Related papers: Quantum lower bound for inverting a permutation wi…
Let $L$ be a finite lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of given $L$ and $f,g \in \mathcal{E}(L)$, finding the greatest lower bound $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ in the…
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 consider the inverse optimization problem associated with the polynomial program f^*=\min \{f(x): x\in K\}$ and a given current feasible solution $y\in K$. We provide a systematic numerical scheme to compute an inverse optimal solution.…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
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…
Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many…
We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even…
We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We prove that the permutation computed by a reversible circuit with $\tilde{O}(nk\cdot \log(1/\varepsilon))$ random $3$-bit gates is $\varepsilon$-approximately $k$-wise independent. Our bound improves on currently known bounds in the…
We develop an operational approach for reconstructing the quantum theory of qubit systems from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is…
A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a…
We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first but, interestingly,…
The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained…
In his seminal work on recording quantum queries [Crypto 2019], Zhandry studied interactions between quantum query algorithms and the quantum oracle corresponding to random functions. Zhandry presented a framework for interpreting various…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
We consider quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semi-classical limit. We show that this reduction is caused by the fact that any elementary quantum…
Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…