Related papers: Lov\'asz Meets Lieb-Schultz-Mattis: Complexity in …
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we…
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.…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
Quantum error correction (QEC) is essential for achieving fault-tolerant quantum computing. While superconducting qubits are among the most promising candidates for scalable QEC, their limited nearest-neighbor connectivity presents…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Quantum state discrimination involves identifying a given state out of a set of possible states. When the states are mutually orthogonal, perfect state discrimination is always possible using a global measurement. In the case of…
Gauss's law-based quantum error correction (GLQEC) offers a promising approach to reducing qubit overhead in lattice gauge theory simulations by leveraging built-in symmetries. For applications of GLQEC to 1+1D lattice quantum…
The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate…
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…
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs,…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and…
Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated…
Quantum computers are growing in size, and design decisions are being made now that attempt to squeeze more computation out of these machines. In this spirit, we design a method to boost the computational power of near-term quantum…
Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC)…
Quantum error correction is fundamentally important for quantum information processing and computation. Quantum error correction codes have been studied and constructed since the pioneering papers of Shor and Steane. Optimal (called MDS)…
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some…
Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing…