Related papers: Nonadaptive quantum query complexity
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
We consider the problem of inserting one item into a list of N-1 ordered items. We previously showed that no quantum algorithm could solve this problem in fewer than log N/(2 log log N) queries, for N large. We transform the problem into a…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
We show that, for almost all N-variable Boolean functions f, at least N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box model with bounded error.
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use…
Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…