Related papers: Certification of the QR factor R, and of lattice b…
Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this…
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of…
Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.}…
Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that…
This is an expository paper intended to introduce the polynomial time lattice basis reduction algorithm first described by Arjen Lenstra, Hendrik Lenstra, and L\'aszl\'o Lov\'asz in 1982. We begin by introducing the shortest vector problem,…
NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for…
A genie-aided decoder for finite dimensional lattice codes is considered. The decoder may exhaustively search through all possible scaling factors $\alpha \in \mathbb{R}$. We show that this decoder can achieve lower word error rate (WER)…
The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the most practical lattice reduction algorithm in digital communications. In this paper, several variants of the LLL algorithm with either lower theoretic complexity or fixed-complexity…
We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
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…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
We designed an search algorithm in order to find a non-transversal but fault-tolerant construction of a logical controlled-phase gate for general [[n,1,d]] degenerate quantum code. Then we give an example to illustrate our algorithm for a…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Quantization-aware training (QAT) receives extensive popularity as it well retains the performance of quantized networks. In QAT, the contemporary experience is that all quantized weights are updated for an entire training process. In this…
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets…