Related papers: Fourier 1-norm and quantum speed-up

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…

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…

In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…

Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general…

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…

Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…

Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems…

Quantum optimisation is emerging as a promising approach alongside classical heuristics and specialised hardware, yet its performance is often difficult to assess fairly. Traditional benchmarking methods, rooted in digital complexity…

Quantum processors are now able to run quantum circuits that are infeasible to simulate classically, creating a need for benchmarks that assess a quantum processor's rate of errors when running these circuits. Here, we introduce a general…

Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…

Shor's factoring algorithm provides a super-polynomial speed-up over all known classical factoring algorithms. Here, we address the question of which quantum properties fuel this advantage. We investigate a sequential variant of Shor's…

Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…

The new model of quantum computation is proposed, for which an effective algorithm of solving any task in NP is described. The work is based and inspired be the Grover's algorithm for solving NP-tasks with quadratic speedup compared to the…

One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…

We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…

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…

For the last few decades, classical machine learning has allowed us to improve the lives of many through automation, natural language processing, predictive analytics and much more. However, a major concern is the fact that we're fast…

Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. Here we introduce Decoded Quantum Interferometry (DQI), a quantum algorithm that uses the quantum Fourier transform to reduce…