Related papers: Quantum Period-Finding using One-Qubit Reduced Den…
The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the…
We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states.…
Quantum computing promises polynomial and exponential speedups in many domains, such as unstructured search and prime number factoring. However, quantum programs yield probabilistic outputs from exponentially growing distributions and are…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
This work presents a new frequency acquisition method using semi-rotational frequency detection (SRFD) algorithm for a reference-less clock and data recovery (CDR) in a serial-link receiver. The proposed SRFD algorithm classifies the…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
We give two quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with $m$ constraint matrices, each of dimension $n$, rank at most $r$, and sparsity $s$. The first algorithm…
Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL)…
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
In the fields of quantum mechanics and quantum information science, the traces of reduced density matrix powers play a crucial role in the study of quantum systems and have numerous important applications. In this paper, we propose a…
Quantum communication complexity studies the efficiency of information communication (that is, the minimum amount of communication required to achieve a certain task) using quantum states. One representative example is quantum…
Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to…