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The time-marching strategy, which propagates the solution from one time step to the next, is a natural strategy for solving time-dependent differential equations on classical computers, as well as for solving the Hamiltonian simulation problem on quantum computers. For more general homogeneous linear differential equations d d t | ψ ( t ) ⟩ = A ( t ) | ψ ( t ) ⟩ , | ψ ( 0 ) ⟩ = | ψ 0 ⟩ , a time-marching based quantum solver can suffer from exponentially vanishing success probability with respect to the number of time steps and is thus considered impractical. We solve this problem by repeatedly invoking a technique called the uniform singular value amplification, and the overall success probability can be lower bounded by a quantity that is independent of the number of time steps. The success probability can be further improved using a compression gadget lemma. This provides a path of designing quantum differential equation solvers that is alternative to those based on quantum linear systems algorithms (QLSA). We demonstrate the performance of the time-marching strategy with a high-order integrator based on the truncated Dyson series. The complexity of the algorithm depends linearly on the amplification ratio, which quantifies the deviation from a unitary dynamics. We prove that the linear dependence on the amplification ratio attains the query complexity lower bound and thus cannot be improved in the worst case. This algorithm also surpasses existing QLSA based solvers in three aspects: (1) A ( t ) does not need to be diagonalizable. (2) A ( t ) can be non-smooth, and is only of bounded variation. (3) It can use fewer queries to the initial state | ψ 0 ⟩ . Finally, we demonstrate the time-marching strategy with a first-order truncated Magnus series, which simplifies the implementation compared to high-order truncated Dyson series approach, while retaining the aforementioned benefits. Our analysis also raises some open questions concerning the differences between time-marching and QLSA based methods for solving differential equations. 

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) . 

Abstract Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem. 

Abstract We present the results of a search for gravitational-wave transients associated with core-collapse supernova SN 2023ixf, which was observed in the galaxy Messier 101 via optical emission on 2023 May 19, during the LIGO–Virgo–KAGRA 15th Engineering Run. We define a five-day on-source window during which an accompanying gravitational-wave signal may have occurred. No gravitational waves have been identified in data when at least two gravitational-wave observatories were operating, which covered ∼14% of this five-day window. We report the search detection efficiency for various possible gravitational-wave emission models. Considering the distance to M101 (6.7 Mpc), we derive constraints on the gravitational-wave emission mechanism of core-collapse supernovae across a broad frequency spectrum, ranging from 50 Hz to 2 kHz, where we assume the gravitational-wave emission occurred when coincident data are available in the on-source window. Considering an ellipsoid model for a rotating proto-neutron star, our search is sensitive to gravitational-wave energy 1 × 10⁻⁴M_⊙c²and luminosity 2.6 × 10⁻⁴M_⊙c²s⁻¹for a source emitting at 82 Hz. These constraints are around an order of magnitude more stringent than those obtained so far with gravitational-wave data. The constraint on the ellipticity of the proto-neutron star that is formed is as low as 1.08, at frequencies above 1200 Hz, surpassing past results. 

Abstract Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of general relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO–Virgo–KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering single-harmonic and dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is 6.4 × 10⁻²⁷for the young energetic pulsar J0537−6910, while the lowest constraint on the ellipticity is 8.8 × 10⁻⁹for the bright nearby millisecond pulsar J0437−4715. Additionally, for a subset of 16 targets, we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of nonstandard polarizations as predicted by the Brans–Dicke theory.