Related papers: Higher-Order Methods for Quantum Simulations
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
We present sixth- and eighth-order Hermite integrators for astrophysical $N$-body simulations, which use the derivatives of accelerations up to second order ({\it snap}) and third order ({\it crackle}). These schemes do not require previous…
It is commonly assumed that calculating third order information is too expensive for most applications. But we show that the directional derivative of the Hessian ($D^3f(x)\cdot d$) can be calculated at a cost proportional to that of a…
Quantum simulation of many-body systems offers a powerful approach to exploring collective quantum dynamics beyond classical computational reach. Although spin and fermionic models have been extensively simulated on digital quantum…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
The paper extends the expectation transformer based analysis of higher-order probabilistic programs to the quantum higher-order setting. The quantum language we are considering can be seen as an extension of PCF, featuring unbounded…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm in which the multiplication of $\hat{H}^{-k}$ to the reference wavefunction is replaced by the Fourier Transformed multiplication of $e^{-i\lambda \hat{H}}$, as a function of…
The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the…
We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…