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Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
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…
Reliable execution of large-scale quantum algorithms requires robust underlying operations and this challenge is addressed by quantum error correction (QEC). Most modern QEC protocols rely on measurements and feed-forward operations, which…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against…
Quantum error correcting codes (QECCs) in quantum communi- cation systems has been known to exhibit improved performance with the use of error-free entanglement bits (ebits). In practical situations, ebits inevitably suffer from errors, and…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
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.…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems,…
We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements. Recently, there has been much interest in Floquet codes and space-time codes. In this work, we define and study the…
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be…
Leakage errors, in which a qubit is excited to a level outside the qubit subspace, represent a significant obstacle in the development of robust quantum computers. We present a computationally efficient simulation methodology for studying…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
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…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…