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The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
Spin ensembles are promising quantum technological platforms, but their utility relies on the ability to perform quantum error correction (QEC) for the specific decoherence in these systems. Typical QEC for ensembles requires addressing…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
The usefulness of solid-state spins in quantum technologies depends on how long they can remain in a coherent superposition of quantum states. This Colloquium discusses how first-principles simulations can predict spin dynamics for…
Shuttling of spin qubits between different locations is a key element in many prospective semiconductor systems for quantum information processing, but the shuttled qubits should be protected from decoherence created by time- and…
We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins,…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Bias-tailored quantum error correcting codes (QECCs) offer a higher error threshold than standard QECCs and have the potential to achieve lower logical errors with less space overhead. The spin-cat qubit, encoded in a large nuclear spin-$F$…
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and…
Given some group $G$ of logical gates, for instance the Clifford group, what are the quantum encodings for which these logical gates can be implemented by simple physical operations, described by some physical representation of $G$? We…
Many efforts have succeeded over the last decade at lengthening the timescale in which spin qubits loss quantum information under free evolution. With these design principles at a mature stage, it is now timely to widen the scope and take…
We present an encoding technique that reduces the effects of noise on quantum spin systems whose operation is driven by Hamiltonian evolution. This technique is widely applicable, being most relevant to the scenarios where there are…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…