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We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…

In pursuit of enhancing the predication capabilities of the neural network, it has been a longstanding objective to create dataset encompassing a diverse array of samples. The purpose is to broaden the horizons of neural network and…

We present a cooling algorithm for ground state preparation of fermionic Hamiltonians. Our algorithm makes use of the Hamiltonian simulation of the considered system coupled to an ancillary fridge, which is regularly reset to its known…

Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…

Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…

Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…

We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…

The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper…

We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register $R$ which…

In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…

We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…

Finding ways to transform a quantum state to another is fundamental to quantum information processing. In this paper, we apply the sparse matrix approach to the quantum state transformation problem. In particular, we present a new approach…

Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new…

Local Hamiltonian Problems (LHPs) are important problems that are computationally QMA-complete and physically relevant for many-body quantum systems. Quantum MaxCut (QMC), which equates to finding ground states of the quantum Heisenberg…

We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which…

Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit…