Related papers: MacWilliams Identities for Intrinsic Quantum Codes
The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…
The social worker scheduling problem is a class of combinatorial optimization problems that combines scheduling with routing issues. These types of problems with classical computing can only be solved, in the best of cases, in an…
We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…
Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Given some group $G$ of logical gates, for instance the Clifford group, what are the quantum encodings for which these logical gates can be implemented by simple physical operations, described by some physical representation of $G$? We…
We define the unique (up to normalization) symbol map from the space of linear differential operators on $R^n$ to the space of polynomial on fibers functions on $T^* R^n$, equivariant with respect to the Lie algebra of projective…
We present a multi-level quantum-classical intermediate representation (IR) that enables an optimizing, retargetable, ahead-of-time compiler for available quantum programming languages. To demonstrate our architecture, we leverage our…
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity.…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
We present a quantum compiler framework that bridges the gap between physics modeling and quantum software development. At the core of this framework is a versatile quantum circuit synthesizer capable of decomposing arbitrary Hamiltonians…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…
We obtain local unitary invariant polynomials for N qubit quantum state from first principles. A basic unit of entanglement, referred to as negativity font, is defined as a two by two matrix of probability amplitudes that determines the…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…