Related papers: Quantum block Krylov subspace projector algorithm …
Resolving degenerate quantum eigenspaces - including topologically ordered ground states and frustrated magnets - requires preparing high-fidelity states that span every direction of the target manifold. Existing variational and projective…
We consider the task of computing solutions of linear systems that only differ by a shift with the identity matrix as well as linear systems with several different right hand sides. In the past Krylov subspace methods have been developed…
The accurate computation of Hamiltonian ground, excited, and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed…
In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA)…
We propose a unifying framework for the state preparation using quantum power method algorithms based on generalized quantum signal processing (GQSP). We apply GQSP to realize quantum analogs of classical power iteration, power Lanczos,…
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
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…
We present an approach to the calculation of arbitrary spectral, thermal and excited state properties within the full configuration interaction quantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian…
Quantum computers are capable of calculating the energy gap of two electronic states by using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference based implementations for the QPDE have been reported so far, but…
Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver…
Nowaday, in study of effective interactions, more attention is devoted to single-particle properties of near-magic nuclei and bulk properties of deformed ones but quasiparticle states of the latter are rarely used so far because of…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…
Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a…
The use of block Krylov subspace methods for computing the solution to a sequence of shifted linear systems using subspace recycling was first proposed in [Soodhalter, SISC 2016], where a recycled shifted block GMRES algorithm (rsbGMRES)…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report…