相关论文: Quantum lower bounds by quantum arguments

The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find…

We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…

The (negative-weighted) quantum adversary bound is a tight characterisation of the quantum query complexity for any partial function. We analyse the extent to which this bound can be generalised. Ambainis et al. [arXiv:1012.2112] and Lee et…

We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…

Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…

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…

We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…

We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and…

We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler (2020). The task is to distinguish whether an input set $x\subseteq [n]$ has size either $k$ or…

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 prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…

We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…

We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…

We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…

We prove tight $\Omega(n^{1/3})$ lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method.…

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…

The polynomial and the adversary methods are the two main tools for proving lower bounds on query complexity of quantum algorithms. Both methods have found a large number of applications, some problems more suitable for one method, some for…

In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…

In this note, we show that quantum lower bounds obtained using the adversary method hold in the Hamiltonian oracle model.

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…