Related papers: Detailed Error Analysis of the HHL Algorithm
Quantum machine learning (QML) algorithms have demonstrated early promise across hardware platforms, but remain difficult to interpret due to the inherent opacity of quantum state evolution. Widely used classical interpretability methods,…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits.…
The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are precise means of characterizing analog quantum…
The learning process for multi layered neural networks with many nodes makes heavy demands on computational resources. In some neural network models, the learning formulas, such as the Widrow-Hoff formula, do not change the eigenvectors of…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
We discuss a surprisingly simple scheme for accounting (and removal) of error in observables determined from quantum algorithms. A correction to the value of the observable is calculated by first measuring the observable with all error…
In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the…
For the first time quaternions have been used for real-time frequency estimation, where the multi-dimensional nature of quaternions allows for the full characterization of three-phase power systems. This is achieved through the use of…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…
Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d \tau$ in terms of an algorithmic time step $\dt$. By studying the accumulative multi-step error…