Related papers: Some Error Analysis for the Quantum Phase Estimati…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the…
Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future,…
Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
Quantum phase estimation is an important component in diverse quantum algorithms. However, it suffers from spectral leakage, when the reciprocal of the record length is not an integer multiple of the unknown phase, which incurs an accuracy…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum…
Many researchers have been heavily investigated on quantum phase estimation (QPE) algorithms to find the unknown phase, since QPE is the core building block of the most quantum algorithms such as the Shor's factoring algorithm, quantum…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires…
We present results of numerical simulations of the evolution of an ion trap quantum computer made out of 18 ions which are subject to a sequence of nearly 15000 laser pulses in order to find the prime factors of N=15. We analyze the effect…
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography.…
Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum…
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…