scholarly journals Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Tomas Jochym-O’Connor ◽  
Aleksander Kubica ◽  
Theodore J. Yoder
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

scholarly journals Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes

2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Theodore J. Yoder ◽  
Ryuji Takagi ◽  
Isaac L. Chuang
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

Scheme for fault-tolerant holonomic computation on stabilizer codes

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
Ognyan Oreshkov ◽  
Todd A. Brun ◽  
Daniel A. Lidar
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

scholarly journals C_3, semi-Clifford and genralized semi-Clifford operations

2010 ◽  
Vol 10 (1&2) ◽  
pp. 41-59
Author(s):  
S. Beigi ◽  
P.W. Shor
Keyword(s):  
Quantum Computation ◽  
Basic Problem ◽  
Fault Tolerant ◽  
Quantum Codes ◽  
Stabilizer Codes

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called ${\mathcal{C}}_k$ hierarchy gates, introduced by Gottesman and Chuang (Nature, 402, 390-392). ${\mathcal{C}}_k$ gates are a generalization of Clifford operators, but our knowledge of these sets is not as rich as our knowledge of Clifford gates. Zeng et al. in (Phys. Rev. A 77, 042313) raise the question of the relation between ${\mathcal{C}}_k$ hierarchy and the set of semi-Clifford and generalized semi-Clifford operators. They conjecture that any ${\mathcal{C}}_k$ gate is a generalized semi-Clifford operator. In this paper, we prove this conjecture for $k=3$. Using the techniques that we develop, we obtain more insight on how to characterize ${\mathcal{C}}_3$ gates. Indeed, the more we understand ${\mathcal{C}}_3$, the more intuition we have on ${\mathcal{C}}_k$, $k\geq 4$, and then we have a way of attacking the conjecture for larger $k$.

scholarly journals Flag fault-tolerant error correction with arbitrary distance codes

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 53 ◽  
Author(s):  
Christopher Chamberland ◽  
Michael E. Beverland
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Parity Check ◽  
Code Length ◽  
Stabilizer Codes ◽  
Low Density Parity Check ◽  
Quantum Error ◽  
First Time

In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting fromvfaults in the circuit have weight greater thanv. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.

Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes

2021 ◽  
Author(s):  
Xiu-Bo Chen ◽  
Li-Yun Zhao ◽  
Gang Xu ◽  
Xing-Bo Pan ◽  
Si-Yi Chen ◽  
...  
Keyword(s):  
Error Correction ◽  
Fault Tolerant ◽  
Stabilizer Codes ◽  
Correction Scheme ◽  
Quantum Stabilizer Codes

scholarly journals SIMPLE FAULT-TOLERANT ENCODING OVER q-ARY CSS QUANTUM CODES

2007 ◽  
Vol 05 (05) ◽  
pp. 705-716
Author(s):  
PEDRO J. SALAS
Keyword(s):  
Fault Tolerant ◽  
Quantum Codes ◽  
Quantum Code ◽  
Simple Method ◽  
Stabilizer Codes ◽  
Css Codes ◽  
Quantum Computations

CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank–Shor–Steane quantum code, defined over a q-ary alphabet, is used.

scholarly journals Fault-Tolerant Logical Gates in Holographic Stabilizer Codes Are Severely Restricted

PRX Quantum ◽  
2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Sam Cree ◽  
Kfir Dolev ◽  
Vladimir Calvera ◽  
Dominic J. Williamson
Keyword(s):  
Fault Tolerant ◽  
Stabilizer Codes

scholarly journals Avoiding coherent errors with rotated concatenated stabilizer codes

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yingkai Ouyang
Keyword(s):  
Fault Tolerant ◽  
Quantum Systems ◽  
Quantum Memory ◽  
Dominant Form ◽  
Amplitude Damping ◽  
Stabilizer Codes ◽  
Outer Code ◽  
Phase Errors ◽  
Stochastic Errors ◽  
Stabilizer Code

AbstractCoherent 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 constant-excitation codes by code concatenation. Namely, by concatenating an [[n, k, d]] stabilizer outer code with dual-rail inner codes, we obtain a [[2n, k, d]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code’s potential as a quantum memory.

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