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This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Obtaining high-fidelity and robust quantum gates is the key for scalable quantum computation, and one of the promising ways is to implement quantum gates using geometric phases, where the influence of local noises can be greatly reduced. To…
Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate…
Quantum computing tries to exploit entanglement and interference to process information more efficiently than the best known classical solutions. Experiments demonstrating the feasibility of this approach have already been performed.…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Recently several quantum search algorithms based on quantum walks were proposed. Those algorithms differ from Grover's algorithm in many aspects. The goal is to find a marked vertex in a graph faster than classical algorithms. Since the…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs)…
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…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient.…
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high…
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted.…
Errors occurring on noisy hardware pose a key challenge to reliable quantum computing. Existing techniques such as error correction, mitigation, or suppression typically separate the error handling from the algorithm analysis and design. In…