Publications

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Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

Olivier Giraud, Mark-Oliver Goerbig, Daniel Braun

SciPost Phys. 16, 085 (2024) · published 25 March 2024 | · pdf

We calculate the quantum Fisher information for a generic many-body fermionic system in a pure state depending on a parameter. We discuss the situations where the parameter is imprinted in the basis states, in the state coefficients, or both. In the case where the parameter dependence of coefficients results from a Hamiltonian evolution, we derive a particularly simple expression for the quantum Fisher information. We apply our findings to the quantum Hall effect, and evaluate the quantum Fisher information associated with the optimal measurement of the magnetic field for a system in the ground state of the effective Hamiltonian. The occupation of electron states with high momentum enforced by the Pauli principle leads to a "super-Heisenberg" scaling of the sensitivity with a power law that depends on the geometry of the sensor.
Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Sebastian Nagies, Botao Wang, Adam C. Knapp, André Eckardt, Nathan L. Harshman

SciPost Phys. 16, 086 (2024) · published 26 March 2024 | · pdf

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.
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 | · 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.
Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states

Dmitri A. Ivanov

SciPost Phys. Core 7, 022 (2024) · published 22 April 2024 | · pdf

It is known that computing the permanent of the matrix 1+A, where A is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I extend this result to a generalization of the matrix permanent: An expectation value in a product of a large number of identical bosonic states with a bounded number of bosons. This result complements earlier studies on the computational complexity in boson sampling and related setups. The proposed technique based on the Gaussian averaging is equally applicable to bosonic and fermionic systems. This also allows us to improve an earlier polynomial complexity estimate for the fermionic version of the same problem.
Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field

Serafim S. Babkin, Andrew P. Higginbotham, Maksym Serbyn

SciPost Phys. 16, 115 (2024) · published 1 May 2024 | · pdf

Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study by [Phys. Rev. Lett. 128, 107701 (2022)] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating $g$-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.
Weakly interacting Bose gas with two-body losses

Chang Liu, Zheyu Shi, Ce Wang

SciPost Phys. 16, 116 (2024) · published 1 May 2024 | · pdf

We study the many-body dynamics of weakly interacting Bose gases with two-particle losses. We show that both the two-body interactions and losses in atomic gases may be tuned by controlling the inelastic scattering process between atoms by an optical Feshbach resonance. Interestingly, the low-energy behavior of the scattering amplitude is governed by a single parameter, i.e. the complex $s$-wave scattering length $a_c$. The many-body dynamics are thus described by a Lindblad master equation with complex scattering length. We solve this equation by applying the Bogoliubov approximation in analogy to the closed systems. Various peculiar dynamical properties are discovered, some of them may be regarded as the dissipative counterparts of the celebrated results in closed Bose gases. For example, we show that the next-order correction to the mean-field particle decay rate is to the order of $|n a_c^{3}|^{1/2}$, which is an analogy of the Lee-Huang-Yang correction of Bose gases. It is also found that there exists a dynamical symmetry of symplectic group Sp$(4,\mathbb{C})$ in the quadratic Bogoliubov master equation, which is an analogy of the SU(1,1) dynamical symmetry of the corresponding closed system. We further confirmed the validity of the Bogoliubov approximation by comparing its results with a full numerical calculation in a double-well toy model. Generalizations of other alternative approaches such as the dissipative version of the Gross-Pitaevskii equation and hydrodynamic theory are also discussed in the last.
The quantum cartpole: A benchmark environment for non-linear reinforcement learning

Kai Meinerz, Simon Trebst, Mark Rudner, Evert van Nieuwenburg

SciPost Phys. Core 7, 026 (2024) · published 7 May 2024 | · pdf

Feedback-based control is the de-facto standard when it comes to controlling classical stochastic systems and processes. However, standard feedback-based control methods are challenged by quantum systems due to measurement induced backaction and partial observability. Here we remedy this by using weak quantum measurements and model-free reinforcement learning agents to perform quantum control. By comparing control algorithms with and without state estimators to stabilize a quantum particle in an unstable state near a local potential energy maximum, we show how a trade-off between state estimation and controllability arises. For the scenario where the classical analogue is highly nonlinear, the reinforcement learned controller has an advantage over the standard controller. Additionally, we demonstrate the feasibility of using transfer learning to develop a quantum control agent trained via reinforcement learning on a classical surrogate of the quantum control problem. Finally, we present results showing how the reinforcement learning control strategy differs from the classical controller in the non-linear scenarios.
Brick wall quantum circuits with global fermionic symmetry

Pietro Richelli, Kareljan Schoutens, Alberto Zorzato

SciPost Phys. 17, 087 (2024) · published 23 September 2024 | · pdf

We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, Hamiltonian limit $H_{\gamma}$ in closed form. We find that the fermionic symmetry pins $H_{\gamma}$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits.
Escaping fronts in local quenches of a confining spin chain

Anna Krasznai, Gábor Takács

SciPost Phys. 16, 138 (2024) · published 29 May 2024 | · pdf

We consider local quenches from initial states generated by a single spin-flip in either the true or the false vacuum state of the confining quantum Ising spin chain in the ferromagnetic regime. Contrary to global quenches, where the light-cone behaviour is strongly suppressed, we find a significant light-cone signal propagating with a nonzero velocity besides the expected localised oscillating component. Combining an analytic representation of the initial state with a numerical description of the relevant excitations using the two-fermion approximation, we can construct the spectrum of post-quench excitations and their overlaps with the initial state, identifying the underlying mechanism. For confining quenches built upon the true vacuum, the propagating signal consists of superpositions of left and right-moving mesons escaping confinement. In contrast, for anti-confining quenches built upon the false vacuum it is composed of superpositions of left and right-moving bubbles which escape Wannier-Stark localisation.

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