arXiv subjects

Julian K. Nauth

Publications and source records attributed to Julian K. Nauth.

6 recordsLinked to original sources

arXiv2026

Optimal stellar rank approximation of squeezed cat states with photon catalysis

Non-Gaussian quantum states and operations constitute essential resources for achieving quantum computational advantage and enabling quantum error correction in bosonic platforms. However, their generation in optical settings remains a challenging experimental task, often relying on probabilistic heralded protocols. Here, we present an in-depth analysis of the suitability of photon catalysis between low number Fock states and squeezed states for the generation of squeezed coherent state superpositions. We employ the stellar rank formalism to characterize the non-Gaussian complexity of input resources (including both states and measurements) and the generated states. This enables a systematic comparison of the fidelity between the catalyzed output and the target states to the maximum fidelity achievable by any protocol with the same non-Gaussian input resources. In this sense, we identify instances where the catalysis protocols considered here are provably optimal. We identify parameter regimes in which high-fidelity approximations of the target states can be achieved with minimal resources. Furthermore, we benchmark the performance of photon catalysis against Gaussian boson sampling-inspired protocols in terms of success probability and state quality, highlighting the advantages of deterministic Fock state sources. We also investigate the generation of related non-Gaussian resources including squeezed Fock states, relevant for quantum error correction. To account for experimental imperfections, we model losses across all optical modes using a Hilbert space truncation approach in the Fock basis and analyze the robustness of the generated states under realistic conditions. Our results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.

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arXiv2023

Dicke-state preparation through global transverse control of Ising-coupled qubits

We consider the problem of engineering the two-excitation Dicke state $|D^{3}_{2}\rangle$ in a three-qubit system with all-to-all Ising-type qubit-qubit interaction, which is also subject to global transverse (Zeeman-type) control fields. The theoretical underpinning for our envisioned state-preparation scheme, in which $|000\rangle$ is adopted as the initial state of the system, is provided by a Lie-algebraic result that guarantees state-to-state controllability of this system for an arbitrary choice of initial- and final states that are invariant with respect to permutations of qubits. This scheme is envisaged in the form of a pulse sequence that involves three instantaneous control pulses, which are equivalent to global qubit rotations, and two Ising-interaction pulses of finite durations between consecutive control pulses. The design of this pulse sequence (whose total duration is $T\approx 0.95\:\hbar/J$, where $J$ is the Ising-coupling strength) leans heavily on the concept of the symmetric sector, a four-dimensional, permutationally-invariant subspace of the three-qubit Hilbert space. We demonstrate the feasibility of the proposed state-preparation scheme by carrying out a detailed numerical analysis of its robustness to systematic errors, i.e. deviations from the optimal values of the eight parameters that characterize the underlying pulse sequence. Finally, we discuss how our proposed scheme can be generalized for engineering Dicke states in systems with $N \ge 4$ qubits. For the sake of illustration, we describe the preparation of the two-excitation Dicke state $|D^{4}_{2}\rangle$ in a four-qubit system.

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arXiv2023

Spectral features of polaronic excitations in a superconducting analog simulator

We investigate spectral properties of polaronic excitations within the framework of an analog quantum simulator based on inductively coupled superconducting transmon qubits and microwave resonators. This system emulates a lattice model that describes a nonlocal coupling of an itinerant spinless-fermion excitation to dispersionless (Einstein-type) phonons through the Peierls and breathing-mode interaction mechanisms. The model is characterized by a sharp, level-crossing transition at a critical value of the effective excitation-phonon coupling strength; above the transition point, the ground state of this model corresponds to a heavily dressed (small-polaron) excitation. Using the kernel-polynomial method, we evaluate the momentum-frequency resolved spectral function of this system for a broad range of parameters. In particular, we underscore the ramifications of the fact that the zero-quasimomentum Bloch state of a bare excitation represents the exact eigenstate of the Hamiltonian of this system for an arbitrary excitation-phonon coupling strength. We also show that -- based on the numerically evaluated spectral function and its well-known relation with the survival probability of the initial, bare-excitation Bloch state (the Loschmidt echo) -- one can make predictions about the system dynamics following an excitation-phonon interaction quench. To make contact with anticipated experimental realizations, we utilize a previously proposed method for extracting dynamical-response functions in systems with local (single-qubit) addressability using the multiqubit (many-body) version of the Ramsey interference protocol.

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arXiv2022

Full time-dependent counting statistics of highly entangled biphoton states

Highly entangled biphoton states, generated by spontaneous parametric processes, find wide applications in many experimental realizations. There is an increasing demand for accurate prediction of their time-dependent detection. Unlike approaches that have emerged so far, this paper presents an approach providing full time-dependent counting statistics in terms of efficiently computable formulas, valid for a wide range of entanglement and arbitrary interaction times. General spatial modes are taken into account to describe free space and fiber propagation. The time intervals that correspond to the statistics are classified according to their widths. Apart from large and small widths compared to the temporal correlation width, intermediate interval widths give access to accidental correlations between separated time intervals. Moreover, the approach is easily applicable to a modular array of arbitrary optical components and external influences. This is demonstrated on phase-time coding, where the detuning of the interferometers affecting Franson interference is investigated. An acceptable range for the detuning is estimated, such that the security of the key is not compromised.

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arXiv2022

Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control

Interconversions of $W$ and Greenberger-Horne-Zeilinger states in various physical systems are lately attracting considerable attention. We address this problem in the fairly general physical setting of qubit arrays with long-ranged (all-to-all) Ising-type qubit-qubit interaction, which are simultaneously acted upon by transverse Zeeman-type global control fields. Motivated in part by a recent Lie-algebraic result that implies state-to-state controllability of such a system for an arbitrary pair of states that are invariant with respect to qubit permutations, we present a detailed investigation of the state-interconversion problem in the three-qubit case. The envisioned interconversion protocol has the form of a pulse sequence that consists of two instantaneous (delta-shaped) control pulses, each of them corresponding to a global qubit rotation, and an Ising-interaction pulse of finite duration between them. Its construction relies heavily on the use of the (four-dimensional) permutation-invariant subspace (symmetric sector) of the three-qubit Hilbert space. In order to demonstrate the viability of the proposed state-interconversion scheme, we provide a detailed analysis of the robustness of the underlying pulse sequence to systematic errors, i.e. deviations from the optimal values of its five characteristic parameters.

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arXiv2022

Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits

Using the quantum-brachistochrone formalism, we address the problem of finding the fastest possible (time-optimal) deterministic conversion between $W$ and Greenberger-Horne-Zeilinger (GHZ) states in a system of three identical and equidistant neutral atoms that are acted upon by four external laser pulses. Assuming that all four pulses are close to being resonant with the same internal (atomic) transition -- the one between the atomic ground state and a high-lying Rydberg state -- each atom can be treated as an effective two-level system ($gr$-type qubit). Starting from an effective system Hamiltonian, which is valid in the Rydberg-blockade regime and defined on a four-state manifold, we derive the quantum-brachistochrone equations pertaining to the fastest possible $W$-to-GHZ state conversion. By numerically solving these equations, we determine the time-dependent Rabi frequencies of external laser pulses that correspond to the time-optimal state conversion. In particular, we show that the shortest possible $W$-to-GHZ state-conversion time is given by $T_{\textrm{QB}}= 6.8\:\hbar/E$, where $E$ is the total laser-pulse energy used, this last time being significantly shorter than the state-conversion times previously found using a dynamical-symmetry-based approach [$T_{\textrm{DS}}=(1.33-1.66)\:T_{\textrm{QB}}$].

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