Related papers: Iterative Quantum Amplitude Estimation
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…
In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA)…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
We present a scalable formal verification methodology for Quantum Phase Estimation (QPE) circuits. Our approach uses a symbolic qubit abstraction based on quantifier-free bit-vector logic, capturing key quantum phenomena, including…
We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that…
Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can…
The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum…
Quantum phase estimation (QPE) is a central algorithmic primitive that estimates eigenvalues of a Hamiltonian up to precision $\epsilon$ in Heisenberg-limited time $T=\Theta(1/\epsilon)$. Standard gate-based implementations of QPE require…
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 consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize…
We discuss the implementation of an iterative quantum phase estimation algorithm, with a single ancillary qubit. We suggest using this algorithm as a benchmark for multi-qubit implementations. Furthermore we describe in detail the smallest…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
Recent advances in quantum computing systems attract tremendous attention. Commercial companies, such as IBM, Amazon, and IonQ, have started to provide access to noisy intermediate-scale quantum computers. Researchers and entrepreneurs…
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…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard…
There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing…
We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation. In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically…
We generalize the Approximate Quantum Compiling algorithm into a new method for CNOT-depth reduction, which is apt to process wide target quantum circuits. Combining this method with state-of-the-art techniques for error mitigation and…