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Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
Local update recovery seeks to maintain quantum information by applying local correction maps alternating with and compensating for the action of noise. Motivated by recent constructions based on quantum LDPC codes in the finite-dimensional…
The Gottesman-Kitaev-Preskill encoding of a qubit in a harmonic oscillator is a promising building block towards fault-tolerant quantum computation. Recently, this encoding was experimentally demonstrated for the first time in trapped-ion…
Physical-level noise on traveling bosonic modes remains a critical bottleneck for scalable quantum information processing. We show that for any single-mode bosonic code (qumode) corrupted by thermal or Gaussian displacement noise at loss…
The integration of diverse quantum resources and the exploitation of more degrees of freedom provide key operational flexibility for universal fault-tolerant quantum computation. In this work, we propose a flexible…
The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode higher-dimensional qudits into individual bosonic modes with, for instance, photonic excitations. Since photons enable the reliable transmission of quantum…
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
We analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode and…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy…
Continuous-variable (CV) cluster states are a universal resource for fault-tolerant quantum computation when supplemented with the Gottesman-Kitaev-Preskill (GKP) bosonic code. We generalize the recently introduced subsystem decomposition…
Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any…
We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multi-qubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent…
There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light)…