Related papers: Reducing quantum resources for observable estimati…
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…
Quantum computers are expected to perform the full-configuration interaction calculations with less computational resources compared to classical ones, thanks to the use of the quantum phase estimation (QPE) algorithms. However, only a…
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown…
We propose an analysis of the Quantum Phase Estimation (QPE) algorithm applied to many-electron systems by investigating its free parameters such as the time step, number of phase qubits, initial state preparation, number of measurement…
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…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
We introduce Quantum Functional Information (QFI), a new metric to quantify the rarity and utility of quantum states and circuits. Unlike standard measures such as fidelity or entropy, QFI captures the balance between functionality and…
Recent efforts in smart manufacturing have enhanced aerospace fuselage assembly processes, particularly by innovating shape adjustment techniques to minimize dimensional gaps between assembled sections. Existing approaches have shown…
The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
Windowed arithmetic [Gidney, 2019] is a technique for reducing the cost of quantum arithmetic circuits with space--time tradeoffs using memory queries to precomputed tables. It can reduce the asymptotic cost of modular exponentiation from…
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\varphi$ whose generator is randomly sampled according to a…
Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects…
Eigenvalue estimation is a central problem for demonstrating quantum advantage, yet its implementation on digital quantum computers remains limited by circuit depth and operational overhead. We present an analog quantum phase estimation…
We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…
Quantum Amplitude Estimation (QAE) -- a technique by which the amplitude of a given quantum state can be estimated with quadratically fewer queries than by standard sampling -- is a key sub-routine in several important quantum algorithms,…
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…
This paper addresses the challenge of integrating sequentially arriving data within the quantile regression framework, where the number of features is allowed to grow with the number of observations, the horizon is unknown, and memory is…
We put forward a strategy to encode a quantum operation into the unmodulated dynamics of a quantum network without the need of external control pulses, measurements or active feedback. Our optimization scheme, inspired by supervised machine…