Related papers: Effects of Cosine Tapering Window on Quantum Phase…
Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…
We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…
While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several…
We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well-studied and effectively used in single-phase estimations, their usage in multiphase situations has…
We present a framework for upper bounding the number of iterations required by first-order optimization algorithms implementing constrained LQR controllers. We derive new bounds for the condition number and extremal eigenvalues of the…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
Quantum policy evaluation (QPE) is a reinforcement learning (RL) algorithm which is quadratically more efficient than an analogous classical Monte Carlo estimation. It makes use of a direct quantum mechanical realization of a finite Markov…
Quantum computer is extensively used in solving financial problems. Quantum amplitude estimation, an algorithm that aims to estimate the amplitude of a given quantum state, can be utilized to determine the expectation value of bonds as the…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
Forecasting, to estimate future events, is crucial for business and decision-making. This paper proposes QxEAI, a methodology that produces a probabilistic forecast that utilizes a quantum-like evolutionary algorithm based on training a…
In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting…
We present several improvements to the recently developed ground state preparation algorithm based on the Quantum Eigenvalue Transformation for Unitary Matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed.…
Estimating the ground state energy of a multiparticle system with relative error $\e$ using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state…
Quantum error correction (QEC) and fault-tolerant (FT) mechanisms are essential for reliable quantum computing. However, QEC considerably increases the computation size up to four orders of magnitude. Moreover, FT implementation has…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…