Related papers: Efficient Fault-Tolerant Single Qubit Gate Approxi…
This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…
Fault-tolerant quantum computing requires gates which function correctly despite the presence of errors, and are scalable if the error probability-per-gate is below a threshold value. To date, no method has been described for calculating…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good…
We introduce a measure for evaluating the efficiency of finite universal quantum gate sets $\mathcal{S}$, called the Quantum Circuit Overhead (QCO), and the related notion of $T$-Quantum Circuit Overhead ($T$-QCO). QCO compares the circuit…
We propose a direct (non-recursive) algorithm for applying a rotation $R_{\theta^\ast}$, $\epsilon$-close to a desired rotation $R_\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly…
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…
We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion $^{43}$Ca$^{+}$ hyperfine clock qubit. We explore the speed/fidelity trade-off for gate times $4.4\leq t_{g}\leq35~\mu$s, and benchmark…
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…
Verifying the correct functioning of quantum gates is a crucial step towards reliable quantum information processing, but it becomes an overwhelming challenge as the system size grows due to the dimensionality curse. Recent theoretical…
Fault tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction can be applied…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
We show how a robust high-fidelity universal set of quantum gates can be implemented using a single form of non-adiabatic rapid passage whose parameters are optimized to maximize gate fidelity and reward gate robustness. Each gate in the…
Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the…
We improve the Solovay--Kitaev theorem and algorithm for a general finite, inverse-closed generating set acting on a qudit. Prior versions of the algorithm efficiently find a word of length $O(n^{3+\delta})$ to approximate an arbitrary…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
Quantum computation requires qubits that can be coupled and realized in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates \cite{DiVincenzo2000, Loss1998}. Strong effort across several fields have…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…