Related papers: Transversal Gates for Highly Asymmetric qLDPC Code…
The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes.…
A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of…
Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them…
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
We construct a family of constant-rate highly-symmetric self-dual qLDPC codes on high dimensional expanders. This is the first self-dual code constructed on high dimensional expanders and also the first such code with a rich (e.g.…
Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[\![N,\Theta(N),\tilde\Theta(N)]\!]$ quantum low-density parity-check codes and $[\![N,\Theta(N),\tilde\Theta(N)]\!]$ quantum locally testable codes with soundness…
Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Historically, a $\sqrt{N}log^{1/2}(N)$ distance barrier for quantum low-density parity-check (LDPC) codes with $N$ qubits persisted for nearly two decades, until the recent discovery of the fibre-bundle code. An open question is whether…
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…
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state…
We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with…
Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…
We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…