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Variational algorithms may enable classically intractable simulations on near-future quantum computers. However, their potential is limited by hardware errors. It is therefore crucial to develop efficient ways to mitigate these errors.…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. Our approach is based on applying an optimal "denoiser"…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is…
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction,…
The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
Optical loss is a common bottleneck in photonic quantum information processing, undermining the quantum advantage over classical approaches. Although several countermeasures, such as quantum distillation and error correction, have been…
A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their…
In this paper, we study decoherence on Grover's quantum searching algorithm using a perturbative method. We assume that each two-state system (qubit) suffers \sigma_{z} error with probability p (0\leq p\leq 1) independently at every step in…
Since there are many examples in which no decoherence-free subsystems exist (among them all cases where the error generators act irreducibly on the system Hilbert space), it is of interest to search for novel mechanisms which suppress…
To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well…