Related papers: Non-binary Unitary Error Bases and Quantum Codes
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
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…
Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the…
Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Recently, many good quantum codes over various finite fields $F_q$ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly…
Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudits, composite constant-excitation Fock-state spaces of many…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…