Consider a qubit \(|\Psi\rangle=\alpha|0\rangle+\beta|1\rangle\) that we are transmitting using a quantum channel, where during transmission \(|\Psi\rangle\) can be flipped giving \(X|\Psi\rangle=\beta|0\rangle+\alpha|1\rangle\) with probability \(p\). This type of channel is called a bit-flip channel. If this bit-flip is not intended, then the three-qubit flip code can protect against such single bit flip. The three-qubit flip... read more
A quantum convolutional neural network combines two key techniques: multi-scale entanglement renormalization ansatz MERA, which is a variational ansatz for many-body wavefunctions, and nested quantum error correction QEC, which detects and corrects local quantum errors without collapsing the wavefunction. We will explore these two components, MERA and QEC, in detail. Next, we will look... read more
Quantum Principal Component Analysis identifies large eigenvalues of unknown density matrices utilizing corresponding eigenvectors in \(O(\log d)\). Where principal component analysis analyzes positive semi-definite Hermitian matrices by decomposing eigenvectors in relation to the largest eigenvalues in the matrix for dimensionality reduction. Improved computational complexity will hopefully allow new methods for... read more
Using quantum computing, the authors exploit quantum mechanics for the algorithmic complexity optimization of a Support Vector Machine with high-dimensional feature space. Where the high-dimensional classical data is mapped non-linearly to Hilbert Space and a hyperplane in quantum space is used to separate and label the data. By using the... read more
In biological intelliegent systems there are multiple mechanisms working in congruence on multiple levels, both at the structural and neurobiological level to develop complex cognitive abilities. What remains unknown is which mechanisms are necessary and sufficent to synthetically replicate these cognitive abilities for artificial intelligence. A neurocomputational model is offered... read more
Quantum Computing Theory is a field of computer science that uses the principles of quantum mechanics, mathematics, and computer science. By borrowing concepts from each field scientists can rigorously define both a broad and narrow theoretical model of a quantum computer and later apply it to the real world. These... read more
A deterministic finite automaton (DFA) is a 5-tuple: \((Q, \Sigma, \delta, q_{0}, F)\) where: \(Q\) is a finite set of states \(\Sigma\) is an alphabet \(\delta\) is a transition function described as \(\delta : Q \times \Sigma \rightarrow Q\) \(q_{0} \in Q\) is the initial state \(F \subseteq Q\) is a... read more
Algorithmic analysis is used to help computer scientists understand the resources required by an algorithm for time, storage, and other uses. Algorithmic anlysis must analyze algorithms in a methodical, universal, and fair way. To do this computer scientist implement mathematical models that describe the resources used by algorithms. This work... read more