Flexible Fault Tolerant Gate Gadgets

Abstract

We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault tolerantly on generic quantum codes, including both stabilizer and non-additive codes. This allows us to demonstrate the first universal fault tolerant gate set for non-additive codes. We consider fault tolerance both with respect to a dephasing channel and a depolarizing channel.

References in corpus (28)

• Quantum Teleportation is a Universal Computational Primitive
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• Surface code quantum computing by lattice surgery
• Methodology for quantum logic gate constructions
• Active stabilisation, quantum computation and quantum state synthesis
• Dephasing of a superconducting qubit induced by photon noise
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Magic State Distillation: Not as Costly as You Think
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Fault-tolerant quantum computation against biased noise
• Dephasing of a superconducting flux qubit
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Using concatenated quantum codes for universal fault-tolerant quantum gates
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• Universal fault-tolerant gates on concatenated stabilizer codes
• Distillation with sublogarithmic overhead
• On Optimality of CSS Codes for Transversal $T$
• The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
• Tailored XZZX codes for biased noise
• A Family of Quantum Codes with Exotic Transversal Gates
• Multispin Clifford codes for angular momentum errors in spin systems
• Efficient quantum error correction of dephasing induced by a common fluctuator
• A family of permutationally invariant quantum codes
• Quantum Codes from Twisted Unitary $t$-groups
• Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates