Srinivasan Arunachalam

activity

20232026

collaborators

16 papers

quant-ph2026

Learning Random Quantum Circuits and the Emergence of Pseudorandomness

Srinivasan Arunachalam, Qizhao Huang, Makrand Sinha

We give an efficient algorithm for learning $k$ -dimensional brickwork random quantum circuits using only copies of the output state obtained by applying $U$ to the all-zero input.…

cs.CC2026

Marton's conjecture in polynomial time

Srinivasan Arunachalam, Arkopal Dutt, Sabee Grewal +1

Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampl…

quant-ph2026

Separating quantum circuits from classical LLMs

Srinivasan Arunachalam, Arkopal Dutt, Hari Krovi +1

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional sepa…

quant-ph2026

No low-degree tests for quantum states

Omar Alrabiah, Srinivasan Arunachalam, Sabee Grewal +1

We study the problem of testing low-degree phase states, namely m-qudit quantum states of the form $q^{- m /2} \sum_{x \in F_{q}^{m}} ω^{f (x)} ∣ x >$ , where $f$ is a degree- $d$ po…

quant-ph2026

Optimal Stabilizer Testing and Learning with Limited Quantum Memory

Srinivasan Arunachalam, Louis Schatzki

We study stabilizer state testing and learning with limited coherent quantum memory. Here an algorithm sequentially receives copies of an unknown $n$ -qubit state, but may keep only…

quant-ph2026

Tomography of quantum states with bounded extent

Srinivasan Arunachalam, Arkopal Dutt

We give a general framework for tomography of states that have bounded-extent with respect to a structured class of states. Let $C$ be a family of $n$ -qubit states such th…

math.CO2026

An algorithmic Polynomial Freiman-Ruzsa theorem

Davi Castro-Silva, Jop Briët, Srinivasan Arunachalam +2

We provide algorithmic versions of the Polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Ann. of Math., 2025). In particular, we give a polynomial-time algorithm…

quant-ph2025

Learning stabilizer structure of quantum states

Srinivasan Arunachalam, Arkopal Dutt

We consider the task of learning a structured stabilizer decomposition of an arbitrary $n$ -qubit quantum state $∣ ψ ⟩$ : for $ε > 0$ , output a state $∣ ϕ ⟩$ with stabilizer-r…

math.CO2025

Algorithmic Polynomial Freiman-Ruzsa Theorems

Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt +1

We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we…

quant-ph2025

Learning depth-3 circuits via quantum agnostic boosting

Srinivasan Arunachalam, Arkopal Dutt, Alexandru Gheorghiu +1

We initiate the study of quantum agnostic learning of phase states with respect to a function class $C \subseteq {c : {0, 1}^{n} \to {0, 1}}$ : given copies of an unk…

quant-ph2024

Testing and learning structured quantum Hamiltonians

Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez

We consider the problems of testing and learning an unknown $n$ -qubit Hamiltonian $H$ from queries to its evolution operator $e^{- i H t}$ under the normalized Frobenius norm. We prov…

quant-ph2024

A note on polynomial-time tolerant testing stabilizer states

Srinivasan Arunachalam, Sergey Bravyi, Arkopal Dutt

We show an improved inverse theorem for the Gowers- $3$ norm of $n$ -qubit quantum states $∣ ψ ⟩$ which states that: for every $γ \geq 0$ , if the $\textsf{Gowers}(|ψ\rangle,3)^8 \…

quant-ph2024

Distributed inner product estimation with limited quantum communication

Srinivasan Arunachalam, Louis Schatzki

We consider the task of distributed inner product estimation when allowed limited quantum communication. Here, Alice and Bob are given $k$ copies of an unknown $n$ -qubit quantum st…

quant-ph2024

Polynomial-time tolerant testing stabilizer states

Srinivasan Arunachalam, Arkopal Dutt

We consider the following task: suppose an algorithm is given copies of an unknown $n$ -qubit quantum state $∣ ψ ⟩$ promised $(i)$ $∣ ψ ⟩$ is $ε_{1}$ -close to a stab…

quant-ph2024

Learning low-degree quantum objects

Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez +1

We consider the problem of learning low-degree quantum objects up to $ε$ -error in $ℓ_{2}$ -distance. We show the following results: $(i)$ unknown $n$ -qubit degree- $d$ (in…

quant-ph2023

One Clean Qubit Suffices for Quantum Communication Advantage

Srinivasan Arunachalam, Uma Girish, Noam Lifshitz

We study the one-clean-qubit model of quantum communication where one qubit is in a pure state and all other qubits are maximally mixed. We demonstrate a partial function that has…