Related papers: Asymptotically Optimal Quantum Amplitude Estimatio…
This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which…
We propose and analyze a simple framework for estimating the amplitudes of a given $n$-qubit quantum state $\ket{\psi} = \sum_{i=0}^{2^n-1} a_i \ket{i}$ in computational basis, utilizing a single-qubit measurement only. Previously, it was a…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…
Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…
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…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
It remains unclear whether quantum machine learning (QML) has real advantages when dealing with practical and meaningful tasks. Encoding classical data into quantum states is one of the key steps in QML. Amplitude encoding has been widely…
We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…
Quantum noise limits the sensitivity of interferometric measurements. It is generally admitted that it leads to an ultimate sensitivity, the ``standard quantum limit''. Using a semi-classical analysis of quantum noise, we show that a…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
How many T gates are needed to approximate an arbitrary $n$-qubit quantum state to within error $\varepsilon$? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is…
For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum…
This paper gives a survey about quantum estimation. We also describes the relation between the quantum central limit theorem and the asymptotic bound of mean square error in quantum state estimation.
How to achieve an arbitrary real-valued probability amplitude in the general single-partite or multipartite quantum system without measuring any other quantum state's probability amplitude? How to achieve an arbitrary real-valued…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…