# Multiplication matrix vektor online dating

Swap test is a procedure that can determine the overlap of two quantum states, which is first introduced for quantum fingerprinting.

By entangling the tested system with an ancillary qubit, one can estimate the inner product of two different states by measuring the ancillary qubit repeatedly. 15, the authors proposed an algorithm for quantum machine learning based on swap test, which is exponentially faster than classical algorithm.

Matrix multiplication is to calculate W = UQ, where .

Here, we represent the two level degree of freedom by alphabet H and V, and the paths degree of freedom by numbers .

Our algorithm shows that hyperparallel quantum computation may provide a useful tool in quantum machine learning and “big data” analysis.).

However, quantum algorithm for matrix multiplication without previous knowledge about the results has not yet been presented.

Given the required accuracy, the steps of obtaining are independent to N. (4) are orthogonal to each other because they are in different stem paths k and k′.

With the assistance of hyperentangled states, the inner product of two vectors can be calculated with a time complexity independent of dimension N.

The key step of the algorithm is mapping the N-dimensional vectors to a log.

Those work show that swap test can play an important role for quantum algorithm.

The stem path of k(k′) with particular accuracy, we apply a series of operations on the space expanded by paths and two level degrees of freedom (see the method section for details), which transform the state |Ψ〉 towherewhere is a constant ensuring that the probability amplitudes of each paths will not exceed 1; and are the approximation of a) denote errors that are introduced by the oracles, which map the information of vectors to the states.

The errors satisfy , where m is the steps required for the oracle.