Enhanced Fault-Tolerant Quantum Computing ind-Level Systems

Enhanced fault-tolerant quantum computing in d-level systems.

Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for d-level qudit systems with prime d. The codes use n=d-1 qudits and can detect up to ∼d/3 errors. We q...

Resource optimization for fault-tolerant quantum computing

Quantum computing offers the potential for efficiently solving otherwise classically difficult problems, with applications in material and drug design, cryptography, theoretical physics, number theory and more. However, quantum systems are notoriously fragile; interaction with the surrounding environment and lack of precise control constitute noise, which makes construction of a reliable quantu...

On Universal and Fault-Tolerant Quantum Computing

Threshold Estimate for Fault Tolerant Quantum Computing

I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor [1] for fault tolerant error correction (FTEC) and the fault tolerant implementation of elementary operations on states encoded by the 7-qubit code. A simple computer simulation sugges...

Fault-tolerant quantum computing with color codes

We have just completed a thorough, multi-year study of fault-tolerant quantum computation with color codes. These codes are amazing—one way to think about them is as a family of codes which generalize the Steane code not by concatenation but by lattice embedding [1]. Our study of fault-tolerant computing with these codes is complete with analytic bounds, numerical simulations, multiple noise mo...