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Bosonic codes provide an alternative option for quantum error correction. An important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP) code has aroused much interest recently. Theoretically, the error correction ability…
Gottesman-Kitaev-Preskill (GKP) encoding holds promise for continuous-variable fault-tolerant quantum computing. While an ideal GKP encoding is abstract and impractical due to its nonphysical nature, approximate versions provide viable…
We present a new control algorithm and system design for a network of quantum repeaters, and outline the end-to-end protocol architecture. Such a network will create long-distance quantum states, supporting quantum key distribution as well…
A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum…
We describe a quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between qubits at intermediate stations of the channel by using a weak dispersive light-matter interaction and…
We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys.…
The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes…
We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model…
The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code. Since the GKP code only protects against small shift errors in $\hat{p}$ and $\hat{q}$ quadratures, it is necessary to concatenate the…
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available…
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of…
Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. We investigate a new approach to QRs in which quantum information can be faithfully transmitted…
We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits…
Straightforward logical operations contrasting with complex state preparation are the hallmarks of the bosonic encoding proposed by Gottesman, Kitaev and Preskill (GKP). The recently reported generation and error-correction of GKP qubits in…
Quantum repeaters hold the promise to prevent the photon losses in communication channels. Most recently, the serious efforts have been applied to achieve scalable distribution of entanglement over long distances. However, the probabilistic…
We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of…
We present an encoded hybrid quantum repeater scheme using qubit-repetition and Calderbank-Shor-Steane codes. For the case of repetition codes, we propose an explicit implementation of the quantum error-correction protocol. Moreover, we…
In this chapter a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z…