Related papers: On the extremal points of the $\Lambda$-polytopes …
Recently, a class of objects, known as $\Lambda$-polytopes, were introduced for classically simulating universal quantum computation with magic states. In $\Lambda$-simulation, the probabilistic update of $\Lambda$ vertices under Pauli…
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…
In this paper we investigate the extremal properties of the sum $$\sum_{i=1}^n|MA_i|^{\lambda},$$ where $A_i$ are vertices of a regular simplex, a cross-polytope (orthoplex) or a cube and $M$ varies on a sphere concentric to the sphere…
Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of…
Recent astonishing experiments with quantum computers have demonstrated unambiguously the existence of a quantum multiverse, where calculations of mind-boggling complexity are effortlessly computed in just a few minutes. Here, we…
We give a new algorithm for computing the robustness of magic - a measure of the utility of quantum states as a computational resource. Our work is motivated by the magic state model of fault-tolerant quantum computation. In this model, all…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. In this context, a `magic number' $m_{\varLambda}$ has the property that…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
The Fibonacci cube $\Gamma_n$ is obtained from the $n$-cube $Q_n$ by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube $\Lambda_n$ is obtained. The…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…
We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computation with single-qubit Pauli measurements. In our model, the…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…