Physics Research

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.

Single-photon sources with high single-photon purity and high brightness are key elements of many future quantum technologies. While photon blockade (PB) is widely exploited in the development of such sources, achieving the coexistence of high purity and high brightness remains a long-standing challenge. Here, we identify a novel mechanism for high-brightness PB and demonstrate that near-ideal purity and near-ideal brightness can be simultaneously achieved in an extended nondegenerate two-photon Jaynes-Cummings model with two-body and three-body interactions. This mechanism is underpinned by a distinctive energy-level structure arising from the combined action of the two interactions. The energy levels in the multi-excitation manifold essentially retain a harmonic ladder of degenerate doublets, whereas in the single-excitation subspace the doublet degeneracy is lifted, with a finite splitting between the two levels. Consequently, when one bosonic mode is driven by a coherent continuous-wave pump, the former degeneracy enables the other bosonic mode to exhibit near-perfect PB even in the strong driving regime, while the latter splitting allows the mean photon number of that mode to approach unity. Our proposed scheme overcomes the outstanding challenge and offers a promising pathway toward realizing ideal single-photon sources.

Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions.

Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimizing the number of logical qubits required to execute this algorithm is a key object. In implementations of Shor's algorithm, the space complexity is largely dictated by the modular inversion operation during point addition. Starting from the extended Euclidean algorithm (EEA), we refine the register-sharing method of Proos and Zalka and propose a space-efficient reversible modular inversion algorithm. We use length registers together with location-controlled arithmetic to store the intermediate variables in a compact form throughout the computation. We then optimize the stepwise update rules and give concrete circuit constructions for the resulting controlled arithmetic components. This leads to a modular inversion circuit that uses $3n + 4\lfloor \log_2 n \rfloor + O(1)$ logical qubits and $204n^2\log_2 n + O(n^2)$ Toffoli gates. By inserting this modular inversion component into the controlled affine point-addition circuit, we obtain a space-efficient algorithm for the ECDLP with $5n + 4\lfloor \log_2 n \rfloor + O(1)$ qubits and $O(n^3)$ Toffoli gates. In particular, for a 256-bit prime-field curve, our estimate reduces the logical-qubit count to 1333, compared with 2124 in the previous low-width implementation of Häner et al.

Symmetry and entanglement are two fundamental concepts in quantum many-body physics. Their interplay is captured by symmetry-resolved entanglement, which decomposes the total entanglement into contributions from different symmetry sectors. Computing symmetry-resolved entanglement in strongly interacting higher-dimensional quantum systems remains challenging. Here, we introduce a quantum Monte Carlo (QMC) approach for computing symmetry-resolved Rényi entropies (SRRE) in large-scale interacting systems by measuring disorder (symmetry-twisted) operators on replica manifolds and reconstructing SRRE from the corresponding charged moments. We apply this method to the transverse-field Ising model (TFIM) in one and two dimensions. In one dimension, we recover the conformal-field-theory prediction for the logarithmic scaling of the disorder operator and observe the expected approach to entanglement equipartition. In two dimensions, our data provide numerical evidence consistent with entanglement equipartition at the (2+1)D Ising critical point. We further apply the framework to the 1D Heisenberg chain and obtain results consistent with the expected asymptotic scaling and finite-size corrections in the U(1)-resolved sectors. Our work establishes a practical numerical route to symmetry-resolved entanglement in interacting lattice models and provides a useful framework for future studies beyond one dimension.

In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter $η$ limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of $η^4$. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as $η^6$. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as $10^{-4}$ for $20$-ion chains.

We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of commutators of the one-body operators associated with these equilibria and the position and momentum operators. We also obtain upper bounds in the magnetic field case for the Fock-Darwin Hamiltonian. Our estimates, in particular, allow us to observe several regimes depending on the joint behavior of the Planck constant, the temperature, and the strength of the magnetic field.

Models of gravity in warped extra dimensions enjoy invariance under diffeomorphism. We derive the nonlinear transformation rules for the metric perturbations in the unitary gauge. As an off-shell symmetry, the main consequence of diffeomorphism is a set of recursive relations linking consecutive orders in the field expansion of the effective Lagrangian. The physical consequences are briefly explored for the Randall-Sundrum model with hard branes.

Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by its entanglement spectrum, invariants of multipartite entanglement structures are comparatively difficult to define and work with. The root cause of this difference is that the bipartite problem can be reduced to the analysis of matrix invariants, while its multipartite version is governed by a much richer space of tensor invariants. The present work explores the latter through the lens of so-called trace-invariants, which are in one-to-one correspondence with combinatorial objects known as colored graphs. We first explain why trace-invariant evaluations can serve as labels of LU-orbits of multipartite pure states, how this strategy extends to random states, and how the effect of local operations (LO) can be analyzed through such data. We then focus on entanglement classification within an (infinite-dimensional) subspace of reference states, whose basic building blocks are GHZ states of various dimensions. We show that relatively simple subclasses of trace-invariants are sufficient to separate the LU-orbits of reference states, and enable a complete (resp. an incomplete) characterization of their relations in the LO (resp. LOCC) resource theory of entanglement. Finally, we investigate how a (still infinite) subclass of reference states of local dimension N can be efficiently distinguished at leading and subleading orders in an asymptotic large-N expansion (among themselves, or from Haar-random states). This analysis relies crucially on combinatorial quantities associated to colored graphs, some of which have already played instrumental roles in the recent literature on random tensors. Results of broader relevance are reported along the way.

We study the power spectrum of the velocity field induced during a first-order phase transition occurring in the radiation-dominated era. We focus on the phase of bubble expansion, assuming that it ends with the onset of the sound-wave regime. The main result we present is a refined template for the velocity spectrum at the beginning of the sound-wave phase, which can be used for studying the resulting anisotropic stresses and gravitational wave production. In particular, we find that the breaks in the velocity spectrum are not associated to the bubble size and the sound shell thickness, as previously proposed, but to the position of the discontinuities. This distinction is particularly relevant for supersonic deflagrations, as it implies that the intermediate slope is more pronounced and the two breaks are more separated when the wall velocity approaches the Chapman-Jouget speed, instead of the sound speed. We also show that the asymptotic branches of the velocity power spectrum are determined by the integral over the single-bubble profiles at large scales, and by the discontinuities of the velocity profiles at small scales. Furthermore, we study the dependence of the two breaks and the intermediate slope on the distribution function of the times of bubble nucleation (exponential and simultaneous). All the results presented in this work have been included in the public Python package CosmoGW.