Related papers: Quantum conditional query complexity
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…