Related papers: Towards local testability for quantum coding
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…
The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
We propose a scheme for a ground-code measurement-based quantum computer, which enjoys two major advantages. First, every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body…
Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We…
Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weight-six parity checks using only two-local measurements. The sparse connectivity and two-local measurements…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the…
Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The…
We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3% for the {4,5}-hyperbolic surface code in a phenomenological noise model (as compared to…
Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum…