Related papers: The State of Factoring on Quantum Computers
The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of…
Quantum computers are analog devices; thus they are highly susceptible to accumulative errors arising from classical control electronics. Fast operation--as necessitated by decoherence--makes gating errors very likely. In most current…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…
In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the…
Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance…
Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world…
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They…
Architectures for quantum computing can only be scaled up when they are accompanied by suitable benchmarking techniques. The document provides a comprehensive overview of the state and recommendations for systematic benchmarking of quantum…
The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of…
Quantum computing could impact various industries, with the automotive industry with many computational challenges, from optimizing supply chains and manufacturing to vehicle engineering, being particularly promising. This chapter…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
The previously proposed Heisenberg-type relation $ E_c t_c >> \hbar {\cal C}$ for the energy used by a quantum computer, the total computation time and the logical ("classical") complexity of the problem is verified for the following…
We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
We analyze the influence of errors on the implementation of the quantum Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of errors are studied: (i) due to spurious transitions caused by pulses and (ii) due to…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…