Papers

We derive the finite-temperature characteristic function of work (CFW) for a driven $O(N)$ Gaussian field theory and obtain closed-form expressions for all zero-temperature excess-work cumulants. For gapped protocols, we use adiabatic perturbation theory (APT) to derive the $\tau_Q^{-2}$ scaling for protocols with a nonzero first derivative at either boundary, where $\tau_Q$ is the protocol duration; smoother boundaries lead to faster decay. For power-law protocols approaching the critical point with exponent $p$, we determine the competition between critical excitations and the regular contribution. The $n$th cumulant's critical contribution follows Kibble–Zurek (KZ) scaling $\tau_Q^{-p(d+n)/(p+2)}$ for $d+n<2p+4$, acquires a logarithmic correction $\tau_Q^{-2p}\log\tau_Q$ at $d+n=2p+4$, and scales as $\tau_Q^{-2p}$ above this condition, where $d$ is the spatial dimension. This analytical study of the APT–KZ crossover in a solvable model provides a basis for studying their competition in interacting field theories.

The local Hamiltonian problem is the canonical $\mathsf{QMA}$-complete problem, and $O(2^n)$ time classical algorithms and $O(2^{n/2})$ time quantum algorithms are known to solve the problem in the worst case. It is not clear how to improve these brute force strategies for a broad class of the problem because ground states are highly entangled in general, and we cannot directly apply known strategies for classical CSPs. In this work, we present exponentially faster classical and quantum algorithms under two mild assumptions: (1) the Hamiltonian is frustration-free on YES instances, and (2) it is approximately regular, meaning that every qubit is acted upon by approximately the same number of constraints. We complement these upper bounds by showing that, assuming (Q)SETH, quantum 5-SAT admits no non-trivial worst-case speedup. Our lower bound further demonstrates that the dependence of our algorithms on regularity is in some sense nearly optimal. Specifically, quantum 5-SAT remains (Q)SETH-hard even for Hamiltonians in which all but $O(\sqrt{n})$ qubits participate in only constantly many constraints, while the remaining $O(\sqrt{n})$ qubits each participate in $O(\sqrt{n})$ constraints. By contrast, if either the size of this high-degree subset or the degrees of its qubits is reduced by a factor of $n^\delta$, for any $\delta>0$, our algorithm solves the problem in time $O(2^{(1- \varepsilon)n})$ for some $\varepsilon>0$. Together, our upper and lower bounds establish a fine-grained complexity dichotomy for quantum satisfiability.

Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum $\hat p_x$, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to $\sy$. The CD term of a two-waveguide coupler is itself proportional to $\sy$, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the $\sigma_z$–$\sigma_x$ plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as $\dot{\xo}=\dot\theta/(\gamma\dbeta^{2})$. The expression agrees with the numerical offset search to $0.3\%$ and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.

Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.

Non-uniform security allows an adversary to receive bounded advice about an oracle before attempting a fresh challenge. This captures the most realistic attacks and has already been studied extensively in prior work. In this work, we introduce an operator-norm approach for non-uniform security in the quantum random oracle and random permutation models. This new approach yields a unified reduction for both search success probability and distinguishing advantage. Previously, the reduction only worked with success probability even in the decision games, yielding a worse bound. Our framework enables tight bounds for Yao's box, both with and without salting, and improved bounds for pseudorandom generators. We also prove an optimal generic salting theorem for decision games. By defining a property of a game, which separates the contributions of the existing queries in the offline stage and subsequent online queries, we obtain stronger bounds for specific salted constructions. These include salted permutation inversion, tight up to logarithmic factors, and salted random-function inversion, tight up to logarithmic factors and the gap already present in classical function inversion.

We prove a separability rigidity theorem for finite-mode Gaussian states. Let $\rho_G$ be Gaussian and let $\mathcal I$ be a fixed partition of the modes. If $\rho_G$ dominates a nonzero positive operator $T$ that is separable across $\mathcal I$, $0\neq T\preccurlyeq \rho_G$, then $\rho_G$ itself is separable across $\mathcal I$. The dominated operator is arbitrary and need not be Gaussian. The theorem has three applications. First, any Gaussian channel admitting a nonzero entanglement-breaking completely positive subchannel is itself entanglement breaking, even when that subchannel is non-Gaussian. Second, if a resource state dominates a positive multiple of a faithful separable state, no finite-copy, postselected separability-preserving protocol can prepare an entangled Gaussian state exactly with nonzero success probability. Third, a connected graph of entangled Gaussian two-mode marginals certifies genuine multipartite entanglement of every compatible global state, even if the global state is non-Gaussian; the certification is robust to sufficiently small trace-norm errors in the marginals. As a structural corollary, mixing states separable across different partitions cannot produce new Gaussian states, so full inseparability and genuine multipartite entanglement coincide for finite-mode Gaussian states and identical copies of a biseparable Gaussian state cannot activate genuine multipartite entanglement.

Quantum fire consists of quantum states that can be efficiently functionally cloned but cannot be transmitted using one-way classical communication. Whereas all previous quantum-fire constructions with proven untelegraphability are relative to an oracle, ours, based on one-shot signatures, is in the standard model. Our construction achieves two further notions that we introduce: (a) keyless untelegraphability, a strengthening of untelegraphability; and (b) conversability, meaning that a flame, though not telegraphable via one-way classical communication, can be transmitted via classical interaction. Hence one-way and two-way classical communication differ qualitatively in their power to transmit this quantum fire. We use these two novel properties of quantum fire, along with its clonability, to give one of the first cryptographic applications of quantum fire. Keyless untelegraphability forces the distribution of serial numbers of valid flames to have high min-entropy, while conversability and clonability allow the corresponding flame to be cloned and transferred using only classical communication. We present two variants of our conversable quantum-fire construction. The first, based on one-shot signatures (instantiable from subexponential iO, subexponentially secure one-way functions, and LWE), supports polynomially many flames, and super-logarithmic min-entropy of the serial-number distribution. The second, under the stronger assumption of exponentially unforgeable one-shot signatures (instantiable relative to a classical oracle), supports exponentially many flames, and linear min-entropy.

Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.

Distributed quantum computing (DQC) has been proposed as a way to scale quantum algorithms for practical applications beyond monolithic quantum processor architectures. Among these applications, quantum chemistry is widely regarded as one of the most promising use cases for quantum computing. In this work, we estimate the distributed-resource requirements of unitary coupled-cluster (UCC) ansätze for quantum chemistry, focusing on unitary coupled-cluster singles and doubles (UCCSD), unitary pair coupled-cluster doubles (UpCCD), and unitary pair coupled-cluster with generalized singles and doubles (UpCCGSD) circuits for hydrogen chains. We focus on a teleportation-based approach to DQC, quantitatively comparing a naive distribution method to the output of the TeleSABRE algorithm. For both approaches, we estimate the cost of handling nonlocal two-qubit gates across a fixed midpoint or quarter-point partition, reporting Bell-pair/classical-communication costs in teleportation. Across Jordan-Wigner and Bravyi-Kitaev, we find that UpCCD with spin-blocked Jordan-Wigner ordering gives the most favorable scaling, while UCCSD incurs substantially larger distributed-resource requirements.

We study a weighted-shift formulation of bivariate bicycle group-algebra (BBGA) codes over finite group algebras. One binary shift acts by right multiplication and the other by left multiplication; associativity ensures that these shifts commute even for a nonabelian seed group. Bivariate polynomials in the shifts, including mixed monomials, therefore define CSS codes. We give explicit sparsity bounds and distinguish nonabelian seed groups from codes that are intrinsically inequivalent to abelian realizations. For $D_3$, a pair of weighted permutation shifts generates a regular $C_6\times C_{12}$ action and recovers the known $[[144,12,12]]$ and $[[144,14,14]]$ bivariate bicycle codes. We also present a computer-verified $[[144,16,12]]$ code over $A_4\times C_6$, with every check of weight eight. This example belongs to the established nonabelian two-block group-algebra family. Exhaustive low-weight enumeration and an intrinsic stabilizer-support invariant certify that it is inequivalent to any ordinary abelian BB or two-block group-algebra realization, even under qubit permutations combined with local Clifford operations. Finally, a nonuniform weighted-shift construction over $\mathbb{F}_2[C_3]$ yields a $[[18,4,3]]$ code with check weights six and eight. An exact enumeration of its minimum stabilizer supports rules out every ordinary binary 2BGA realization at that length, under the same equivalence. This establishes that the unrestricted weighted-shift formulation extends beyond the ordinary 2BGA class, even with an abelian seed group.

Quantum mechanics is justifiably held to be the most successful physical theory ever created; yet no universally accepted interpretation of its mathematical formalism exists after a century of debate. We examine the specific claim that classical physics stands as the low-action limit of quantum mechanics, arguing that the deep interpretive difficulties exposed by the quantum formalism, the measurement problem, the subject-object divide, and the nature of scientific representation, were already latent in classical physics, constituting what we call a blind spot of objectivity. Taking quantum theory as an invitation to re-examine the implicit metaphysical commitments bundled with 'classical physics', we explore two key issues-the objective/subjective split and the nature of theoretical representation-and argue that quantum mechanics does not represent a break with classical physics per se but rather brings previously unacknowledged philosophical assumptions into the limelight. We discuss the London-Bauer interpretation and QBism as exemplars of interpretations that embrace this broader reconceptualisation.

We consider the problem of simulating dynamics under geometrically local Lindbladians acting on a lattice of qudits. We present an algorithm to approximate the time evolution under these Lindbladians for evolution time $t$ and on $N$ qudits to diamond norm error $\varepsilon$ using geometrically local circuits of depth $O(t \ \polylog(Nt/\varepsilon))$. Our results thus achieve a performance comparable to that of the Haah-Hastings-Kothari-Low (HHKL) algorithm for lattice Hamiltonian simulation.

We derive a partially linearized version of the mapping approach to surface hopping (MASH) that provides a new method for simulating nonadiabatic dynamics in molecular systems. As in the original MASH formalism, trajectories travel on adiabatic surfaces with hops determined by the dynamics of a spin vector on the Bloch sphere. However, because the new approach is based on the partially linearized density matrix (PLDM), it has two spin vectors, which may be in the same or different hemispheres of the Bloch sphere. The former scenario describes an electronic population moving on a single adiabatic surface, whereas the latter describes a coherence moving on the average surface. We show that this new method, called MASH-PLDM, leads to improved results over the original MASH dynamics for a variety of scattering problems and spin-boson models, especially in cases where coherences play an important role. A further benefit of the new methodology is that it can treat multi-time correlation functions such as those required for nonlinear spectroscopy. We demonstrate this capability with a proof-of-principle simulation of time-resolved pump-probe spectroscopy.

In this paper, we study the conditions under which covert communication at positive rates is feasible over discrete memoryless classical, classical-quantum, and quantum channels. For classical point-to-point channels, we show that if the dimension of the channel input probability simplex exceeds that of the channel output probability simplex, equivalently, if the input alphabet has larger cardinality than the output alphabet, then positive covert rates are achievable for certain classes of Discrete Memoryless Channels (DMCs). We further show that allowing the innocent symbol (i.e., the symbol transmitted in the no-communication mode) to be chosen appropriately can enlarge the class of DMCs for which positive covert rates are achievable. We also study covert communication over classical Multiple-Access Channels (MACs), where the additional transmitter effectively enlarges the set of available channel input pairs, and we show that the conditions required to satisfy the covertness constraint are less restrictive for MACs than for point-to-point channels. We extend these results to classical-quantum DMCs by showing that if the dimension of the input probability simplex exceeds the affine dimension of the set of output states that can be induced at the channel output, then positive covert rates are achievable for certain classes of classical-quantum DMCs. Finally, for quantum channels, we show that if the innocent state (i.e., the state transmitted in the no-communication mode) is mixed, then the covertness constraint can always be satisfied by a non-trivial input ensemble. Consequently, positive covert rates are achievable whenever the legitimate receiver can distinguish at least two states in a suitable such ensemble.

Unitary process tomography is the act of learning how an unknown unitary gate acts on a quantum system. It is an essential procedure for realizing a functioning quantum computer. As quantum technologies develop, it is important to understand the computational resources needed to conduct unitary process tomography using a variety of types of circuits. In particular, when measuring error in diamond distance, it is known how to achieve optimal query complexity using a sequential circuit architecture, but it had not been known whether a parallel circuit architecture could achieve the same optimal query complexity. In this work, we prove that unitary process tomography with near-optimal query complexity is indeed possible using a parallel circuit by introducing an explicit, novel parallel procedure. This closes the gap between sequential and parallel circuits up to a logarithmic factor, showing that parallel and sequential strategies are nearly equally capable for this task.

Understanding what limits many-body quantum entanglement is a central problem in physics. Spatial locality has long provided a fundamental mechanism: correlations between a region and its complement must be mediated through a small spatial interface, thereby constraining their entanglement. Here we show that universal constraints on entanglement can persist even when interactions are strongly nonlocal, through collectivity: many weak interactions generate fluctuations controlled by their square-summed, rather than total, strength. We establish this mechanism rigorously for generic gapped Hamiltonians with Kac-normalized power-law interactions $r^{-\alpha}$ on a $D$-dimensional lattice. For arbitrary bipartitions, we prove that the ground-state entanglement scales at most logarithmically with system size for $\alpha<D/2$ and subextensively for $D/2<\alpha<D$, due to suppressed collective fluctuations around individual sites. For spatially regular bipartitions with codimension-one boundaries, we use a renormalization-group construction to extend this suppression to larger length scales, yielding polylogarithmic scaling for $D/2 < \alpha < (D+1) / 2$ and parametrically stronger subvolume bounds for $(D+1)/2<\alpha<D$. We also establish the corresponding optimality results: for arbitrary bipartitions, the logarithmic scaling for $\alpha<D/2$ is optimal and $\alpha=D/2$ marks the optimal threshold for universal logarithmic bounds, while for regular bipartitions the threshold at $\alpha=(D+1)/2$ is likewise optimal for universal polylogarithmic bounds when $D\ge2$. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.

Quantifying non-Markovianity is a fundamental problem in the theory of open quantum systems, as it is essential for exploiting environmental memory as a resource in quantum technologies. Existing resource-theoretic and operational quantifiers, however, generally require complete knowledge of the intermediate dynamical map and are therefore experimentally demanding. Here, we develop a witness-based framework for the quantification of non-Markovianity that bypasses complete reconstruction of the Choi state associated with the intermediate dynamical map. We first show that every non-Markovianity witness provides a certifiable lower bound on the geometric resource measure of non-Markovianity and identify the necessary and sufficient conditions under which this bound is tight. Motivated by the fact that non-positive-semidefinite witnesses are generally difficult to measure in real experimental scenario, we then focus on positive-semidefinite witnesses, which admit a natural implementation as positive operator valued measure (POVM) elements. We prove that every positive witness yields a certified lower bound on the Rivas–Huelga–Plenio (RHP) measure, thereby establishing a complete hierarchy connecting witness-based quantification, the RHP measure, and the geometric distance measure. Applying our framework to amplitude-damping and general Pauli dynamics, we find that the optimal positive witnesses reduce to simple Bell-parity projectors. Furthermore, we show that the resulting witness values can be obtained directly from a small number of experimentally accessible correlation measurements, thereby eliminating the need for complete Choi-state reconstruction and providing an efficient and experimentally feasible approach for the quantification of non-Markovianity in open quantum systems.

A variational state optimized in a symmetry-projected space need not be the state prepared by exponentiating the corresponding unprojected parent generators. For an orthogonal target-space projector $P$, $Q=I-P$, and an anti-Hermitian generator $A$, exact equivalence for all amplitudes requires target-space invariance, $QAP=0$. We formulate this condition as a representation-equivalence audit for open-shell ADAPT-VQE. For a canonical CAS(15e,9o) type-1 Cu(II) Hamiltonian, 274 of 323 bare Hartree–Fock-origin single, double, and triple excitations violate this condition. Projected-doublet ADAPT reaches 1.5719 m$E_h$ with 121 operators, whereas the same amplitudes in the corresponding full-space sequence give 464.730 m$E_h$ error, 0.07343 fidelity with the projected state, and 54.45% quartet weight. Reoptimizing the same 121 parent generators in the same order under the hard constraint $p_D\ge0.999$ reduces the best converged error to 8.482 m$E_h$, showing that the catastrophic same-angle failure is primarily a representation/parameter-transfer failure but is not completely repaired by full-space reoptimization of the fixed sequence. An independent 12-qubit NO benchmark exhibits the same mechanism more mildly. A spin-preserving generalized full-space construction removes the representation ambiguity and reaches 1.493 and 1.181 m$E_h$ at 18 and 24 qubits. For the 18-qubit positive control, selectively refining only four Suzuki-2 factors and re-transpiling with a fixed compiler seed passes the predeclared circuit-equivalence gate at 19,660 controlled-X (CX) gates and depth 23,016. Circuit synthesis and final-energy measurement therefore constitute separate validation layers. The contribution is a validation framework, not a new spin-adapted ADAPT algorithm.

Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor $\eta_p$ to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For $0<P<1$ and $0<\eta_m<1$, the QFIM in $(P,\chi,\eta_m)$ is diagonal, with $\mathcal{H}^{\rm mode}_{\chi\chi}=C_{\eta_m}^2$ and $\mathcal{H}^{\rm mode}_{\xi_m\xi_m}=C_{\eta_m}^2/(1-\eta_m^2)$, where $\xi_m=-\ln\eta_m$. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for $(\theta_{23},\delta_{\rm CP},\xi_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At $\Gamma_0=10^{-23}\,\mathrm{GeV}$, the fixed-coordinate ratio $\mathcal{F}^{\rm flav}_{\delta\delta}/\mathcal{H}_{\delta\delta}$ is approximately $0.010$, $0.013$, and $0.105$, respectively; all three points show strong $\theta_{23}$–$\xi_{31}$ incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.

Out-of-time-ordered correlators (OTOCs) provide a powerful probe of quantum chaos and scrambling. While the Lindblad formalism is often used to describe OTOCs in open systems, microscopic mechanisms that give rise to the Lindblad equation at the level of time-ordered correlation functions do not necessarily justify this approach at the level of OTOCs. Starting from a microscopic model of a subsystem coupled to a random bath, we show that the resulting OTOC dynamics contains an additional contribution compared to the standard Lindblad approach. This contribution, induced by correlations between different replicas, allows key properties of the underlying unitary dynamics such as long-time freeness to be retained and information scrambling to be captured more faithfully. As an application, we show that this extended formalism can be used to numerically study OTOCs in large closed systems by replacing part of the system with a dissipative boundary, offering a way to study operator spreading and higher-order correlations beyond directly accessible system sizes.

Adaptive circuits use measurements and outcome-conditioned feedback to implement nonreciprocal dynamics without postselection. We show that fermion circuits host independently tunable density and coherence skin effects. The stationary state has an exact density tilt set only by measurement strength and feedback displacement: conditioned-gate details cancel, yielding an exponential one-particle profile and, at any filling, a tilted ensemble of configuration weights. Decaying coherences instead obey, in the bulk, an effective Hatano-Nelson generator controlled by the conditioned gates through a relative occupation phase. Tuning this phase drives a point-gap topological transition and reverses coherence localization at fixed density, allowing density and coherence to localize at opposite edges. We derive both exponents for conditioned $U(2)$ gates and propose a correlator-ratio probe using ensemble-averaged observables.

Several physically interesting Lindbladians, such as those describing generic open quantum system models as well as engineered state preparation processes, are often rapidly mixing, that is, they relax to steady states in time scaling polylogarithmically with the system size. Owing to the short mixing times, it is physically expected that local perturbations do not substantially increase the mixing time. In this work we question this expectation and ask whether rapid mixing survives. We provide counterexamples showing that rapid mixing is not stable in general, even when the perturbation does not change the steady state. We also show that arbitrarily weak local Hamiltonian perturbations can destroy rapid mixing. Complementing these results, we develop an array of sufficient conditions which imply stable rapid mixing, including several classes of quasifree fermionic systems, commuting Lindbladians, and local spin systems. We also identify conditions under which modified logarithmic Sobolev inequalities (MLSIs), a stronger form of convergence, lead to stable rapid mixing. As a further implication of our results, we show that rapid mixing does not imply a positive MLSI constant.

We study fermionic non-local magic in higher-dimensional free-fermion systems through the lens of the entanglement spectrum. For translationally invariant Gaussian states in strip geometries, dimensional reduction maps the problem to independent lower-dimensional momentum sectors, leading in two dimensions to a multiplicative logarithmic violation of the boundary law analogous to Gioev-Klich-Widom scaling. We further show that the second Rényi fermionic non-local magic is bounded by the capacity of entanglement and introduce an entanglement-temperature deformation that probes the low-energy structure of the entanglement Hamiltonian. Applied to the matter-Majorana sector of the Kitaev model, this response is exponentially suppressed in the Abelian phase and algebraic in the non-Abelian phase, where its ratio with the capacity approaches a universal constant. Out of equilibrium, we extend the quasi-particle description to fermionic non-local magic in higher-dimensional quenches and show that random Gaussian circuits exhibit diffusive spreading in two spatial dimensions.

Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex $k$-cut polytope problem, with $k$ the number of distinct phases in these commutation relations, and prove it NP-complete for every finite $k$. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from $\mathrm{O}(m)$ pulses, with $m$ the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an $\mathrm{O}(\sqrt{m})$ approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with $\mathrm{O}(m)$ pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.

Spin squeezed states (SSSs) are conventionally viewed as analog resources for quantum metrology. Here we develop algorithms to efficiently generate and exploit SSSs on a digital quantum computer. We introduce an adaptive local-circuit protocol that prepares SSSs with squeezing parameter $\xi$ in depth $\mathrm{O}\left(\log{1/\xi}\right)$, yielding an exponential improvement over non-adaptive approaches. We prove that this depth is optimal for permutation symmetric SSSs by deriving a matching lower bound on entanglement entropy. We further leverage the squeezing paradigm to deterministically prepare the Dicke states using asymptotically fewer resources than prior methods. Remarkably, classical simulations of our preparation protocols under realistic noise models predicts a metrological gain of 4.2 dB beyond the standard quantum limit with 55 superconducting qubits in total including ancillae. Our work paves the way for performing quantum metrology on near-term digital quantum devices.

The out-of-time-order correlator (OTOC) has emerged as an important diagnostic for quantum information scrambling and a key signature of quantum chaos. In this work, we discuss out-of-time-order correlators, analytically and numerically, for the so-called Volcano potentials. This family of potentials parametrically interpolates between bounded wells and confining walls, and includes Pöschl-Teller as a specific case. Through a combination of numerical diagonalization and semiclassical analysis, we investigate various regimes of the potential parameter regimes containing regions of both positive and negative curvatures. Moreover, we demonstrate in this case that short-time exponential growth of the OTOC does not necessarily signal global quantum chaos; instead, it correlates with the sampling of negative curvature regions by excited states.

We determine asymptotic global fidelities of cloning generic mixed states with simple (non-degenerate) full-rank spectra. In fixed dimension $d$, let $n$ inputs and $m_n$ outputs satisfy $m_n/n\to\gamma>1$. For a known simple full-rank spectrum $p_1>\cdots>p_d>0$, we prove that the optimal root fidelity between the entire output and the product target state is $$ F_\rm{orb}(\gamma,p) =\prod_{i<j} \frac{\sqrt{\gamma}+\sqrt{q_{ij}(\gamma-1+q_{ij})}} {\gamma+q_{ij}}, \qquad q_{ij}=\frac{p_j}{p_i}. $$ When the spectrum is unknown, one spectrum-independent cloner attains $$ F_\rm{univ}(\gamma,p) =\left(\frac{2\sqrt\gamma}{1+\gamma}\right)^{(d-1)/2} F_\rm{orb}(\gamma,p), $$ uniformly on compact subsets of the simple full-rank chamber and is minimax optimal. The two factors quantify spectral and eigenbasis uncertainty. Our channels combine classical processing of Schur–Weyl labels with a covariant Cartan-sector channel. Local asymptotic normality and a Gaussian fidelity bound against arbitrary channels yield the converses. For flat projector states $\rho=P/r$, with $P$ a rank-$r$ orthogonal projector, we separately prove the optimum $\gamma^{-r(d-r)/2}$. Furthermore, we estimate the exact asymptotic fidelity of purify–clone–trace (PCT), and show that our cloners strictly outperform PCT at every fixed gain for simple full-rank spectra and rank-$r$ projector states with $1<r<d$.

The kinetic uncertainty relation (KUR) constrains fluctuations of individual currents in classical nonequilibrium systems in terms of the dynamical activity, which quantifies the average number of transitions per unit of time. Here, we derive a multi-current KUR (MKUR) establishing the precision limit for multiple currents generated in classical stochastic processes in the nonequilibrium steady state. We then apply our theory to identify quantum devices whose correlated current fluctuations surpass this classical limit by comparing the quantum system to a classical emulator with the same average currents in the steady state. In this way, violations of the emulator's MKUR have a clear physical meaning, i.e., that the quantum-coherent evolution reduces joint current fluctuations below what is possible for a classical Markovian system with the same energy-level structure and incoherent resources. Since the MKUR incorporates correlations between currents, its violation pinpoints nonclassical fluctuations in parameter regimes where the single-current KUR is satisfied. We illustrate the essential and complementary role of these bounds for characterizing joint current precision with two examples: a coherently driven two-level system and an experimentally motivated model of a three-level heat engine subject to parasitic environmental couplings.

Topological phases of matter are characterized by global properties of quantum states beyond conventional local order parameters. The Chern number is a central invariant in this characterization, linking the geometry of quantum states to robust physical observables and making its determination key to understanding quantum matter. We construct a nearly optimal quantum algorithm for estimating the Chern number of a smooth Hamiltonian family over a two-dimensional parameter torus with a unique, gapped ground state, including interacting many-body systems. The algorithm transports and reuses two ground-state copies prepared at a single reference point and uses generalized quantum signal processing to coherently accumulate geometric phases. It achieves a Hamiltonian-oracle evolution time of $\tilde{O}(L_xL_y/\Delta_{\min}^3)$, where $L_x,L_y$ bound the parameter derivatives of the Hamiltonian and $\Delta_{\min}$ is a known spectral-gap lower bound. We prove a matching worst-case oracle lower bound, even when the Chern number is promised to be zero or one, establishing optimality up to polylogarithmic factors. For local Hamiltonian families with an inverse-polynomial gap and a supplied guiding state, exact Chern-number computation is in $\mathsf{FBQP}$ and is $\mathsf{BQP}$-hard, and merely deciding whether the Chern number is zero or one is already $\mathsf{BQP}$-complete. These results establish how efficiently quantum computers can estimate a quantized topological invariant and provide evidence for quantum advantage in characterizing topological phases.

We study the topological band theory of quantum Hall systems in which the adiabatic flux parameters of an external gauge potential form a high-dimensional manifold. This situation arises both for strongly correlated matter on spatial Riemann surfaces of genus $g > 1$, as well as in the formal study of matter on compact oriented manifolds of dimension $4\ell+2 = 2p$ coupled to $p$-form gauge potentials. In these cases, the underlying topological invariants defined over the parameter space are significantly richer than the low-dimensional (i.e., two-dimensional) case and involve both the curvature (i.e., first Chern class) as well as higher order curvature invariants. These higher curvature invariants correspond to topologically protected contributions to Kubo-like formulae, constructed from correlation functions of the physical current operators. We illustrate these general considerations with an explicit example from hyperbolic band theory based on the genus-two Bolza Riemann surface, a case which has recently been simulated on a synthetic-dimension platform.