arXiv subjects

Joshua Nevin

Publications and source records attributed to Joshua Nevin.

8 recordsLinked to original sources

arXiv2025

Noise-Robustness for Delegated Quantum Computation in the Circuit Model

Cloud-based quantum computing, coupled with the rapid progress in quantum algorithms, brings to the forefront the question of verifiability in delegated quantum computations. In the current landscape of noisy quantum devices, this question must be addressed alongside noise tolerance. In this work, we revisit the circuit-based framework for verifiable quantum computation introduced by Broadbent [Theory of Computing, 2018], and extend it to the setting of server-side noise. Our contribution is an improved upper bound on the noise-tolerance threshold, achieved through a protocol that interleaves computation and test rounds in an indistinguishable manner. This structure enables a concise security proof against arbitrary deviations by the server, while ensuring robustness to realistic noise.

quant-ph↗

arXiv2025

Exact Non-Identity Check and Gate-Teleportation-Based Indistinguishability Obfuscation are NP-hard for Low-T-Depth Quantum Circuits

In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where the limiting factor in the efficiency of the protocol is the difficulty, on input a quantum circuit $C$, of the classical task of producing a description of the unitary obtained by conjugating a Pauli $P$ (corresponding to a Bell-measurement outcome) by $C$, where this description only depends on the input-output functionality of $CPC^{\dagger}$. The task above, in turn, is at least as hard as the problem of determining whether two $n$-qubit quantum circuits are perfectly equivalent up to global phase. In 2009, Tanaka defined the corresponding decision problem Exact Non-Identity Check (ENIC) and showed that ENIC is NQP-complete in general. Motivated by this, we consider in this work what happens when we pass from low T-count to low T-depth. In particular, we show that, for Clifford+T circuits of T-depth $O(\log(n))$, deciding ENIC is NP-hard. This effectively rules out the possibility, for Clifford+T circuits of logarithmic T-depth, of either efficient ENIC or efficient gate-teleportation based computational indistinguishability obfuscation, unless P=NP.

quant-ph↗

arXiv2022

Distant 2-Colored Components on Embeddings Part III: The General Case

This is the third in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is at least $2^{\Omega(g)}$ and the precolored components are of distance at least $2^{\Omega(g)}$ apart. This provides an affirmative answer to a generalized version of a conjecture of Thomassen and also generalizes a result from 2017 of Dvo\v{r}\'ak, Lidick\'y, Mohar, and Postle about distant precolored vertices. In a previous paper, we proved that the above result holds for a restricted class of embeddings which have no separating cycles of length three or four. In this paper, we use this special case to prove that the result holds in the general case.

math.CO↗

arXiv2022

Distant 2-Colored Components on Embeddings Part II: The Short-Inseparable Case

This is the second in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is at least $2^{\Omega(g)}$ and the precolored components are of distance at least $2^{\Omega(g)}$ apart. This provides an affirmative answer to a generalized version of a conjecture of Thomassen and also generalizes a result from 2017 of Dvo\v{r}\'ak, Lidick\'y, Mohar, and Postle about distant precolored vertices. In this paper we prove that the above result holds for a restricted class of embeddings, i.e. those embeddings which satisfy certain triangulation conditions and do not have separating cycles of length at most four.

math.CO↗

arXiv2022

Some Extensions of Thomassen's Theorem to Longer Paths

Let $G$ be a planar embedding with list-assignment $L$ and outer cycle $C$, and let $P$ be a path of length at most four on $C$, where each vertex of $G\setminus C$ has a list of size at least five and each vertex of $C\setminus P$ has a list of size at least three. In this paper, we prove some results about partial $L$-colorings $\phi$ of $C$ with the property that any extension of $\phi$ to an $L$-coloring of $\textrm{dom}(\phi)\cup V(P)$ extends to $L$-color all of $G$. We use these results in a later sequence of papers to prove some results about list-colorings of high-representativity embeddings on surfaces.

math.CO↗

arXiv2022

Extensions of Thomassen's Theorem to Paths of Length At Most Four: Part II

Let $G$ be a planar embedding with list-assignment $L$ and outer cycle $C$, and let $P$ be a path of length at most four on $C$, where each vertex of $G\setminus C$ has a list of size at least five and each vertex of $C\setminus P$ has a list of size at least three. This is the second paper in a sequence of three papers in which we prove some results about partial $L$-colorings $\phi$ of $C$ with the property that any extension of $\phi$ to an $L$-coloring of $\textrm{dom}(\phi)\cup V(P)$ extends to $L$-color all of $G$, and, in particular, some useful results about the special case in which $\textrm{dom}(\phi)$ consists only of the endpoints of $P$. We also prove some results about the other special case in which $\phi$ is allowed to color some vertices of $C\setminus\mathring{P}$ but we avoid taking too many colors away from the leftover vertices of $\mathring{P}\setminus\textrm{dom}(\phi)$. We use these results in a later sequence of papers to prove some results about list-colorings of high-representativity embeddings on surfaces.

math.CO↗

arXiv2022

Extensions of Thomassen's Theorem to Paths of Length At Most Four: Part III

Let $G$ be a planar embedding with list-assignment $L$ and outer cycle $C$, and let $P$ be a path of length at most four on $C$, where each vertex of $G\setminus C$ has a list of size at least five and each vertex of $C\setminus P$ has a list of size at least three. This is the final paper in a sequence of three papers in which we prove some results about partial $L$-colorings $\phi$ of $C$ with the property that any extension of $\phi$ to an $L$-coloring of $\textrm{dom}(\phi)\cup V(P)$ extends to $L$-color all of $G$, and, in particular, some useful results about the special case in which $\textrm{dom}(\phi)$ consists only of the endpoints of $P$. We also prove some results about the other special case in which $\phi$ is allowed to color some vertices of $C\setminus\mathring{P}$ but we avoid taking too many colors away from the leftover vertices of $\mathring{P}\setminus\textrm{dom}(\phi)$. We use these results in a later sequence of papers to prove some results about list-colorings of high-representativity embeddings on surfaces.

math.CO↗

arXiv2022

Distant 2-Colored Components on Embeddings Part I: Connecting Faces

This is the first in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is $2^{\Omega(g)}$ and the precolored components are of distance $2^{\Omega(g)}$ apart. This provides an affirmative answer to a generalized version of a conjecture of Thomassen and also generalizes a result from 2017 of Dvo\v{r}\'ak, Lidick\'y, Mohar, and Postle about distant precolored vertices.

math.CO↗