Related papers: Eigenvalue Estimation of Differential Operators
The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well…
Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown…
We prove a two-term Weyl-type asymptotic law, with error term O(1/n), for the eigenvalues of the operator psi(-Delta) in an interval, with zero exterior condition, for complete Bernstein functions psi such that x psi'(x) converges to…
Effective spin-spin interactions between N+1 qubits enable the determination of the eigenvalue of an arbitrary Pauli product of dimension N with a constant, small number of multi-qubit gates that is independent of N and encodes the…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp, and imply an O(N^{3/4} log N) quantum upper…
We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
We present a quantum algorithm to evaluate matrix elements of functions of unitary operators. The method is based on calculating quadrature nodes and weights using data collected from a quantum processor. Given a unitary $U$ and quantum…
The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this…
We show a certain kind of non-local operations can be simulated by sampling a set of local operations with a quasi-probability distribution when the task of a quantum circuit is to evaluate an expectation value of observables. Utilizing the…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…