Related papers: Exponential Separation Criteria for Quantum Iterat…

This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…

There has been much recent interest in near-term applications of quantum computers, i.e., using quantum circuits that have short decoherence times due to hardware limitations. Variational quantum algorithms (VQA), wherein an optimization…

Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue…

Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…

Quantum imaginary time evolution (QITE) is one of the promising candidates for finding eigenvalues and eigenstates of a Hamiltonian. However, the original QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary time…

The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point…

Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited…

Gradient ascent pulse engineering algorithm (GRAPE) is a typical method to solve quantum optimal control problems. However, it suffers from an exponential resource in computing the time evolution of quantum systems with the increasing…

Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…

Variational Quantum Algorithms (VQA) have emerged with a wide variety of applications. One question to ask is either they can efficiently be implemented and executed on existing architectures. Current hardware suffers from uncontrolled…

Quantum error correction offers a promising path to suppress errors in quantum processors, but the resources required to protect logical operations from noise, especially non-Clifford operations, pose a substantial challenge to achieve…

Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…

The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…

We introduce Exchange Quantum Polynomial Time (XQP) circuits, which comprise quantum computation using only computational basis SPAM and the isotropic Heisenberg exchange interaction. Structurally, this sub-universal model captures…

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error…

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…

Machine learning models can solve complex tasks but often require significant computational resources during inference. This has led to the development of various post-training computation reduction methods that tackle this issue in…