Related papers: Puncturing Quantum Stabilizer Codes
We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
Quantum Fourier analysis is an important topic in mathematical physics. We introduce a systematic protocol for testing and measuring ``magic'' in quantum states and gates, using a quantum Fourier approach. Magic, as a quantum resource, is…
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the…
Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have…
Stabilizer channels are stabilizer circuits that implement logical operations while mapping from an input stabilizer code to an output stabilizer code. They are widely used to implement fault tolerant error correction and logical operations…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known stabilizer code…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
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…
Quantum computers have the potential to change the way we solve computational problems. Due to the noisy nature of qubits, the need arises to correct physical errors occurring during computation. The surface code is a promising candidate…
Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computations. While conventional methods use a number of extra qubits linear in the weight of the syndrome, several improvements have been…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…