相关论文: Generation of eigenstates using the phase-estimati…

We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…

We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…

Quantum protocols often require the generation of specific quantum states. We describe a quantum algorithm for generating any prescribed quantum state. For an important subclass of states, including pure symmetric states, this algorithm is…

The phase estimation algorithm, which is at the heart of a variety of quantum algorithms, including Shor's factoring algorithm, allows a quantum computer to accurately determine an eigenvalue of an unitary operator. Quantum nondemolition…

Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…

Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…

This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…

The initial state creation is a starting point of many quantum algorithms and usually is considered as a separate subroutine not included into the algorithm itself. There are many algorithms aimed on creation of special class of states. Our…

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…

Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…

We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits $n_q$, it is shown that the…

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…

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…

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…

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…

The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…