Related papers: Codes and Protocols for Distilling $T$, controlled…
The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to…
We introduce the qudit ZH-calculus and show how to generalise all the phase-free qubit rules to qudits. We prove that for prime dimensions d, the phase-free qudit ZH-calculus is universal for matrices over the ring Z[e^2(pi)i/d]. For…
Fault-tolerant quantum computing requires large-scale superconducting processors, yet monolithic architectures face increasing constraints from wiring density, crosstalk, and fabrication yield. Modular superconducting platforms offer a…
We propose a scheme for the fault-tolerant implementation of arbitrary Clifford circuits. To achieve this, we extend previous work on flag gadgets for syndrome extraction to a general framework that flags any Clifford circuit. This…
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…
Modern recommendation and search systems typically employ multi-stage ranking architectures to efficiently handle billions of candidates. The conventional approach uses distinct L1 (candidate retrieval) and L2 (re-ranking) models with…
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…
We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best…
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…
Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\varepsilon$, $3\log_2(1/\varepsilon) + o(\log(1/\varepsilon))$ $T$ gates are sufficient to…
An $(n+1)$-bit Toffoli gate is mainly utilized to construct other quantum gates and operators, such as Fredkin gates, arithmetical adders, and logical comparators, where $n \geq 2$. Several researchers introduced different methods to…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…
We develop a theory of entanglement distillation that exploits a convolutional coding structure. We provide a method for converting an arbitrary classical binary or quaternary convolutional code into a convolutional entanglement…
We propose hardware-efficient schemes for implementing logical H and S gates transversally on rotated surface codes with reconfigurable neutral atom arrays. For logical H gates, we develop a simple strategy to rotate code patches…
A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic…
We propose a scalable way to construct a 3D cluster state for fault-tolerant topological one-way computation (TOWC) even if the entangling two-qubit gates succeed with a small probability. It is shown that fault-tolerant TOWC can be…