Related papers: Quantum Lower Bound for Approximate Counting Via L…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates,…
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.
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
We study the quantum summation QS algorithm of Brassard, Hoyer, Mosca and Tapp, which approximates the arithmetic mean of a Boolean function defined on $N$ elements. We present sharp error bounds of the QS algorithm in the worst-average…
The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon…
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
Using higher-order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
We study the problem of estimating the size of the maximum matching in the sublinear-time setting. This problem has been extensively studied, with several known upper and lower bounds. A notable result by Behnezhad (FOCS 2021) established a…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
In order to assess whether quantum resources can provide an advantage over classical computation, it is necessary to characterize and benchmark the non-classical properties of quantum algorithms in a practical manner. In this paper, we show…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
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 achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly…