相关论文: Homomorphic Logical Measurements

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…

Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…

It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C^{\perp} \subseteq C, and which can be enlarged to C' = [n,k' > k+1, d'], can be converted into a quantum code of parameters [[ n, k+k' - n, min(d,…

Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…

Measuring the similarity of curves is a fundamental problem arising in many application fields. There has been considerable interest in several such measures, both in Euclidean space and in more general setting such as curves on Riemannian…

In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the…

Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…

We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…

Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding…

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…

Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different…

Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum…

Many engineering failures in orientation-dependent systems are geometric failure modes: changing the geometry can eliminate what changing the material merely delays. The mono-monostatic property (exactly one stable equilibrium under…

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics…

We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called…

Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical…

Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return…

The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…

The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient…