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Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical…

Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…

Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…

In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…

With the intense interest in small, noisy quantum computing devices comes the push for larger, more accurate -- and hence more useful -- quantum computers. While fully fault-tolerant quantum computers are, in principle, capable of achieving…

We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle…

Quantum information processing and its associated technologies has reached an interesting and timely stage in their development where many different experiments have been performed establishing the basic building blocks. The challenge…

Engineering quantum operations is one of the main abilities we need for developing quantum technologies and designing new fundamental tests. Here we propose a scheme for realising a controlled operation acting on a travelling quantum field,…

This paper presents a scheme for linear-optical implementation of a programmable quantum router. Polarization encoded photon qubit is coherently routed to various spatial modes according to the state of several control qubits. In our…

Among the objectives toward large-scale quantum computation is the quantum interconnect: a device which uses photons to interface qubits that otherwise could not interact. However, current approaches require photons indistinguishable in…

We present a scheme for correcting qubit loss error while quantum computing with neutral atoms in an addressable optical lattice. The qubit loss is first detected using a quantum non-demolition measurement and then transformed into a…

The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this…

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single…

Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using…

This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…

Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are…

The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…

One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally…

In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…