Publications

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• General quantum-classical dynamics as measurement based feedback

  Antoine Tilloy

  SciPost Phys. 17, 083 (2024) · published 18 September 2024 | Toggle abstract · pdf

  This note derives the stochastic differential equations and partial differential equation of general hybrid quantum--classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this approach is an explicit parameterization, without additional positivity constraints. The construction also neatly separates the different effects: how the quantum influences the classical and how the classical influences the quantum. This modular presentation gives a better intuition of what to expect from hybrid dynamics, especially when used to construct possibly fundamental theories.

  4 citations

• Riemannian optimization of photonic quantum circuits in phase and Fock space

  Yuan Yao, Filippo Miatto, Nicolás Quesada

  SciPost Phys. 17, 082 (2024) · published 18 September 2024 | Toggle abstract · pdf

  We propose a framework to design and optimize generic photonic quantum circuits composed of Gaussian objects (pure and mixed Gaussian states, Gaussian unitaries, Gaussian channels, Gaussian measurements) as well as non-Gaussian effects such as photon-number-resolving measurements. In this framework, we parametrize a phase space representation of Gaussian objects using elements of the symplectic group (or the unitary or orthogonal group in special cases), and then we transform it into the Fock representation using a single linear recurrence relation that computes the Fock amplitudes of any Gaussian object recursively. We also compute the gradient of the Fock amplitudes with respect to phase space parameters by differentiating through the recurrence relation. We can then use Riemannian optimization on the symplectic group to optimize $M$-mode Gaussian objects, avoiding the need to commit to particular realizations in terms of fundamental gates. This allows us to "mod out" all the different gate-level implementations of the same circuit, which now can be chosen after the optimization has completed. This can be especially useful when looking to answer general questions, such as bounding the value of a property over a class of states or transformations, or when one would like to worry about hardware constraints separately from the circuit optimization step. Finally, we make our framework extendable to non-Gaussian objects that can be written as linear combinations of Gaussian ones, by explicitly computing the change in global phase when states undergo Gaussian transformations. We implemented all of these methods in the freely available open-source library MrMustard, which we use in three examples to optimize the 216-mode interferometer in Borealis, and 2- and 3-modes circuits (with Fock measurements) to produce cat states and cubic phase states.

  6 citations

• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity

  Dominic Gribben, Jamir Marino, Shane P. Kelly

  SciPost Phys. Core 7, 060 (2024) · published 9 September 2024 | Toggle abstract · pdf

  We study a random unitary circuit model of an impurity moving through a chaotic medium. The exchange of information between the medium and impurity is controlled by varying the velocity of the impurity, $v_d$, relative to the speed of information propagation within the medium, $v_B$. Above supersonic velocities, $v_d> v_B$, information cannot flow back to the impurity after it has moved into the medium, and the resulting dynamics are Markovian. Below supersonic velocities, $v_d< v_B$, the dynamics of the impurity and medium are non-Markovian, and information is able to flow back onto the impurity. We show the two regimes are separated by a continuous phase transition with exponents directly related to the diffusive spreading of operators in the medium. This is demonstrated by monitoring an out-of-time-order correlator (OTOC) in a scenario where the impurity is substituted at an intermediate time. During the Markovian phase, information from the medium cannot transfer onto the replaced impurity, manifesting in no significant operator development. Conversely, in the non-Markovian phase, we observe that operators acquire support on the newly introduced impurity. We also characterize the dynamics using the coherent information and provide two decoders which can efficiently probe the transition between Markovian and non-Markovian information flow. Our work demonstrates that Markovian and non-Markovian dynamics can be separated by a phase transition, and we propose an efficient protocol for observing this transition.

  5 citations

• Flux-tunable hybridization in a double quantum dot interferometer

  Christian G. Prosko, Ivan Kulesh, Michael Chan, Lin Han, Di Xiao, Candice Thomas, Michael J. Manfra, Srijit Goswami, Filip K. Malinowski

  SciPost Phys. 17, 074 (2024) · published 6 September 2024 | Toggle abstract · pdf

  Quantum interference of electron tunneling occurs in any system where multiple tunneling paths connect states. This unavoidably arises in two-dimensional semiconducting qubit arrays, and must be controlled as a prerequisite for the manipulation and readout of hybrid topological and parity qubits. Studying a loop formed by two quantum dots, we demonstrate a magnetic-flux-tunable hybridization between two electronic levels, an irreducibly simple system where quantum interference is expected to occur. Using radio-frequency reflectometry of the dots’ gate electrodes we extract an interdot coupling exhibiting oscillations with a periodicity of one flux quantum. In different tunneling regimes we benchmark the oscillations’ contrast, and find their amplitude varies with the charge state of the quantum dots. These results establish the feasibility and limitations of parity readout of qubits with tunnel couplings tuned by flux.

  1 citation

• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

  Calvin Krämer, Jan Alexander Koziol, Anja Langheld, Max Hörmann, Kai Phillip Schmidt

  SciPost Phys. 17, 061 (2024) · published 23 August 2024 | Toggle abstract · pdf

  We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents $\nu_\mathrm{s}$ and $\nu_\mathrm{w}$ as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent $\beta$ and the critical exponent $\nu_{\mathrm{av}}$ of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent $z'$ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

  1 citation

• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice

  Viktor Kott, Matthias Mühlhauser, Jan Alexander Koziol, Kai Phillip Schmidt

  SciPost Phys. 17, 053 (2024) · published 15 August 2024 | Toggle abstract · pdf

  We investigate the quantum robustness of the topological order in the toric code on the honeycomb lattice in the presence of a uniform parallel field. For a field in $z$-direction, the low-energy physics is in the flux-free sector and can be mapped to the transverse-field Ising model on the honeycomb lattice. One finds a second-order quantum phase transition in the 3D Ising$^\star$ universality class for both signs of the field. The same is true for a postive field in $x$-direction where an analogue mapping in the charge-free sector yields a ferromagnetic transverse-field Ising model on the triangular lattice and the phase transition is still 3D Ising$^\star$. In contrast, for negative $x$-field, the charge-free sector is mapped to the highly frustrated antiferromagnetic transverse-field Ising model on the triangular lattice which is known to host a quantum phase transition in the 3D XY$^\star$ universality class. Further, the charge-free sector does not always contain the low-energy physics for negative $x$-fields and a first-order phase transition to the polarized phase in the charge-full sector takes place at larger negative field values. We quantify the location of this transition by comparing quantum Monte Carlo simulations and high-field series expansions. The full extension of the topological phase in the presence of $x$- and $z$-fields is determined by perturbative linked-cluster expansions using a full graph decomposition. Extrapolating the high-order series of the charge and the flux gap allows to estimate critical exponents of the gap closing. This analysis indicates that the topological order breaks down by critical lines of 3D Ising$^\star$ and 3D XY$^\star$ type with interesting potential multi-critical crossing points. All findings for the toric code on the honeycomb lattice can be transferred exactly to the toric code on the triangular lattice.

• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering

  Alexander Schnell, Christof Weitenberg, André Eckardt

  SciPost Phys. 17, 052 (2024) · published 14 August 2024 | Toggle abstract · pdf

  Floquet engineering is an important tool for realizing topologically nontrivial band structures for charge-neutral atoms in optical lattices. However, the preparation of a topological-band-insulator-type state of fermions, with one nontrivial quasi-energy band filled completely and the others empty, is challenging as a result of both driving induced heating as well as imperfect adiabatic state preparation (with the latter induced by the unavoidable gap closing when passing the topological transition). An alternative procedure that has been proposed is to prepare such states dissipatively, i.e. as a steady state that emerges when coupling the system to reservoirs. Here we discuss a concrete scheme that couples the system to a weakly interacting Bose condensate given by second atomic species acting as a heat bath. Our strategy relies on the engineering of the potential for the bath particles, so that they occupy weakly coupled tubes perpendicular to the two-dimensional system. Using Floquet-Born-Markov theory, we show that the resulting nonequilibrium steady state of the driven-dissipative system approximates a topological insulator. We even find indications for the approximate stabilization of an anomalous Floquet topological insulator, a state that is impossible to realize in equilibrium.

  2 citations

• Precision magnetometry exploiting excited state quantum phase transitions

  Qian Wang, Ugo Marzolino

  SciPost Phys. 17, 043 (2024) · published 9 August 2024 | Toggle abstract · pdf

  Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.

• Quantum work capacitances: Ultimate limits for energy extraction on noisy quantum batteries

  Salvatore Tirone, Raffaele Salvia, Stefano Chessa, Vittorio Giovannetti

  SciPost Phys. 17, 041 (2024) · published 9 August 2024 | Toggle abstract · pdf

  We present a theoretical analysis of the energy recovery efficiency for quantum batteries composed of many identical quantum cells undergoing noise. While the possibility of using quantum effects to speed up the charging processes of batteries have been vastly investigated, In order to traslate these ideas into working devices it is crucial to assess the stability of the storage phase in the quantum battery elements when they are in contact with environmental noise. In this work we formalize this problem introducing a series of operationally well defined figures of merit (the work capacitances and the Maximal Asymptotic Work/Energy Ratios) which gauge the highest efficiency one can attain in recovering useful energy from quantum battery models that are formed by large collections of identical and independent elements (quantum cells or q-cells). Explicit evaluations of such quantities are presented for the case where the energy storing system undergoes through dephasing and depolarizing noise.

  5 citations

• Topological photonic band gaps in honeycomb atomic arrays

  Pierre Wulles, Sergey E. Skipetrov

  SciPost Phys. Core 7, 051 (2024) · published 7 August 2024 | Toggle abstract · pdf

  lattice of two-level atoms coupled by the in-plane electromagnetic field may exhibit band gaps that can be opened either by applying an external magnetic field or by breaking the symmetry between the two triangular sublattices of which the honeycomb one is a superposition. We establish the conditions of band gap opening, compute the width of the gap, and characterize its topological property by a topological index (Chern number). The topological nature of the band gap leads to inversion of the population imbalance between the two triangular sublattices for modes with frequencies near band edges. It also prohibits a transition to the trivial limit of infinitely spaced, noninteracting atoms without closing the spectral gap. Surrounding the lattice by a Fabry-Pérot cavity with small intermirror spacing $d < \pi/k_0$, where $k_0$ is the free-space wave number at the atomic resonance frequency, renders the system Hermitian by suppressing the leakage of energy out of the atomic plane without modifying its topological properties. In contrast, a larger $d$ allows for propagating optical modes that are built up due to reflections at the cavity mirrors and have frequencies inside the band gap of the free-standing lattice, thus closing the latter.