Related papers: An Explicit Construction of Quantum Expanders
We generalize the zig-zag product construction to produce infinite families of regular graphs of any constant degree. We analyze the second largest eigenvalue of this new zig-zag product to show that the modified zig-zag product of good…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
Quantum channels can describe all transformations allowed by quantum mechanics. We provide an explicit universal protocol to construct all possible quantum channels, using a single qubit ancilla with quantum non-demolition readout and…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
We introduce a general notion of quantum universal enveloping algebroids (QUE algebroids), or quantum groupoids, as a unification of quantum groups and star-products. Some basic properties are studied including the twist construction and…
Quantum computing is a growing field with significant potential applications. Learning how to code quantum programs means understanding how qubits work and learning to use quantum gates. This is analogous to creating classical algorithms…
We present qcor - a language extension to C++ and compiler implementation that enables heterogeneous quantum-classical programming, compilation, and execution in a single-source context. Our work provides a first-of-its-kind C++ compiler…
We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we show that the Postnikov tower of a simplicial commutative…
An original presentation of Categorical Quantum Physics, in the line of Abramsky and Coecke, tries to introduce only objects and assumptions that are clearly relevant to Physics and does not assume compact closure. Adjoint arrows, tensor…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit…
We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of…
In this work, quantum transformers are designed and analysed in detail by extending the state-of-the-art classical transformer neural network architectures known to be very performant in natural language processing and image analysis.…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of certain half-integral weight modular forms. These served as early prototypes of a…
The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of $\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its input. T.…