Related papers: Efficient classical algorithms for simulating symm…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
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…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a…
The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…