Related papers: Initialization Errors in Quantum Data Base Recall
We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations…
We use the mapping between two computation frameworks , Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover search algorithm into the AQC regime. We then apply Trotterization on the…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
Most quantum error correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $\ket{0}$, which can be used as ancilla qubits to prepare multi-qubit logical states. In this report, we examine the…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…
We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…
Quantifying the impact of individual data samples on machine learning models is an open research problem. This is particularly relevant when complex and high-dimensional relationships have to be learned from a limited sample of the data…
Catastrophic forgetting is a problem of neural networks that loses the information of the first task after training the second task. Here, we propose a method, i.e. incremental moment matching (IMM), to resolve this problem. IMM…
This article introduces an enhancement to the Grover search algorithm to speed up computing the probability of finding good states. It suggests incorporating a rotation phase angle determined mathematically from the derivative of the model…
The phenomenon of grokking in over-parameterized neural networks has garnered significant interest. It involves the neural network initially memorizing the training set with zero training error and near-random test error. Subsequent…
Quantum neural networks (QNNs) have been a promising framework in pursuing near-term quantum advantage in various fields, where many applications can be viewed as learning a quantum state that encodes useful data. As a quantum analog of…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
In conventional sparse representations based dictionary learning algorithms, initial dictionaries are generally assumed to be proper representatives of the system at hand. However, this may not be the case, especially in some systems…
Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…
Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a…
Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix…