Related papers: Quantum Search on Bounded-Error Inputs
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
The quantum search algorithm consists of an alternating sequence of selective inversions and diffusion type operations, as a result of which it can find a target state in an unsorted database of size N in only sqrt(N) queries. This paper…
We prove that, to compute a Boolean function $f$ on $N$ variables with error probability $\epsilon$, any quantum black-box algorithm has to query at least $\frac{1 - 2\sqrt{\epsilon}}{2} \rho_f N = \frac{1 - 2\sqrt{\epsilon}}{2} \bar{S}_f$…
The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well…
Amplitude estimation is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. The main drawback from the…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
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…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed…
We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…
Quantum algorithms can be analyzed in a query model to compute Boolean functions. Function input is provided in a black box, and the aim is to compute the function value using as few queries to the black box as possible. A repetition code…
Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
It's the key research topic of signal processing that recognizing genuine targets real time from the disturbed signal which has giant amount of data. A quantum algorithm for pattern recognition of classical signal which has time complexity…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this…
Quantum span program algorithms for function evaluation commonly have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these speed-ups persist even without…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…