Related papers: No invariant perfect qubit codes
Crosstalk is a key obstacle to scaling up quantum computers. It may arise from persistent qubit-qubit couplings or dynamically during gate operation, with the latter being particularly difficult to detect. Here, we introduce the perfect…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical…
The equivalence between absolutely separable states and absolutely positive partial transposed (PPT) states in general remains an open problem in quantum entanglement theory. In this work, we study an analogous question for symmetric…
The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of…
We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two…
By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of…
Traditional ionic/covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum hall effect systems, do not typically display…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon entropy of the vector of singular values…
In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al. proposed a sufficient condition detecting the genuinely entangled pure states. In this paper, we indicate that generally, the coefficient vector of a pure product…
The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Remark.9 in Bose-Dasgupta-Rubin (2002) review states that when a non-negative integer-valued infinitely divisible law has an atom at unity then its support cannot have any gaps. Here one has two questions. (i) Why there are no gaps and (ii)…
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families…
In this work, we uncover a collection of non invertible topological operators linked to the 0-, 2-, 4- and 6-form symmetries related to the type IIB superstring effective theory. By pinpointing the $\text{SL}(2,\mathbb{Z})$-covariant…
The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of…
The concept of positively and negatively compatible null vectors arises in the study of Clifford geometric algebras with a Lorentz-Minkowski metric. In previous works, the basic properties of such algebras have been set down in terms of a…
Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal…
This paper explores text classification on quantum computers. Previous results have achieved perfect accuracy on an artificial dataset of 100 short sentences, but at the unscalable cost of using a qubit for each word. This paper…