arXiv subjects

Sahar Atallah

Publications and source records attributed to Sahar Atallah.

3 recordsLinked to original sources

arXiv2026

Cylindrical Matter: A beyond-quantum many-body system for efficient classical simulation of quantum pure-Ising like systems

Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum descriptions of many-body systems. We explore this question in the context of quantum interactions that are diagonal in the computational basis. We construct a hypothetical model of a continuous time dynamical many-body system that is based upon lattices of interacting particles called "cylindrical bits", a concept first introduced in [6]. In the language of [5] our toy model is {\it non-free}, as we need spatial constraints on how the particles interact to ensure valid probabilities. We investigate these constraints and explore the resulting `entangled' states that can exist. Certain pure {\it quantum} entangled systems can be faithfully mimicked by our cylindrical worlds. This allows us to simulate efficiently classically, in the sense of sampling measurement outcomes, a variety of previously unknown quantum systems. Examples include some states created by pure Ising interactions algebraically decaying faster than $\sim 1/r^{3D/2}$, with spatial dimension $D$, under measurements in the $Z$ eigenbasis or eigenbases of $aX+bY$ for $a,b \in \mathbb{R}$. We also explore whether another choice of non-quantum `particle' could expand the applicability of the classical simulation by defining and partially optimising a figure-of-merit that attempts to capture how useful various possibilities may be.

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arXiv2024

Efficient classical simulation of cluster state quantum circuits with alternative inputs

We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch sphere, $CZ$ gates are applied, and finally the qubits are measured adaptively using $Z$ measurements or measurements of $\cos(θ)X + \sin(θ)Y$ operators. We consider what happens when the initialisation step is modified, and show that for lattices of finite degree $D$, there is a constant $λ\approx 2.06$ such that if the qubits are prepared in a state that is within $λ^{-D}$ in trace distance of a state that is diagonal in the computational basis, then the system can be efficiently simulated classically in the sense of sampling from the output distribution within a desired total variation distance. In the square lattice with $D=4$ for instance, $λ^{-D} \approx 0.056$. We develop a coarse grained version of the argument which increases the size of the classically efficient region. In the case of the square lattice of qubits, the size of the classically simulatable region increases in size to at least around $\approx 0.070$, and in fact probably increases to around $\approx 0.1$. The results generalise to a broader family of systems, including qudit systems where the interaction is diagonal in the computational basis and the measurements are either in the computational basis or unbiased to it. Potential readers who only want the short version can get much of the intuition from figures 1 to 3.

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arXiv2023

Classically efficient regimes in measurement based quantum computation performed using diagonal two qubit gates and cluster measurements

In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit undergoes at most $D$ diagonal gates, (iii) each qudit is destructively measured in the computational basis or bases unbiased to it, and (iv) each qudit is initialised within $\lambda^{-D}$ of a diagonal state according to a particular distance measure. In this work we explicitly compute $\lambda$ for any two qubit diagonal gate, thereby extending the computation of arXiv:2201.07655v2 beyond CZ gates. For any finite degree graph this allows us to describe a two parameter family of pure entangled quantum states (or three parameter family of thermal states) which have a non-trivial classically efficiently simulatable "phase" for the permitted measurements, even though other values of the parameters may enable ideal cluster state quantum computation. The main the technical tool involves considering separability in terms of "cylindrical" sets of operators. We also consider whether a different choice of set can strengthen the algorithm, and prove that they are optimal among a broad class of sets, but also show numerically that outside this class there are choices that can increase the size of the classically efficient regime.

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