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As part of the PIP-II project at Fermilab, a pre-production cryomodule featuring 325 MHz Single Spoke Resonator type 2 (SSR2) superconducting RF cavities is under construction. These SSR2 cavities are fabricated by industry partners and undergo initial cold testing at our collaborating institution, IJCLab in France, utilizing low-power coupler. Subsequently, the cavities are subjected to final qualification at Fermilab, complete with tuner and high-power coupler assemblies. This paper provides an overview of the ongoing efforts dedicated to high-power testing of jacketed SSR2 cavities in the Spoke Test Cryostat (STC) at Fermilab. Performance parameters obtained from these tests are presented, offering valuable insights into the cavities operational characteristics and readiness for integration into the PIP-II cryomodule., Comment: 32nd Linear Accelerator Conference (LINAC 2024)

We investigate the topological properties of the Su-Schrieffer-Heeger (SSH) model under dissipative dynamics using the quantum trajectory approach. Our study explores the preservation or breakdown of topological edge states, particularly focusing on the effects of symmetry-preserving and symmetry-breaking dissipations. We employ the Disconnected Entanglement Entropy (DEE) as a marker for detecting topological phases in the system, which is subjected to Lindblad dynamics. The analysis reveals that, while dissipation in the bulk minimally affects the system's topological features, dissipation at the boundary leads to the destabilization of the edge modes, independently of the symmetry properties of the dissipation., Comment: 22 pages, 12 figures

A key challenge in observing measurement-induced phase transitions is the mitigation of the post-selection barrier, which causes the reproducibility of specific sequences of measurement readouts--the trajectory--to be exponentially small in system size. Recent studies suggest that some classes of monitored infinite-range systems alleviate this problem by exhibiting a fast saturation of entanglement, resulting in only a polynomial post-selection overhead. This paper answers whether this feature is inherent in infinite-range systems, due to their underlying semiclassical dynamics. We consider three experimentally relevant monitored models: a Tavis-Cummings model, a Superradiance model, and a Bose-Hubbard dimer, each exhibiting non-trivial monitored dynamics. We unveil the occurrence of entanglement phase transitions in these models, showing how the saturation time is strongly affected by bistability regions, which also prevent the mitigation of the post-selection barrier. Finally, we propose experimental realizations of these models, providing a discussion of post selection from an experimental perspective., Comment: 31 pages, 27 figures

Recently, digitized-counterdiabatic (CD) corrections to the quantum approximate optimization algorithm (QAOA) have been proposed, yielding faster convergence within the desired accuracy than standard QAOA. In this manuscript, we apply this approach to a fully-connected spin model with random couplings. We show that the performances of the algorithm are related to the spectral properties of the instances analyzed. In particular, the larger the gap between the ground state and the first excited states, the better the convergence to the exact solution.

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a $T=\infty$ thermal bath through its leftmost site. By analyzing local magnetizations, we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance -- a global quantity measuring localization -- thermalizes over a time scale exponential both in disorder strength and system size is in agreement with these results., Comment: 12 pages, 8 figures. More references on logarithmic light cones in MBL. Discussion on the particle-number nonconserving case added

We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form \begin{equation*} \mathcal{F}(v;\Omega)= \int_{\Omega} f (x, Dv) dx \end{equation*} under $(p,q)$-growth conditions. The main novelty is that, beside a suitable regularity assumption on the partial map $x\mapsto f(x,\xi)$, we do not assume any special structure for the energy density as a function of the $\xi$-variable.

We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular and chaotic regimes. At finite size, we describe the system dynamics using stochastic quantum trajectories. We find that the asymptotic nonstabilizerness (alias the magic, a measure of quantum complexity), averaged over trajectories, mirrors to some extent the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit., Comment: 16 pages, 15 figures

Beamline components, such as superconducting radio frequency cavities and focusing lenses, need to be assembled together in a string while in a cleanroom environment. The present contribution identifies and characterizes materials for additive manufacturing that can be used in a cleanroom. The well known advantages of additive manufacturing processes would highly benefit the design and development of tooling needed for the mechanical support and alignment of string components. Cleanliness, mechanical properties, and leak tightness of the chosen materials are the main focus of this contribution, which also paves the way for the integration of such materials in cryomodule assemblies. Results reported here were obtained in the framework of the PIP-II project at Fermilab., Comment: 21st International Conference on Radio-Frequency Superconductivity (SRF 2023)

Typical measures of nonstabilizerness of a system of $N$ qubits require computing $4^N$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension $2^N$. For permutationally invariant systems, this exponential overhead can be reduced to just $O(N^3)$ expectation values on a state with a dimension $O(N)$. We exploit this simplification to study the nonstabilizerness phase transitions of systems with hundreds of qubits., Comment: 6 + 4 pages, 4 + 6 figures

A prototype cryomodule containing eight Single Spoke Resonators type-1 (SSR1) operating at 325 MHz and four superconducting focusing lenses was successfully assembled, cold tested, and accelerated beam in the framework of the PIP-II project at Fermilab. The impact of induced residual magnetic fields from the solenoids on performance of cavities is presented in this contribution. In addition, design optimizations for the production cryomodules as a result of this impact are highlighted., Comment: SRF2023 Conference

We consider local weak solutions of widely degenerate or singular elliptic PDEs of the type \begin{equation*} -\,\mathrm{div}\left((\vert Du\vert-\lambda)_{+}^{p-1}\frac{Du}{\vert Du\vert}\right)=f \,\,\,\,\,\,\, \text{in}\,\,\Omega, \end{equation*} where $\Omega$ is an open subset of $\mathbb{R}^{n}$ for $n\geq2$, $\lambda$ is a positive constant and $(\,\cdot\,)_{+}$ stands for the positive part. We establish some higher differentiability results, under essentially sharp conditions on the datum $f$. For $\lambda=0$, our results give back those contained in [12, 25].

We propose a Floquet period-doubling time-crystal model based on a disordered interacting long-range spin chain where the periodic swapping of nearby spin couples is applied. This protocol can be applied to systems with any local spin magnitude $s$ {and in principle also to systems with nonspin (fermionic or bosonic) local Hilbert space}. We explicitly consider the cases $s = 1/2$ and $s = 1$, using analytical and numerical methods to show that the time-crystal behavior appears in a range of parameters. In particular, we study the persistence of period-doubling oscillations in time, the time-crystal properties of the Floquet spectrum (quasienergy $\pi$-spectral pairing and long-range correlations of the Floquet states), and introduce a quantity (the local imbalance) to assess what initial states give rise to a period-doubling dynamics. We also consider the average level spacing ratio and find that the interval of parameters where the system does not thermalize and persistent period-doubling is possible corresponds to the one where the Floquet spectrum shows time-crystal properties., Comment: 19 pages, 18 figures

This contribution reports the design of the production Single Spoke Resonator Type 1 Cryomodule (SSR1 CM) for the PIP-II project at Fermilab. The innovative design is based on a structure, the strongback, which supports the coldmass from the bottom, stays at room temperature during operations, and can slide longitudinally with respect to the vacuum vessel. The Fermilab style cryomodule developed for the prototype Single Spoke Resonator Type 1 (pSSR1), the prototype High Beta 650 MHz (pHB650), and preproduction Single Spoke Resonator Type 2 (ppSSR2) cryomodules is the baseline of the present design. The focus of this contribution is on the results of calculations and finite element analyses performed to optimize the critical components of the cryomodule: vacuum vessel, strongback, thermal shield, and magnetic shield., Comment: 21st Intl Conf Radio Frequency Superconductivity (SRF 2023). arXiv admin note: substantial text overlap with arXiv:2209.01282

The Proton Improvement Plan II (PIP-II) project is an essential upgrade to Fermilab's particle accelerator complex to enable the world's most intense neutrino beam for LBNF/DUNE and a broad particle physics program for many decades to come. PIP-II will deliver 1.2 MW of proton beam power from the Main Injector, upgradeable to multi-MW capability. The central element of PIP-II is an 800 MeV superconducting radio frequency (SRF) linac, which comprises a room temperature front end followed by an SRF section. The SRF section consists of five different flavors of cavities/cryomodules, including Half Wave Resonators (HWR), Single Spoke and elliptical resonators operating at, or above, state-of-the-art parameters. The first two PIP-II cryomodules, Half Wave Resonator (HWR) and Single Spoke Resonator 1 (SSR1) were installed in the PIP-II Injector Test facility (PIP2IT) and have accelerated beam to above 17 MeV. PIP-II is the first U.S. accelerator project that will be constructed with significant contributions from international partners, including India, Italy, France, United Kingdom and Poland. The project was baselined in April 2022, and the construction phase is underway., Comment: 21st Intl Conf Radio Frequency Superconductivity (SRF 2023)

We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the ellipticity exponent.

Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed.

The Proton Improvement Plan-II (PIP-II [1]) linac will include 35 Single Spoke Resonators type 2 (SSR2). A preproduction SSR2 cryomodule will contain 5 jacketed cavities. Several units are already manufactured and prepared for cold testing. In this work, data collected from the fabrication, processing and preparation of the cavities will be presented and the improvements implemented after the completion of the first unit will be highlighted.

Five 325 MHz high-power couplers will be integrated into the pre-production Single Spoke Resonator Type-II (ppSSR2) cryomodule for the PIP-II project at Fermilab. Couplers were procured by both Fermilab and IJCLAB for this effort. The design of the coupler is described, including design optimizations from the previous generation. This paper then describes the coupler life cycle, including design, manufacturing, and assembly, along with the lessons learned at each stage.

We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling sub-extensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the post-selection measurement problem, even in the case of imperfect monitoring., Comment: 7 + 4 pages, 3 + 4 figures

Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|\psi\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a numerical method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the states $|\psi(\lambda(t))\rangle$, starting from a simple state $|\psi_0\rangle$ with a known $\hat{\mathcal{H}}_0$, generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. The method, implemented through a projection onto a set of local operators, only requires the knowledge of local expectation values, and, for long annealing times, leads to an approximate parent Hamiltonian whose degree of locality depends on the correlations built up by the states $|\psi(\lambda)\rangle$. We illustrate the method on two paradigmatic models: the Kitaev fermionic chain and a quantum Ising chain in longitudinal and transverse fields., Comment: In this second version, inverse annealing is also applied to a quantum Ising chain in longitudinal and transverse fields

In this paper, we study the regularity of weak solutions to the following strongly degenerate parabolic equation \begin{equation*} u_t-\div\left(\left(\left|Du\right|-1\right)_+^{p-1}\frac{Du}{\left|Du\right|}\right)=f\qquad\mbox{ in }\Omega_T, \end{equation*} where $\Omega$ is a bounded domain in $\mathbb{R}^{n}$ for $n\geq2$, $p\geq2$ and $\left(\,\cdot\,\right)_{+}$ stands for the positive part. We prove the higher differentiability of a nonlinear function of the spatial gradient of the weak solutions, assuming only that $f\in L^{2}_{\loc}\left(\Omega_T\right)$. This allows us to establish the higher integrability of the spatial gradient under the same minimal requirement on the datum $f$.

We present Counterdiabatic Reverse Annealing, a novel quantum annealing protocol that extends the range of application of reverse annealing to the previously inaccessible short-time domain. This is achieved by exploiting approximate counterdiabatic driving expanded in low-order nested commutators. In this work, we offer a comparative study of the performance of this new technique to that of unassisted reverse annealing in terms of metrics such as the ground-state fidelity and the time to solution. We provide a quantitative measure of the energetic cost of counterdiabatic reverse annealing and show that significant improvements are possible even using local counterdiabatic potentials, paving the way toward the experimental implementation in near-term quantum devices., Comment: 11 pages, 14 figures

A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory (LSTM) neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training., Comment: 10 pages, 8 figures