Related papers: Fault-tolerant quantum algorithms
Fault-tolerant protocols enable large and precise quantum algorithms. Many such protocols rely on a feed-forward processing of data, enabled by a hybrid of quantum and classical logic. Representing the control structure of such programs can…
We study effects of static inter-qubit interactions and random errors in quantum gates on the stability of various quantum algorithms including the Grover quantum search algorithm and the quantum chaos maps. For the Grover algorithm our…
Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…
The design of time-independent local Hamiltonians that realise quantum algorithms is derived from the study of perfect state transfer. The novel features of this evolution are the perfect realisation of the computation, and the ability to…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and…
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally…
This paper researches how the systematic errors in phase inversions affect the success rate and the number of iterations in optimized quantum random-walk search algorithm. Through geometric description of this algorithm, the model of the…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the…
We consider the problem of fault-tolerant quantum computation in the presence of slow error diagnostics, either caused by measurement latencies or slow decoding algorithms. Our scheme offers a few improvements over previously existing…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
I discuss a variety of issues relating to near-future experiments demonstrating fault-tolerant quantum computation. I describe a family of fault-tolerant quantum circuits that can be performed with 5 qubits arranged on a ring with…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We present an implementation of Grover's algorithm in the framework of Feynman's cursor model of a quantum computer. The cursor degrees of freedom act as a quantum clocking mechanism, and allow Grover's algorithm to be performed using a…