Related papers: Quantum computation and real multiplication
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
We give a realization of the quantum affine Lie algebras $\uqa$ and $\uqc$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being related to the statistical parameter…
Universal set of quantum gates are realized from the conduction-band electron spin qubits of quantum dots embedded in a microcavity via two-channel Raman interaction. All of the gate operations are independent of the cavity mode states,…
We construct a topos of quantum sets and embed into it the classical topos of sets. We show that the internal logic of the topos of sets, when interpreted in the topos of quantum sets, provides the Birkhoff-von Neumann quantum propositional…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The pursuit of quantum advantage in simulating many-body quantum systems on quantum computers has gained momentum with advancements in quantum hardware. This work focuses on leveraging the symmetry properties of these systems, particularly…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. We introduce several algorithmic improvements for…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…