Related papers: Universal fault-tolerant gates on concatenated sta…
We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…
Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as…
Solid-state spin qubits are a promising platform for quantum computation and quantum networks. Recent experiments have demonstrated high-quality control over multi-qubit systems, elementary quantum algorithms and non-fault-tolerant error…
Physical implementation of scalable quantum architectures faces an immense challenge in form of fragile quantum states. To overcome it, quantum architectures with fault tolerance is desirable. This is achieved currently by using surface…
Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical…
In this work, we propose and study in depth a universal quantum computing architecture based on a quantum construction of transistors. Our teleportation-based quantum transistors, called ``telesistors'', are ground states of systems with…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…
Transversal logical gates offer the opportunity for fast and low-noise logic, particularly when interspersed by a single round of parity check measurements of the underlying code. Using such circuits for the surface code requires decoding…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
Motivated by their central role in fault-tolerant quantum computation, we study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of `nearly diagonal' semi-Clifford gates. The Clifford hierarchy…
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…
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 present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet…
In this paper, we focus on the problem of computing the set of diagonal transversal gates fixing a CSS code. We determine the logical actions of the gates as well as the groups of transversal gates that induce non-trivial logical gates and…