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Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal…
Quantum error correction represents a significant milestone in large-scale quantum computing, with the surface code being a prominent strategy due to its high error threshold and experimental feasibility. However, it is challenging to…
We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…
The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In…
Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing fault-tolerant logical operations on the encoded qubits. One of the most resource…
Quantum error correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
We report a resource estimation pipeline that explicitly compiles quantum circuits expressed using the Clifford+T gate set into a surface code lattice surgery instruction set. The cadence of magic state requests from the compiled circuit…
Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching…
Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction…
Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation…
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…
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 transverse non-Clifford…
We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…
Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…
Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded…
Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from…
The $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates, but…