Related papers: Efficient Quantum Algorithms for State Measurement…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
We propose a scalable method for implementing linear optics quantum computation using the ``linked-state'' approach. Our method avoids the two-dimensional spread of errors occurring in the preparation of the linked-state. Consequently, a…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…
An optimal estimator of quantum states based on a modified Kalman Filter is presented in this work. Such estimator acts after state measurement, allowing to obtain an optimal estimation of quantum state resulting in the output of any…
We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum…
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
I generalize the well-known classical Metropolis-Hastings algorithm into a quantum algorithm that can equilibrate, measure, and mix a quantum thermal state on a quantum computer. It performs non-symmetric transitions on labels of state…