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A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Device imperfections and memory effects can result in undesired correlations among the states generated by a realistic quantum source. These correlations are called source correlations. Proving the security of quantum key distribution (QKD)…
We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans.…
We study how entanglement among the register qubits affects the gate fidelity in the one-way quantum computation if a measurement is inaccurate. We derive an inequality which shows that the mean gate fidelity is upper bounded by a…
The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more…
The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
The resource overhead required to achieve net computational benefits from quantum error correction (QEC) limits its utility while current systems remain constrained in size, despite exceptional progress in experimental demonstrations. In…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
We describe and analyze leakage errors of singlet-triplet qubits. Even though leakage errors are a natural problem for spin qubits encoded using quantum dot arrays, they have obtained little attention in previous studies. We describe the…
Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification,…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding…
Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC). In a QEC circuit, leakage builds over time and spreads through multi-qubit…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…