7 citations · 22 across the 14 of their papers we have counts for
15 papers
Semi-Cliffordness of the Clifford hierarchy for a single qudit in composite dimensions
Yifei Qi, Rahul Sarkar
An important question in quantum information theory asks whether every gate in the Clifford hierarchy is semi-Clifford or not, as such gates admit resource-efficient implementation…
A finite arithmetic form of Robin's inequality and its equivalence to the Riemann hypothesis
Challenger Mishra, Rahul Sarkar
Robin's inequality reformulates the Riemann hypothesis as a bound on the sum-of-divisors function . We introduce a finite-truncation version of Robin's inequality determined int…
Constrained minimax approximation for quantum signal processing
Yulong Dong, James B. Larsen, Lin Lin +1
Quantum signal processing (QSP) provides a simple and efficient framework for implementing polynomial transformations using quantum circuits. Its classical design stage leads to a…
Quantum element-wise transforms
Zane M. Rossi, Rahul Sarkar
Quantum algorithms for basic numerical linear algebraic tasks have proven essential for translating diverse problems to a unified quantum computational context. Many of these tasks…
Overlapped groupings for quantum energy estimation: Maximal variance reduction and deterministic algorithms for reducing variance
Jeremiah Rowland, Rahul Sarkar, Nicolas PD Sawaya +2
Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups,…
Inverse nonlinear fast Fourier transform on SU(2) with applications to quantum signal processing
Hongkang Ni, Rahul Sarkar, Lexing Ying +1
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on has been widel…
Time-dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence
Di Fang, Diyi Liu, Rahul Sarkar
Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such…
Uniform Approximation of -Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations
Soumya Ganguly, Khoa Tran, Rahul Sarkar
For any subgroup of the symmetric group on symbols, we present results for the uniform approximation of -invariant functions by -invar…
Mathematical conjecture generation using machine intelligence
Challenger Mishra, Subhayan Roy Moulik, Rahul Sarkar
Conjectures have historically played an important role in the development of pure mathematics. We propose a systematic approach to finding abstract patterns in mathematical data, i…
The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
Rahul Sarkar, Theodore J. Yoder
Qudits with local dimension can have unique structure and uses that qubits () cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and…
An improvement to a result about graph isomorphism networks using the prime factorization theorem
Rahul Sarkar
The unique prime factorization theorem is used to show the existence of a function on a countable set so that the sum aggregator function is injective on all multiset…
Density theorems with applications in quantum signal processing
Rahul Sarkar, Theodore J. Yoder
We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain…
A graph-based formalism for surface codes and twists
Rahul Sarkar, Theodore J. Yoder
Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for const…
The Index of Invariance and its Implications for a Parameterized Least Squares Problem
Léopold Cambier, Rahul Sarkar
We study the problem , with , for a subspace of ($\mathbb{F} = \…
On sets of commuting and anticommuting Paulis
Rahul Sarkar, Ewout van den Berg
In this work we study the structure and cardinality of maximal sets of commuting and anticommuting Paulis in the setting of the abelian Pauli group. We provide necessary and suffic…