Related papers: No invariant perfect qubit codes
The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward…
This dissertation explores quantum computation using qudits encoded into large spins, emphasizing the concept of quantum co-design to harness the unique capabilities of physical platforms for enhanced quantum information processing. First,…
Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet…
The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…
In this paper, considering the linearized Einstein equation with a two-parameter family of linear covariant gauges in de Sitter spacetime, we examine possible vacuum states for the gravitons field with respect to invariance under the de…
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence…
In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis…
Qubits encoded in a decoherence-free subsystem and realized in exchange-coupled silicon quantum dots are promising candidates for fault-tolerant quantum computing. Benefits of this approach include excellent coherence, low control…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real…
The main goal of the paper is to establish the existence of tensor product decompositions for those prime ideals P of the generic algebra A of quantum n by n matrices which are invariant under winding automorphisms of A. More specifically,…
We revisit the question of universality in quantum computing and propose a new paradigm. Instead of forcing a physical system to enact a predetermined set of universal gates (e.g., single-qubit operations and CNOT), we focus on the…
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum…
Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass…
The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial…
We examine the complementarity among coherence (visibility), predictability, and entanglement for qubit and qutrit systems subjected to noisy quantum channels. Using the system-path entanglement framework, analytical expressions for all…
By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit…
In the standard construction of Quantum Field Theory, a vacuum state is required. The vacuum is a vector in a separable, infinite-dimensional Hilbert space often referred to as Fock space. By definition the vacuum wavestate depends on…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…
We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The…