Related papers: Generating the Kochen-Specker Sets with 36, 38 and…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets…
The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line,…
Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from various perspectives. We emphasise the many mathematical structures intimately related to Kochen-Specker proofs, ranging through functional analysis, sheaf…
In this work are presented sets of projectors for reconstruction of a density matrix for an arbitrary mixed state of a quantum system with the finite-dimensional Hilbert space. It was discussed earlier [quant-ph/0104126] a construction with…
The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
We nearly triple the number of logical qubits per physical qubit of surface codes in the teraquop regime by concatenating them into high-density parity check codes. These "yoked surface codes" are arrayed in a rectangular grid, with parity…
We define an extension of parity from the integers to the rational numbers. Three parity classes are found -- even, odd and `none'. Using the 2-adic valuation, we partition the rationals into subgroups with a rich algebraic structure. The…
The number of triangulations of a planar n point set is known to be $c^n$, where the base $c$ lies between $2.43$ and $30.$ The fastest known algorithm for counting triangulations of a planar n point set runs in $O^*(2^n)$ time. The fastest…
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…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
We investigate the generation of EPR pairs between three observers in a general causally structured setting, where communication occurs via a noisy quantum broadcast channel. The most general quantum codes for this setup take the form of…
We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We…
A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. We provide such an algorithm when k >= 3 for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
The Kochen-Specker Theorem is widely interpreted to imply that non-contextual hidden variable theories that agree with the predictions of Copenhagen quantum mechanics are impossible. The import of the theorem for a novel observer…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
Several types of nonclassical structures within the $N$-qubit Pauli group that can be seen as fundamental resources for quantum information processing are presented and discussed. Identity Products (IDs), structures fundamentally related to…
Using a recently introduced framework, we derive criteria for quantum k-separability, which are very easily computed. In the case k = 2, our criteria are equally strong to the best methods known so far, while in all other cases there are…