arXiv subjects

Benjamin Commeau

Publications and source records attributed to Benjamin Commeau.

6 recordsLinked to original sources

arXiv2024

Non-Local to Local Eigenbasis Permutations of Pauli Product Diagonal Operators

This paper investigates the feasibility of mapping non-local, sparse, diagonal forms of quantum Hamiltonians to local forms via eigenbasis permutations. We prove that such a mapping is not always possible, definitively refuting the "Quasiparticle Locality Conjecture." This refutation is achieved by establishing a lower bound, denoted $G_m$, on the number of non-zero terms in a localized diagonal form. Remarkably, $G_m$ reaches cosmologically large values, comparable to the entropy of the observable universe for certain localities $m$. While this theoretically guarantees the conjecture's falsity, the immense scale of $G_m$ motivates us to explore the implications for practically sized systems through a probabilistic approach. We construct a set of random, non-local, sparse, diagonal forms and hypothesize their probability of finding a local representation. Our hypothesize suggests a sharp transition in this probability, linked to the Hamiltonian's sparsity relative to the Bekenstein-Hawking entropy of neutron stars to black holes transition. This observation hints at a potential connection between Hamiltonian sparsity, localizability, critical phenomena warranting further investigation into their interplay in both theoretical and astrophysical contexts.

quant-ph↗

arXiv2021

Long-time simulations with high fidelity on quantum hardware

Moderate-size quantum computers are now publicly accessible over the cloud, opening the exciting possibility of performing dynamical simulations of quantum systems. However, while rapidly improving, these devices have short coherence times, limiting the depth of algorithms that may be successfully implemented. Here we demonstrate that, despite these limitations, it is possible to implement long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on the Rigetti and IBM quantum computers, maintaining a fidelity of at least 0.9 for over 600 time steps. This is a factor of 150 longer than is possible using the iterated Trotter method. Our simulations are performed using a new algorithm that we call the fixed state Variational Fast Forwarding (fsVFF) algorithm. This algorithm decreases the circuit depth and width required for a quantum simulation by finding an approximate diagonalization of a short time evolution unitary. Crucially, fsVFF only requires finding a diagonalization on the subspace spanned by the initial state, rather than on the total Hilbert space as with previous methods, substantially reducing the required resources. We further demonstrate the viability of fsVFF through large numerical implementations of the algorithm, as well as an analysis of its noise resilience and the scaling of simulation errors.

quant-ph↗

arXiv2020

Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation

Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. This has led to recent proposals for variational approaches to dynamical simulation. In this work, we aim to make variational dynamical simulation even more practical and near-term. We propose a new algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. VHD allows for fast forwarding, i.e., simulation beyond the coherence time of the quantum computer with a fixed-depth quantum circuit. It also removes Trotterization error and allows simulation of the entire Hilbert space. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. Moreover, we prove that the VHD cost function does not exhibit a shallow-depth barren plateau, i.e., its gradient does not vanish exponentially. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics.

quant-ph↗

arXiv2019

Polynomial Scaling of Numerical Diagonalization of the 1D Transverse Field Ising Model into a Commuting Basis using the Pauli Product Representation

We report numerical results on the diagonalization of 1D transverse field Ising model. Numerical simulations using the Pauli product representation yield diagonalization from 3 spins to 22 spins in the transverse field Ising model with the number of global Jacobi unitary transformations and number of final terms in diagonalized spin z representation both grew polynomial with the number of spins. These results computed on a classical computer show promise in constructing a quantum circuit to simulate diagonalized generic many-particle Hamiltonians using polynomial number of gates.

quant-ph↗

arXiv2018

Chemical-Strain Induced Tilted Dirac Nodes in (BEDT-TTF)$_2$X$_3$ (X = I, Cl, Br, F) Based Charge-Transfer Salts

The identification of novel multifunctional Dirac materials has been an ongoing effort. In this connection quasi 2-dimensional (BEDT-TTF)-based charge transfer salts are widely discussed. Here, we report about the electronic structure of $α$-(BEDT-TTF)$_2$I$_3$ and $κ$-(BEDT-TTF)$_2$I$_3$ under a hypothetical substitution of iodine with the halogens bromine, chlorine and fluorine. The decreasing size of the anion layer corresponds to applying chemical strain which increases tremendously in the case of (BEDT-TTF)$_2$F$_3$. We performed structural optimization and electronic structure calculations in the framework of density functional theory, incorporating, first, the recently developed strongly constrained and appropriately normed semilocal density functional SCAN, and, second, van der Waals corrections to the PBE exchange correlation functional by means of the dDsC dispersion correction method. In the case of $α$-(BEDT-TTF)$_2$F$_3$ the formation of over-tilted Dirac-type-II nodes within the quasi 2-dimensional Brillouin zone can be found. For $κ$-(BEDT-TTF)$_2$F$_3$, the recently reported topological transition within the electronic band structure cannot be revealed.

cond-mat.mtrl-sci↗

arXiv2017

Structural and electronic properties of $α,β$-(BEDT-TTF)$_2$I$_3$ and $κ$-(BEDT-TTF)$_2$X$_3$ (X=I,F,Br,Cl) organic charge transfer salts

(BEDT-TFF)$_2$I$_3$ charge transfer salts are reported to show superconductivity and pressure induced quasi two-dimensional Dirac cones at the Fermi level. By performing state of the art ab initio calculations in the framework of density functional theory, we investigate the structural and electronic properties of the three structural phases $α$, $β$ and $κ$. \edit{We furthermore report about the irreducible representations of the corresponding electronic band structures, symmetry of their crystal structure, and discuss the origin of band crossings. Additionally, we discuss the chemically induced strain in $κ$-(BEDT-TTF)$_2$I$_3$ achieved by replacing the Iodine layer with other Halogens: Fluorine, Bromine and Chlorine. In the case of $κ$-(BEDT-TTF)$_2$F$_3$, we identify topologically protected crossings within the band structure. These crossings are forced to occur due to the non-symmorphic nature of the crystal.} The calculated electronic structures presented here are added to the organic materials database (OMDB).

cond-mat.mtrl-sci↗