arXiv subjects

Etienne Granet

Publications and source records attributed to Etienne Granet.

At least 37 records · Page 2Linked to original sources

arXiv2024

A noise-limiting quantum algorithm using mid-circuit measurements for dynamical correlations at infinite temperature

It is generally considered that the signal output by a quantum circuit is attenuated exponentially fast in the number of gates. This letter explores how algorithms using mid-circuit measurements and classical conditioning as computational tools (and not as error mitigation or correction subroutines) can be naturally resilient to complete decoherence, and maintain quantum states with useful properties even for infinitely deep noisy circuits. Specifically, we introduce a quantum channel built out of mid-circuit measurements and feed-forward, that can be used to compute dynamical correlations at infinite temperature and canonical ensemble expectation values for any Hamiltonian. The unusual property of this algorithm is that in the presence of a depolarizing channel it still displays a meaningful, non-zero signal in the large depth limit. We showcase the noise resilience of this quantum channel on Quantinuum's H1-1 ion-trap quantum computer.

quant-ph↗

arXiv2023

Continuous Hamiltonian dynamics on digital quantum computers without discretization error

We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number of gates comes at the cost of an attenuation of the measured expectation value by a known amplitude, requiring more shots per circuit. The gate count for simulation up to time $t$ is $O(t^2μ^2)$ with $μ$ the $1$-norm of the Hamiltonian, without dependence on the precision desired on the result, providing a significant improvement over previous algorithms. The only dependence in the norm makes it particularly adapted to non-sparse Hamiltonians. The algorithm generalizes to time-dependent Hamiltonians, appearing for example in adiabatic state preparation. These properties make it particularly suitable for present-day relatively noisy hardware that supports only circuits with moderate depth.

quant-ph↗

arXiv2023

Antiunitary symmetry breaking and a hierarchy of purification transitions in Floquet non-unitary circuits

We consider how a maximally mixed state evolves under $(1+1)D$ Floquet non-unitary circuits with an antiunitary symmetry that squares to identity, that serves as a generalized $\mathcal{PT}$ symmetry. Upon tuning a parameter, the effective Hamiltonian of the Floquet operator demonstrates a symmetry breaking transition. We show that this symmetry breaking transition coincides with different kinds of purification transitions. Gaussian non-unitary circuits are mixed (not purifying) on both sides of the symmetry breaking transition, while interacting but integrable non-unitary circuits are mixed on the symmetric side and ``weakly purifying" on the symmetry breaking side. In the weakly purifying phase, the initial mixed state purifies on a time scale proportional to the system size. We obtain numerically the critical exponents associated with the divergence of the purification time at the purification transition, which depend continuously on the parameters of the model. Upon adding a symmetric perturbation that breaks integrability, the weakly purifying phase becomes strongly purifying, purifying in a time independent of the system size, for sufficiently large system size. Our models have an extra $U(1)$ symmetry that divides the Hilbert space into different magnetization sectors, some of which demonstrate logarithmic scaling of entanglement in the weakly purifying phase.

quant-ph↗

arXiv2023

Wavelet representation of hardcore bosons

We consider the 1D Tonks-Girardeau gas with a space-dependent potential out of equilibrium. We derive the exact dynamics of the system when divided into $n$ boxes and decomposed into energy eigenstates within each box. It is a representation of the wave function that is mixed between real space and momentum space, whose basis elements are plane waves localized in a box, motivating the word "wavelet". In this representation we derive the emergence of generalized hydrodynamics in appropriate limits without assuming local relaxation. We emphasize in particular that a generalized hydrodynamic behaviour emerges in a high-momentum and short-time limit, besides the more common large-space and late-time limit, which is akin to a semi-classical expansion. In this limit, conserved charges do not require a large number of particles to be described by generalized hydrodynamics. Besides, we show that this wavelet representation provides an efficient numerical algorithm for a complete description of out-of-equilibrium dynamics of hardcore bosons.

cond-mat.quant-gas↗

arXiv2023

Exact mean-field solution of a spin chain with short-range and long-range interactions

We consider the transverse field Ising model with additional all-to-all interactions between the spins. We show that a mean-field treatment of this model becomes exact in the thermodynamic limit, despite the presence of 1D short-range interactions. This is established by looking for eigenstates as coherent states with an amplitude that varies through the Hilbert space. We study then the thermodynamics of the model and identify the different phases. Among its peculiar features, this 1D model possesses a second-order phase transition at finite temperature and exhibits inverse melting.

cond-mat.stat-mech↗

arXiv2023

Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit

We consider Gaussian quantum circuits that alternate unitary gates and post-selected weak measurements, with spatial translation symmetry and time periodicity. We show analytically that such models can host different kinds of measurement-induced phase transitions detected by entanglement entropy, by mapping the time evolution and weak measurements to Möbius transformations. We demonstrate the existence of a log-law to area-law transition, as well as a volume-law to area-law transition. For the latter, we compute the critical exponent $ν$ for the Hartley, von Neumann and Rényi entropies exactly.

quant-ph↗

arXiv2022

BBGKY Hierarchy and Generalised Hydrodynamics

We consider fermions defined on a continuous one-dimensional interval and subject to weak repulsive two-body interactions. We show that it is possible to perturbatively construct an extensive number of mutually compatible conserved charges for any interaction potential. However, the contributions to the densities of these charges at second order and higher are generally non-local and become spatially localized only if the potential fulfils certain compatibility conditions. We prove that the only solutions to the first of these conditions are the Cheon-Shigehara potential (fermionic dual to the Lieb-Liniger model) and the Calogero-Sutherland potentials. We use our construction to show how Generalized Hydrodynamics (GHD) emerges from the Bogoliubov--Born--Green--Kirkwood--Yvon hierarchy, and argue that GHD in the weak interaction regime is robust under non-integrable perturbations.

cond-mat.stat-mech↗

arXiv2022

Regularization of energy-dependent pointlike interactions in 1D quantum mechanics

We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $δ$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike interactions in 1D. Such classification was made by requiring the pointlike interaction to be hermitian. But we show that although our Hamiltonian is hermitian for the standard inner product when the range of the potential is finite, it becomes hermitian for a different inner product in the zero-range limit. This inner product attributes a finite probability (and not probability density) for the particle to be exactly located at the position of the potential. Such pointlike interactions can then be used to construct potentials with a finite support with an energy-dependent coupling.

quant-ph↗

arXiv2022

Duality between weak and strong interactions in quantum gases

In one dimensional quantum gases there is a well known "duality" between hard core bosons and non-interacting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long standing problem. Our derivation relies on regularizing the only point-like interaction between fermions in 1D that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularisations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model.

quant-ph↗

arXiv2021

Regularization of a strong-weak duality between pointlike interactions in one dimension

Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong-weak duality since the coupling constants in the bosonic and fermionic cases are inversely proportional to each other. We present a regularization of these pointlike interactions that preserves the strong-weak duality, contrary to previously known regularizations. This is proven rigorously. This allows one to use this duality perturbatively and we illustrate it in the Lieb-Liniger model at strong coupling.

math-ph↗

arXiv2021

Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that $all$ correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter one-point function, dynamical two-point function and equal-time three-point function.

cond-mat.stat-mech↗

arXiv2021

Quantum computing critical exponents

We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the transition due to a slowdown of the quantum algorithm when crossing the phase transition. In order to assess performance of the quantum algorithm and compute correlations in a system of up to 752 qubits, we use techniques from integrability to derive closed-form analytical expressions for expectation values with respect to the output of the quantum circuit. We also reduce a conjecture made by Ho and Hsieh about the exact preparation of the transverse field Ising ground state to a system of equations.

quant-ph↗

arXiv2021

Low-density limit of dynamical correlations in the Lieb-Liniger model

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any interaction strength $c>0$, and are the leading order of an expansion in ${\cal D}$. This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.

math-ph↗

arXiv2021

Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

We consider the time evolution of local observables after an interaction quench in the repulsive Lieb-Liniger model. The system is initialized in the ground state for vanishing interaction and then time-evolved with the Lieb-Liniger Hamiltonian for large, finite interacting strength $c$. We employ the Quench Action approach to express the full time evolution of local observables in terms of sums over energy eigenstates and then derive the leading terms of a $1/c$ expansion for several one and two-point functions as a function of time $t > 0$ after the quantum quench. We observe delicate cancellations of contributions to the spectral sums that depend on the details of the choice of representative state in the Quench Action approach and our final results are independent of this choice. Our results provide a highly non-trivial confirmation of the typicality assumptions underlying the Quench Action approach.

cond-mat.stat-mech↗

arXiv2020

A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a $1/c$ expansion. The $n^{\rm th}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a 'bare' $1/c$ expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order $1/c^2$. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.

cond-mat.stat-mech↗

arXiv2020

Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

cond-mat.stat-mech↗

arXiv2020

Stroboscopic exclusion process: a first-moment-driven dynamics

We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we compute the time evolution of the particle density starting from an arbitrary initial configuration, with closed boundary conditions. The core of the argument is the analysis of the time evolution of the moments. Numerical results are compared with the prediction and give excellent agreement.

cond-mat.stat-mech↗

arXiv2020

Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains

We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another 'pseudo-vacuum' sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the $SL(2,\mathbb{C})$ integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [1] (for the case of spins $s=0, \bar{s}=-1$) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of $SL(2,\mathbb{C})$ non-compact spin chains in the thermodynamic limit.

math-ph↗