propagating modes $|\pm l\rangle$ of a straight annular electron guide while the transported electron-wave support remains field free. In a spin-resolved Dirac treatment, the phase is carried by the overlap of the field-free vector potential $A_\phi$ with the mode's azimuthal conserved-current texture. The spin-dependent radial-gradient current becomes a boundary term that cancels when the complete finite-wall evanescent tail is retained, leaving the spin-independent orbital phase $\Delta\phi_{ln}\propto l\Phi L_{\rm int}\langle\rho^{-2}\rangle_{ln}/v_z$. The matched $|\pm l\rangle$ modes therefore realize a same-path $R_z(2\delta_l)$ gate, with differential internal-mode readout and common-mode phase rejection. For $a=75\,\mathrm{nm}$, $R=95\,\mathrm{nm}$, $L_{\rm int}=1\,\mathrm{mm}$, $E_z=10\,\mathrm{meV}$, and $|l|=10$, the gate angle is $2.315\,\mathrm{rad/G}$ and $R_z(\pi)$ occurs at $1.357\,\mathrm{G}$. Finite-barrier, mode-spacing, disorder-mismatch, and readout-visibility checks quantify the main implementation constraints. More broadly, the result connects a mode-resolved AB energy shift to a measurable propagation operation and shows how the spatially distributed conserved current of a Dirac wave can become an operational quantum-control resource.

Parasitic two-level-system (TLS) defects are a major source of energy relaxation and temporal instability in superconducting quantum processors. Our sub-second adaptive spectroscopy reveals telegraphic switching of TLSs with a characteristic timescale of a few seconds and spectral diffusion with diffusivity $D \approx 0.9~\mathrm{MHz}^2/\mathrm{s}$. These timescales are about $3 \times 10^2$ times faster than what is observed in conventional nonadaptive spectroscopy, which typically requires hours of measurement time. We resolve such fast dynamics on a field-programmable gate array (FPGA)-based controller that enables measurement of frequency- and time-resolved relaxations with sub-second temporal resolution in flux-tunable superconducting qubits. We observe similar defect dynamics across multiple qubits in independently fabricated devices measured in different laboratories. We correlate TLS-induced fluctuations with gate-level errors using randomized benchmarking. Our results reveal a previously inaccessible regime of frequency-resolved TLS dynamics and redefine the timescales relevant to TLS-aware characterization and calibration of superconducting quantum processors.