Related papers: Limits of quantum speed-ups for computational geom…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
Quantum optimization algorithms promise advantages for difficult problems but are costly to simulate and analyze on classical machines. Recently, constrained quantum optimization has been investigated through the lens of Quantum Zeno…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
With the help of recent developments in quantum algorithms for semidefinite programming, we discuss the possibility for quantum speedup for the numerical conformal bootstrap in conformal field theory. We show that quantum algorithms may…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…
Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
We revisit the classical problem of determining the largest copy of a simple polygon $P$ that can be placed into a simple polygon $Q$. Despite significant effort, known algorithms require high polynomial running times. (Barequet and…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We present a multi-step quantum algorithm for solving the $3$-bit exact cover problem, which is one of the NP-complete problems. Unlike the brute force methods have been tried before, in this algorithm, we showed that by applying the…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…
We discuss the problem of finite-horizon dynamic programming (DP) on a quantum computer. We introduce a query model for studying quantum and classical algorithms for solving DP problems, and provide example oracle constructions for the…
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most…
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…