相关论文: A Lower Bound for Quantum Phase Estimation

We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and…

While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical…

In this work we investigate a binned version of Quantum Phase Estimation (QPE) set out by [Somma 2019] and known as the Quantum Eigenvalue Estimation Problem (QEEP). Specifically, we determine whether the circuit decomposition techniques we…

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…

Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…

We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the…

Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…

We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative…

We study the extremal Forrelation problem, where, provided with oracle access to Boolean functions $f$ and $g$ promised to satisfy either $\textrm{forr}(f,g)=1$ or $\textrm{forr}(f,g)=-1$, one must determine (with high probability) which of…

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We…

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 show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…

Quantum finite automata (QFAs) literature offers an alternative mathematical model for studying quantum systems with finite memory. As a superiority of quantum computing, QFAs have been shown exponentially more succinct on certain problems…

Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is…

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…

Quantum-limited estimation of an optical phase using adaptive (i.e. real-time feedback) techniques is reviewed. One case is explored in detail, as it can be understood using only elementary concepts such as photonic shot-noise and error…

In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a…

We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…

This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…