Related papers: Approximation Errors
This dissertation treats the topics of threshold calculation, ancilla construction, and non-standard error models. Chapter 2 introduces background material ranging from quantum mechanics to classical coding to thresholds for quantum…
The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…
I derive a tight bound between the quality of estimating the state of a single copy of a $d$-level system, and the degree the initial state has to be altered in course of this procedure. This result provides a complete analytical…
Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of $B$ bits of resolution, i.e. it might support only $2^B$ possible…
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…
In this paper we present an enhancement of the regression-based variance reduction approaches recently proposed in Belomestny et al. This enhancement is based on a truncation of the control variate and allows for a significant reduction of…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to…
We investigate the effect of analog control errors which deterministically occurs on isolated quantum dynamics. Quantum information technologies require careful control for preparing a desired quantum state used as an information resource.…
When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This…
Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum…
Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the…