arXiv subjects

David Raveh

Publications and source records attributed to David Raveh.

7 recordsLinked to original sources

arXiv2025

Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading term in the entanglement scaling, based on the analytic properties of the inhomogeneous potential. This method is applicable to a broad class of models with smooth spatial inhomogeneities. As a case study, we apply this approach for a family of exactly-solvable models characterized by orthogonal polynomials of the Askey scheme, finding a perfect match between the numerical and analytical results.

cond-mat.stat-mech↗

arXiv2024

Dicke states as matrix product states

We derive an exact canonical matrix product state (MPS) representation for Dicke states $|D^n_k\rangle$ with minimal bond dimension $\chi=k+1$, for general values of $n$ and $k$, for which the W-state is the simplest case $k=1$. We use this MPS to formulate a quantum circuit for sequentially preparing Dicke states deterministically, relating it to the recursive algorithm of B\"artschi and Eidenbenz. We also find exact canonical MPS representations with minimal bond dimension for higher-spin and qudit Dicke states.

quant-ph↗

arXiv2024

Estimating Bethe roots with VQE

Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver (VQE) approach to estimating Bethe roots of the spin-1/2 XXZ quantum spin chain, by using Bethe states as trial states, and treating Bethe roots as variational parameters. In numerical simulations of systems of size up to 6, we obtain estimates for Bethe roots corresponding to both ground states and excited states with up to 5 down-spins, for both the closed and open XXZ chains. This approach is not limited to real Bethe roots.

quant-ph↗

arXiv2024

Deterministic Bethe state preparation

We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-1/2 XXZ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.

quant-ph↗

arXiv2024

Spin-s Dicke states and their preparation

We introduce the notion of $su(2)$ spin-$s$ Dicke states, which are higher-spin generalizations of usual (spin-1/2) Dicke states. These multi-qudit states can be expressed as superpositions of $su(2s+1)$ qudit Dicke states. They satisfy a recursion formula, which we use to formulate an efficient quantum circuit for their preparation, whose size scales as $sk(2sn-k)$, where $n$ is the number of qudits and $k$ is the number of times the total spin-lowering operator is applied to the highest-weight state. The algorithm is deterministic and does not require ancillary qudits.

quant-ph↗

arXiv2023

$q$-analog qudit Dicke states

Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their $d$-level generalization. We define here $q$-deformed qudit Dicke states using the quantum algebra $su_q(d)$. We show that these states can be compactly expressed as a weighted sum over permutations with $q$-factors involving the so-called inversion number, an important permutation statistic in Combinatorics. We use this result to compute the bipartite entanglement entropy of these states. We also discuss the preparation of these states on a quantum computer, and show that introducing a $q$-dependence does not change the circuit gate count.

quant-ph↗

arXiv2023

Qudit Dicke state preparation

Qudit Dicke states are higher-dimensional analogues of an important class of highly-entangled completely symmetric quantum states known as (qubit) Dicke states. A circuit for preparing arbitrary qudit Dicke states deterministically is formulated. An explicit decomposition of the circuit in terms of elementary gates is presented, and is implemented in cirq for the qubit and qutrit cases.

quant-ph↗