Related papers: A Constant Rate Quantum Computer on a Line
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
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 low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…
Fault-tolerant modular quantum computing requires stabilizer measurements across the modules in a quantum network. For this, entangled states of high quality and rate must be distributed. Currently, two main types of entanglement…
We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions.…
Proving the quantum Hamming bound for degenerate nonbinary stabilizer codes has been an open problem for a decade. In this note, I prove this bound for double error-correcting degenerate stabilizer codes. Also, I compute the maximum length…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all unitary quantum gates, and it is found that the…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
Error correcting codes use multi-qubit measurements to realize fault-tolerant quantum logic steps. In fact, the resources needed to scale-up fault-tolerant quantum computing hardware are largely set by this task. Tailoring next-generation…