Related papers: Initialization Errors in Quantum Data Base Recall
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
We systematically study the localization effect in discrete-time quantum walks on a honeycomb network and establish the mathematical framework. We focus on the Grover walk first and rigorously derive the limit form of the walker's state,…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…
Existing approaches to quantum reservoir computing can be broadly categorized into restart-based and continuous protocols. Restart-based methods require reinitializing the quantum circuit for each time step, while continuous protocols use…
The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…
Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the ground-state energy of the +/-J Ising spin glass model on the…
Free recall of random lists of words is a standard paradigm used to probe human memory. We proposed an associative search process that can be reduced to a deterministic walk on random graphs defined by the structure of memory…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled…
The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
We address the fundamental task of converting $n$ uses of an unknown unitary transformation into a quantum state (i.e., storage) and later retrieval of the transformation. Specifically, we consider the case where the unknown unitary is…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
This work focuses on learning deep visual representation models for retrieval by exploring the interplay between a new loss function, the batch size, and a new regularization approach. Direct optimization, by gradient descent, of an…