Papers

Nonreciprocal quantum batteries harness reservoir engineering for controlled energy transfer, heralding a paradigm shift for quantum energy storage. A prior study utilizing the Metelmann-Clerk formalism reported a fourfold enhancement in nonreciprocal energy accumulation over reciprocal counterparts. This fourfold enhancement, however, appears to stem from a Lindblad master equation that exhibits fundamental inconsistencies, which may systematically understate the actual nonreciprocal advantage. Our approach is rooted in the rigorously established cascaded open quantum systems formalism, which ensures both mathematical consistency and physical fidelity. Remarkably, we surpass the previously reported fourfold benchmark, attaining a regime-independent sixteenfold steady-state nonreciprocal energy advantage over reciprocal systems. We further uncover a dissipation-dependent battery-to-charger efficiency, fourfold under symmetric damping, surpassing this benchmark when the battery is less dissipative, and lower otherwise. This work establishes the cascaded formalism as a mathematically rigorous and experimentally viable foundation for high-performance quantum energy storage.

Nonlinear dynamics generate non-Gaussian states and operations, but they also make continuously monitored quantum systems difficult to track. A quantum filter performs this task by compressing a noisy measurement record into a set of evolving variables that predict future observables. For Gaussian dynamics, this compression is exact and finite. In nonlinear systems, conventional moment equations generally expand without bound, but the failure of one representation does not prove that every finite description is impossible. Here we formulate quantum filtering as a realization problem for general quantum input–output maps. We introduce the linearized observable Hankel operator $K_O$, which maps changes in the past measurement record to changes in a future conditional observable. Any finite-dimensional smooth filter forces $K_O$ to have finite rank, so infinite rank provides a coordinate-independent proof that no exact finite-dimensional filter exists. Applied to single-mode polynomial bosonic systems under continuous quadrature monitoring, this yields a sharp boundary: Gaussian dynamics and the measurement-aligned Conditional Momentum Moment class admit finite realizations, whereas dynamics outside these classes produce infinitely many response directions and admit no finite-dimensional smooth exact filter. Exact impossibility, however, need not imply large practical complexity. The singular values of $K_O$ quantify how many response directions matter at a chosen local accuracy, defining the effective memory of an observable. For the Kerr and Duffing oscillators, these singular values decay rapidly despite infinite exact rank, showing that infinite exact memory can coexist with low finite-accuracy complexity. The framework therefore separates exact realizability from effective complexity in nonlinear quantum filtering.

I construct a family of time-independent, excitation-preserving spin Hamiltonians realising perfect state transfer from a localised two-excitation state to the symmetric two-excitation Dicke state, for every $N\ge4$. The Hamiltonian has the physical form $H=\sum_{i<j}J_{ij}(\sigma_i^+\sigma_j^-+\sigma_j^+\sigma_i^-)+\sum_i\epsilon_i n_i$ with real couplings, and satisfies $e^{-iHt}|110\cdots0\rangle=e^{i\phi}|D_N^{(2)}\rangle$ at a finite time. An $S_{N-2}$ permutation symmetry on the unoccupied spins reduces the dynamics to a four-dimensional invariant subspace. Requiring $(|\psi_0\rangle+|D_N^{(2)}\rangle)/2$ to be a zero eigenvector fixes the on-site energies in closed form and leaves three coupling parameters free. The inverse spectral problem then becomes two polynomial equations in two coupling ratios; eliminating one gives a degree-six reciprocal polynomial, which $z=x+x^{-1}$ converts to a cubic. For the spectral family $(-n,-1,1)$ with odd $n$, factorising the cubic's leading coefficient and evaluating it at $z=-2$ shows that some odd $n$ always produces a real root below $-2$, which a subresultant lifts back to the original system. The existence argument is symbolic and uses no numerical optimisation. Since that coefficient contains no odd powers of $n$, the required $n$ comes with an explicit threshold, not an asymptotic guarantee. I also cost the construction: couplings grow as $N^{1/2}$ and the on-site range as $N^{3/2}$, the transfer time stays within a factor 2.3-3.0 of the Mandelstam-Tamm limit at every size, and the fidelity is sensitive to systematic drift of the spectator-spectator coupling class but tolerant of independent bond disorder, which self-averages. This is a constrained analogue of perfect state transfer: for general real states an unconstrained real symmetric matrix suffices, whereas here the Hamiltonian must have excitation-preserving spin-network form.

Computing the optimal success probability for transmitting classical messages through a single use of a quantum channel is NP-hard, even for two messages. An existing semidefinite programming hierarchy based on symmetric extensions provides convergent upper bounds with an a priori error estimate that decays as the inverse square root of the extension level. In this work, we construct a Hermitian sum-of-squares hierarchy for an arbitrary number of messages and prove quadratic convergence in its level. The error bound is proportional to the advantage over random guessing. Our approach combines state-discrimination duality with positive polynomial kernels on products of spheres to construct feasible polynomial dual certificates. For binary messages, the resulting bounds give a multiplicative approximation from above of the trace-norm contraction coefficient.

We investigate whether quantum fluctuations of a circular probe string develop a quantum-chaotic response while traversing a wormhole throat. The classical circular-string embedding is periodic and radially stable, but its two physical transverse polarizations experience time-dependent tidal potentials. Expanding the world-sheet action to quadratic order, we canonically quantize these modes and construct out-of-time-ordered correlator(OTOC) amplitudes from their unequal-time commutators. For the Ellis–Bronnikov wormhole, both polarizations exhibit finite intervals of approximately exponential OTOC growth associated with the first throat passage. The corresponding dimensionless rate measured with respect to physical time is positive over the parameter range studied and generally decreases as the probe energy is increased relative to the throat scale. In the global-monopole extension, increasing the solid-angle deficit narrows the band of locally amplifiable modes and suppresses the extracted rates; a sufficiently strong defect can nearly quench the radial signal, while the angular channel retains a polarization-dependent non-monotonic structure when the energy-to-throat-scale ratio is small. These quantities characterize finite-time dynamical sensitivity in the Gaussian fluctuation sector and should not be identified with asymptotic many-body chaos or a thermodynamic phase transition. Although the numerical analysis uses two representative wormhole geometries, the construction depends only on covariant world-sheet fluctuations and real-time commutators. It therefore provides a transferable, non-holographic framework for applying quantum-chaos diagnostics directly to quantum probes in curved spacetimes.

We study the structure of Gibbs states in weakly perturbed interacting fermionic systems. First, for a sparse Hamiltonian $H=H_0+V$ with a quadratic term $H_0$ and a non-quadratic perturbation $V$ of scale $\epsilon$, we show that the Gibbs state $\rho_{\beta}$ decomposes into a convex combination of Gaussian states whenever the inverse temperature satisfies $\beta \le O(\log(1/\epsilon))$. Moreover, we prove that this bound is asymptotically tight by establishing that $\beta \le \Theta(\log(1/\epsilon))$ is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-$\vert{}U\vert{}$) regime of the Fermi–Hubbard model with hopping $t$ and on-site interaction $U$ on any graph of maximum degree $D$. Complementarily, in the strong-coupling (small-$\vert{}t\vert{}$) regime, we show that the Gibbs state remains convex-Gaussian up to $\beta \le O\big(\vert{}U\vert{}^{-1}\log(\vert{}U\vert{}/(D\vert{}t\vert{}))\big)$, revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.

In this paper, we study the quantum information-geometric structure underlying short-time nonequilibrium relaxation in quantum Markov dynamics, and derive bounds on the nonequilibrium correction to the short-time relaxation curvature. These bounds generalize the information-geometric structure underlying Auconi's classical nonequilibrium relaxation inequality to quantum Markov dynamics. We consider the von Neumann relative entropy as quantum divergence, and parametrize perturbations through the Kubo-Mori map, which converts the second-order expansion of the relative entropy into the Bogoliubov-Kubo-Mori (BKM) inner product at all temperatures. For a quantum Markov semigroup with full-rank stationary state, the induced tangent-space generator admits a canonical decomposition into a BKM-symmetric and a BKM-antisymmetric part, and the leading nonequilibrium curvature correction takes the exact form of the expectation of the commutator between the dissipative and the transport part of the generator. This correction is bounded by the product of a BKM-symmetric dissipative activity and a transport-sector activity. The bound is verified on a noncommuting qubit model and a driven-dissipative qutrit, and the full chain is confirmed numerically on a two-dimensional Fokker-Planck steady state. In the high-temperature and overdamped limit the quantum formula reduces to the position-space Fokker-Planck expression and reproduces Auconi's entropy-production bound with the correct temperature factor.

Understanding how thermal fluctuations modify or suppress quantum-enhanced sensing is a central problem in quantum metrology. Closely related questions arise in quantum thermodynamics, particularly regarding the relation between the work induced by a signal and the information acquired by a sensor. Here, we establish general relations among the sensitivity of thermal quantum states, as quantified by different quantum Fisher information metrics, their temperature dependence, and the work induced by a unitary signal. We further show that, at high temperature, all monotone QFI metrics coincide to leading order with a universal quantity that can be expressed as the variance of a simple observable and itself defines a lesser-known QFI metric. This emergent uniqueness is reminiscent of the uniqueness of classical Fisher information in information geometry. In continuous-variable systems, the infinite-temperature limit is finite and generically non-zero for quadratic Gaussian signals, while it diverges for higher-degree signals. Remarkably, for any purely quadratic signal generator, the infinite-temperature QFI is at least twice the zero-temperature SLD QFI or, equivalently, at least eight times the ground-state variance of the generator. Consequently, the Cramér–Rao lower bound on the estimator variance is reduced by at least a factor of two. We illustrate these results using harmonic chains of bosonic modes relevant to trapped-ion platforms and quantum field-theoretic models.

We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score $S=Q\times T$, where $Q$ is peak logical qubit width and $T$ is average executed Toffoli count. Participants reduced $S$ by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving $Q\times T\approx1.496$ billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is $\hat{p}=0.99809$, giving $Q\times T/\hat{p}\approx1.961$ billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.

Spatiotemporal fluctuations across multiple scales govern and characterize the emergent properties, phase boundaries, and low-energy excitations of strongly correlated matter. However, capturing these dynamics has remained a major experimental challenge, as conventional probes typically offer either high spatial or temporal resolution, but not both simultaneously. Here, we leverage high-fidelity wide-field imaging of dense diamond nitrogen vacancy center ensembles to measure the momentum and frequency power spectral density of magnetic fluctuations. To access spatial wavevectors below the diffraction limit, we tune the sensing volume continuously through optical depletion. This approach enables study of equilibrium and driven fluctuations across three orders of magnitude in spatial scale and tunable frequency bands, providing a direct means to map low-energy, long-wavelength fluctuations in correlated systems.

We all know that a density matrix $\rho$ is pure if and only if $\mathrm{Tr} \,\rho^2 = 1$. But is this the only way to prove the purity of $\rho$ using the trace of its powers? Here I systematically study the necessary and sufficient conditions of the more general question of guaranteeing that all eigenvalues of a Hermitian matrix belong to a specified set through its trace of powers. More importantly, these characterization results are automatically witnesses certifying a quantum state as entangled, a Hermitian operator has least one negative eigenvalue and a linear operator as non-Hermitian. I demonstrate the effectiveness of these witnesses, analyze their performance, and study their strength, weakness together with resource requirement through numerical simulation as well as analytical work. I also discuss briefly the effects of numerical stability, uncertainty in measurement and rounding errors on these problems.

The stabilizer Rényi entropy is a quantitative measure of non-stabilizerness, or magic, and has typically been found to scale extensively with system size $N$ (i.e., $\Theta(N)$) for a variety of many-body quantum states. In this note, we study the stabilizer Rényi entropy of the ground state of the spin-$\frac{1}{2}$ Dyck-Fredkin chain and its $t$-deformation, a local frustration-free model with unusual spectral-gap scaling. Exploiting the combinatorial structure, we carry out numerically exact finite-size calculations, which indicate asymptotic behavior depending on $t$: $\Theta(N)$ for $t<1$, $\Theta(\log N)$ at $t=1$, and $\Theta(1)$ for $t>1$. The scaling at $t=1$ could be another manifestation of the unconventional criticality of the model, while the contrast with the behavior of the entanglement entropy suggests that non-stabilizerness might provide a new window into quantum many-body systems.

The Carleman lattice Boltzmann method replaces the quadratic collision of the lattice Boltzmann equation by a linear map on a lifted state. Existing block encodings of this map succeed with probability $10^{-5}$ to $10^{-2}$ per step, so that the probability of a multi-step evolution decays exponentially with the number of steps. This study develops multi-relaxation-time Carleman lattice Boltzmann, a representation split in which the Carleman-lifted collision is performed in a moment basis on the amplitude-encoded state, while streaming remains a permutation in population space. The level-2 hierarchy closes under collision but not under streaming, which generates the work of pressure, advection and stress on the momentum flux. The state therefore remains the full pair array, and the moment representation is an orthogonal change of basis of the population one, with identical dynamics and truncation error. The operator to be block encoded changes with the basis, and with it the success probability of a quantum step. In the weighted Hermite basis with the amplitude encoding $f_i/\sqrt{w_i}$, the relaxation is a diagonal operator of norm one, and the level-2 collision stage becomes this diagonal plus a sparse coupling from products of conserved moments. A structured block encoding of this form raises the single-step success probability on the D2Q9 lattice from $10^{-2}$ for the best population encoding to 0.98. With the pair sector in relative coordinates and scaled, one step requires $O(\log^2 N)$ Toffoli gates and is verified by statevector simulation. The encoding and readout overhead of a $T$-step run is then polynomial in $T$ and $N$ rather than accumulating a factor $p^T$. For resolved flows, the remaining exponential loss in coherent multi-step Carleman lattice Boltzmann evolution is set by the non-equilibrium norm relaxed by dissipation rather than by the block encoding.

Power-grid defenses that rely on digital telemetry remain vulnerable to stealthy attacks that preserve plausible reported states while altering the underlying physical system. We study when Nitrogen-Vacancy (NV) sensing provides a useful independent physical channel, and when coherent processing before measurement adds value. Across IEEE 14-, 30-, and 118-bus simulations with Lindblad NV models, we evaluate standard FDIA, BDD-stealth, statistical-stealth, and concealed topology attacks. The results reveal an observability hierarchy: evidence shifts from digital telemetry, to reported-versus-physical consistency, to the physical NV state. Quantum Computational Sensing (QCS) follows this selectivity, becoming informative only when the physical state itself carries attack evidence. We then compare QCS, conventional 4-setting NV readout, and tomography under matched measurement budgets. At a matched total budget of only 40 physical trials per sensor on case14, QCS reaches AP $0.944$, versus 0.800 for conventional NV readout and 0.751 for tomography; the same low-budget ordering holds on case30 and case118. Multi-setting methods recover as additional measurements become affordable, showing that the QCS benefit is a measurement-efficiency advantage rather than a universal accuracy advantage. Finally, we ask where the benefit varies across the three case simulations. Although the quantum-to-classical Fisher-information ratio increases from 1.21x to 1.54x, Normal–Attack Helstrom separation collapses in the harder regimes, and interleaved control substantially increases that separation only on case14, thereby quantum sensitivity does not necessarily imply task-relevant distinguishability. Our results show that realized QCS utility depends on the full chain from physical perturbation to state separation, coherent processing, and measurement under the resource constraints of the task.

The Quantum Approximate Optimisation Algorithm is the canonical near-term heuristic, yet on real superconducting hardware its behaviour is set by device physics, not by the algorithm. Hardware demonstrations rarely prove the intended coupling is realised, that genuine entanglement is prepared, or what controls it. We report a pre-registered single-device study on the nine-qubit superconducting processor Red at the Barcelona Supercomputing Center, using its five-qubit component. Across six calibrations we certify bipartite entanglement of a corrected QAOA cost layer on the good coupler at depth one by two-qubit tomographic negativity: 0.077, BCa 95% CI [0.065, 0.091], excluding zero every day, while the coupling-off twin stays separable and the degraded coupler equals zero. We then measure the device physics directly: in a pre-registered manipulation on a fixed Bell preparation (not the QAOA layer), reducing the CZ pulse amplitude causally reduces the certified negativity along a positive, well-fit slope (R^2 = 0.83-0.96), every rung-level interval excluding zero and surviving Holm and Benjamini-Hochberg correction. This is a local linearisation of a peaked response, not a global monotone law: the negativity peaks at conditional phase |zeta| = pi, which the nominal amplitude overshoots. The J=0 twin is a separate off-state control and the fringe visibility is constant, so the effect is coherent. The average gate fidelity is non-monotone in the drive and is reported only as a diagnostic. A per-circuit statevector guardrail excludes a diagonal compilation fault we disclose and repair. A randomized-measurement witness is consistent with entanglement but underpowered. The certificate collapses by depth three, and a pre-registered sixteen-instance depth-three ensemble shows no optimisation signal (one-sided Wilcoxon p = 0.15). We claim no advantage; the instances are classically trivial.

Determining the highest amount of noise that quantum circuits can handle is an interesting and crucial task in the development of fault-tolerant quantum computation. Previous work has constrained this upper limit for local depolarizing noise to $\approx 45~\%$ for circuits constructed using the universal Clifford with T gate set by finding the noise threshold where the gate set loses universality. In this work, we use a similar method with the matchgate with non-Gaussian resource universal gate set to find a limit of $p=(8 - 2 \sqrt{6})/5$ or $\approx 62~\%$ for fermionic quantum computing that is independent of circuit depth. To do this, we use Uhlmann-Wootters concurrences for a 4-mode fermionic Choi state representing a resourceful gate combined with local depolarizing noise to determine when the combined channel is convex Gaussian. These bounds are not directly comparable due to differences in noise model making the bound of $\approx 62~\%$ the best known for fermions.

Ultracold atomic quantum systems offer an unprecedentedly powerful platform for exploring interacting symmetry-protected topological phases. Here, we show that their characteristic control over temperature provides a resource for engineering effective topological regimes with no zero-temperature counterpart. Employing finite-temperature matrix-product-state calculations, we investigate experimentally accessible Hamiltonians - the interacting bosonic Su-Schrieffer-Heeger and spin-1 XXZ chains - that host a topological phase at zero temperature, as well as a fermionic dipolar ladder model whose ground state exhibits no topological order. By tracking complementary topological markers, we identify an intriguing mechanism rooted in the structure of the zero-temperature phase diagrams: in finite-size systems, excitation gaps with different magnitudes define an intermediate-temperature window where the correlations associated with the lower gap are suppressed, while those protected by the larger gap persist. This enables the emergence of effective finite-temperature regimes exhibiting topological features that are either absent or qualitatively different from those at zero temperature. Our results establish a novel route toward exploring effective topological phases in ultracold atomic quantum systems.

Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods.

The Josephson energy $E_J$ is a key parameter governing the properties of transmon superconducting qubits. In Al/AlO$_x$/Al junctions, $E_J$ is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute $E_J$ by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al$_2$O$_3$ barrier against ten junctions with melt–quenched amorphous Al$_2$O$_3$ barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar–Baratoff relation, we obtain a mean $E_J/h$ of $2.78$ GHz for the amorphous ensemble, with a standard deviation of $4.67$ GHz, compared with $0.73$ GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic $200\times200$ nm$^2$ junction self-averages over more than $2\times10^4$ such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale $E_J$.

We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert–Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.

Active learning is a paradigm of machine learning that can be utilized to model expensive black-box functions by training a surrogate model from actively queried training points. The performance of this framework depends heavily on the choice of the surrogate model. When the surrogate is Gaussian Process Regression (GPR), its performance is largely determined by the expressivity of the underlying kernel. In this work, we investigate the peculiarities of using a quantum kernel to change the computational dynamics of active learning with GPR, focusing on the sensitivity to regularization by hyperparameter tuning. While generic, unstructured kernels suffer from exponential concentration at large scale, we empirically demonstrate that even at small scale overfitting can collapse GPR performance. Kernel regularization can be used to counteract this effect, but due to the smoothness of the quantum fidelity kernel, regularization must be carefully chosen to balance expressivity and overfitting. Our qualitative results transfer to the practical application of restricted quantum kernels designed to avoid exponential concentration and also present the kinds of noise that may be valuable to kernel training in near-term quantum devices.

The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.

Quantum information science is entering a second phase, the Quantum Evolution 2.0, in which the challenge has shifted from demonstrating coherent control of individual quantum states to building scalable multi-qubit processors and networks. This transition places materials science at the center of the field. Across superconducting circuits, quantum defects, quantum photonic devices, and emerging materials platforms, including two-dimensional materials and heterostructures, performance is now limited less by device design than by poorly controlled surfaces, buried interfaces, and defects whose atomic identities remain incompletely known. This review surveys the materials challenges of these quantum platforms together with the characterization methods needed to resolve them. For each platform we identify the dominant decoherence mechanisms, the current state of materials understanding, and the most pressing open materials problems. A cross-platform comparison then reveals a shared structure-coherence problem. The implicated material chemistry recurs across platforms, involving light elements in disordered or buried environments, yet no platform can quantitatively connect a specific atomic-scale structure to a measured change in coherence. We close by identifying three needs, mechanistic understanding of decoherence at the atomistic level, high-throughput proxy metrics predictive of device performance, and characterization tools built for quantum materials, whose resolution would advance coherence, scalability, and integration across all platforms.

We study thermodynamic state transformations in the resource theory of work and heat when the initial quantum state is unknown. Moving beyond state-dependent protocols, we develop a universal framework in which a single transformation applies to all admissible input states. For mutually commuting conserved charges, we construct charge-conserving protocols whose transformation error, quantified by trace distance, decays super-polynomially with the number of system copies. As an application, we demonstrate universal work extraction: asymptotically optimal work can be extracted without microscopic knowledge of the initial state, with a super-polynomially small error. Our results show that thermodynamic state transformations remain achievable under limited prior information and establish a universal framework for resource-theoretic thermodynamics beyond the state-aware setting.

The entanglement-breaking index of a quantum channel is the smallest number of self-compositions after which the channel destroys all entanglement with any reference system. A photonic experiment has fixed an index of 2; to our knowledge no larger index has been located by measuring the n-round channel across rounds. We give a protocol for doing so on a programmable processor, for any qubit channel realised as a collision model whose ancillas are prepared in states diagonal in a known basis, so that the bath polarisation is set exactly by weighting basis-state configurations in the analysis. Single-qubit process tomography of the n-round channel gives the smallest eigenvalue of its partially transposed Choi matrix, read against zero at a pre-registered five standard deviations; entanglement breaking survives further rounds, so the readings are monotone in n and the index follows. Comparing each direct measurement with the composition of the measured single-round map tests the repeated-interaction assumption. We show that a readable step needs margins on both sides, show how depolarising and reset errors move the readings, and give a power-based pilot rule. As a worked example we take one round of a three-qubit feedback loop, compiled to eight CZ gates on a heavy-hex path with mid-circuit reset, with certified ideal indices 3, 2 and 2 for three baths. The run is estimated to cost a few hundred seconds of processor time, and simulations under a device noise model, with the pilot's shot raise at low noise, recover all three indices.

A fault-tolerant quantum computer runs behind a telemetry stream logging syndromes, decoder actions, resets and timing separately from the answer. Can it reveal the logical input? For a distance-$d$ rotated surface-code memory on a fixed schedule of $T=\Theta(d)$ rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is $e^{-\Theta(d)}$-close in diamond norm to one that ignores the input. A statement of this kind follows generically from correctability-privacy duality. Anisotropy does not. Each logical axis pays the distance of its own coset, so under amplitude damping the computational-basis label is governed by the code's $Z$-distance $d_Z\ge d_{\min}$ and not by the code distance. Two codes of quantum distance $1$ make the gap concrete. A phase-flip code's $X$-syndrome transcript is exactly input-independent under unobserved damping, while a repetition code leaks at first order. A matched converse identifies the records that do expose it, among them a lattice-surgery parity readout. On a 156-qubit superconducting processor our sufficient certificate misses by $21.5\times$, so the theorem cannot be invoked there. Measured directly, a $d_Z=1$ memory's record identifies its input with total variation $\ge 0.927$ under randomised, label-balanced acquisition. Holding the code fixed and varying the damping exposure reproduces the parameter-free law, with exponent $0.85\pm0.03$ against a predicted $0.86$. Randomized encoding returns the statistic to the floor at no two-qubit-gate cost. Fault tolerance does not grant transcript privacy. It relocates it, and only to the logical state, not to the circuit's identity.

Fermionic quantum cellular automata (QCA) are automorphisms of local fermionic operator algebras ($\mathbb Z_2$-graded superalgebras) that have bounded spread: they map local operators to nearby operators. We prove that every 2-dimensional fermionic QCA on a locally finite-dimensional algebra is a composition of local automorphisms and a fermionic shift. This is implied by our result that every locally finite-dimensional fermionic invertible subalgebra in a one-dimensional lattice is Brauer trivial, i.e., it is stably bounded-spread isomorphic to a tensor product fermionic algebra.

Directional amplification, in which signals are amplified selectively depending on their propagation direction, is a key resource for quantum information processing and stands in one-to-one correspondence with non-trivial non-Hermitian topology. So far, this correspondence has concerned the mean fields, and thus classical response. Here we turn to the quantum fluctuations, giving access to correlations and entanglement. For phase-preserving amplifiers, we derive analytic expressions for the normal and anomalous correlations, showing that non-trivial topology produces correlations that grow exponentially with the distance between modes and approach the largest values compatible with the uncertainty relations. The associated correlation length diverges at the topological phase transition. Entanglement nonetheless remains local, set by the competition between normalised anomalous correlations and the asymmetry of the mode occupations. For the bosonic Kitaev chain, a phase-sensitive amplifier, the system instead splits into two halves that are internally fully correlated yet mutually uncorrelated. Our work prepares the ground for exploring the quantum properties of non-Hermitian topological systems with state-of-the-art platforms such as cavity optomechanics and superconducting circuits.

Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. We show that this expectation fails in low dimensions by studying the quantum binary annihilation, $A+A \to \emptyset$, where reaction processes acquire singular fluctuation corrections below the upper critical dimension $D_c=2$. Consequently, fluctuations dominate the asymptotic kinetics for $D<2$. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime with $n\sim t^{-1/2}$, governed by a quantum-Zeno scale even for arbitrarily weak loss. At $D=2$, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions. In $D>1$, these collisions redistribute momentum populations and are parametrically faster than losses in the transport-limited regime, allowing the system to approach a quasi-stationary thermal state.

Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity $7.44\times 10^{-9}$ using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity $10^{-3}$ with as few as 5584 CNOTs.