相关论文: Quantum Boolean Summation with Repetitions in the …

Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…

This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…

This paper proposes a quantum circuit for computing the mean value from a given set of quantum states. The circuit consults a Quantum Random Access Memory to get the values of the set, and by using superposition, interference and…

In 1998, Brassard, Hoyer, Mosca, and Tapp (BHMT) gave a quantum algorithm for approximate counting. Given a list of $N$ items, $K$ of them marked, their algorithm estimates $K$ to within relative error $\varepsilon$ by making only $O\left(…

The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…

In this work, we provide the first QFT-free algorithm for Quantum Amplitude Estimation (QAE) that is asymptotically optimal while maintaining the leading numerical performance. QAE algorithms appear as a subroutine in many applications for…

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…

Quantum computing offers the potential of exponential speedups for certain classical computations. Over the last decade, many quantum machine learning (QML) algorithms have been proposed as candidates for such exponential improvements.…

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.…

The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]] quantum code, together with a fault-tolerant syndrome extraction by means of several ancilla states, have been numerically studied. A simple probability expression to…

Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of…

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…

In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely…

Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…

We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…

Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…

The quantum approximate optimization algorithm (QAOA) is widely seen as a possible usage of noisy intermediate-scale quantum (NISQ) devices. We analyze the algorithm as a bang-bang protocol with fixed total time and a randomized greedy…

The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger…

Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…

Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…