8 citations · 26 across the 17 of their papers we have counts for
18 papers
Error-Transparent Code Switching Between Permutation-Invariant Codes with Transversal Clifford and Icosahedral Gates
Zachary P. Bradshaw
Code switching moves an encoded qubit between two codes whose transversal gates together are universal, but the switching operation itself is usually not transversal and can spread…
What is Smoothness?
Zachary P Bradshaw
Smoothness of a function on the real line is reflected in the decay of its Fourier transform, which suggests that smoothness of a function in for a group should mean c…
Inherent interpretability provides inherent value in quantum machine learning
Kaitlin Gili, Zachary P. Bradshaw
The field of quantum machine learning (QML) evolved to value models believed to most directly rival those providing utility in classical ML, namely large-scale neural networks. Thi…
Proof of a Conjectured Ramanujan Type Master Theorem for Powers of the Cosecant
Zachary P. Bradshaw
We prove a conjecture of Bradshaw and Atale asserting a Ramanujan type master theorem for the kernel , whose poles at the non-positive integers have order . The…
What Your Model Threw Away and Why You'll Want It Back: Masking, Fingerprinting, and Privacy from Discarded Geometry
Zachary P. Bradshaw
We develop a framework for the information discarded by machine learning models whose inputs carry a Lie group action. Given a representation of a Lie group on a space …
Approximate Error Correction for Quantum Simulations of SU(2) Lattice Gauge Theories
Zachary P. Bradshaw
We present a protocol for actively suppressing Gauss law violations in quantum simulations of SU(2) lattice gauge theory. Mid-circuit measurements extract a syndrome char…
Symmetry-Based Quantum Codes Beyond the Pauli Group
Zachary P. Bradshaw, Margarite L. LaBorde, Dillon Montero
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theore…
Introduction to Quantum Error Correction with Stabilizer Codes
Zachary P. Bradshaw, Jeffrey J. Dale, Ethan N. Evans
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest…
A Closed Form for Moment-Based Entanglement Tests Associated to the PPT Criterion
Zachary P. Bradshaw, Margarite L. LaBorde
Neven et al. have explored an unexpected alliance between the mathematical insights of Sir Isaac Newton and René Descartes which culminates in the reduction of the Positive Partial…
Learning Equivariant Maps with Variational Quantum Circuits
Zachary P. Bradshaw, Ethan N. Evans, Matthew Cook +1
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studi…
A Generalized Ramanujan Master Theorem and Integral Representation of Meromorphic Functions
Zachary P. Bradshaw, Omprakash Atale
Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin transforms which has wide applications in both mathematics and high energy physics. The unconventional m…
Berndt-type Integrals: Unveiling Connections with Barnes Zeta and Jacobi Elliptic Functions
Zachary P. Bradshaw, Christophe Vignat
We address a class of definite integrals known as Berndt-type integrals, highlighting their role as specialized instances within the integral representation framework of the Barnes…
Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attention
Ethan N. Evans, Matthew Cook, Zachary P. Bradshaw +1
The recent exploding growth in size of state-of-the-art machine learning models highlights a well-known issue where exponential parameter growth, which has grown to trillions as in…
Quantum Entanglement & Purity Testing: A Graph Zeta Function Perspective
Zachary P. Bradshaw, Margarite L. LaBorde
We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of t…
Dubious Identities: A Visit to the Borwein Zoo
Zachary P. Bradshaw, Christophe Vignat
We contribute to the zoo of dubious identities established by J.M. and P.B. Borwein in their 1992 paper, "Strange Series and High Precision Fraud" with five new entries, each of a…
Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties
Erin T. Albertin, Zachary P. Bradshaw, Kaitlyn M. Kirt +2
The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a genera…
An Operational Calculus Generalization of Ramanujan's Master Theorem
Zachary P. Bradshaw, Christophe Vignat
We give a formal extension of Ramanujan's master theorem using operational methods. The resulting identity transforms the computation of a product of integrals on the half-line to…
Cycle Index Polynomials and Generalized Quantum Separability Tests
Zachary P. Bradshaw, Margarite L. LaBorde, Mark M. Wilde
The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedne…