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This article aims to review the developments, both theoretical and experimental, that have in the past decade laid the ground for a new approach to solid state quantum computing. Measurement-based quantum computing (MBQC) requires neither…

In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential…

We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems - multi-atomic coherent ensembles, squids or quantum dots in quantum…

Silicon-based qubits are often made by trapping individual electrons in quantum dots defined by electric gates. Quantum information can then be stored using the spin states of the electrons. However, the nuclei of the surrounding atoms also…

Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is…

Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a…

In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…

An electron inside liquid helium forms a bubble of 17 \AA in radius. In an external magnetic field, the two-level system of a spin 1/2 electron is ideal for the implementation of a qubit for quantum computing. The electron spin is well…

A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics…

We propose a scalable quantum-computing architecture based on cold atoms confined to sites of a tight optical lattice. The lattice is placed in a non-uniform magnetic field and the resulting Zeeman sublevels define qubit states. Microwave…

Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid state systems. Here we present a protocol that achieves a complete set of…

This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantum processor. The goal is to store over long times…

Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual…

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…

As an extension of two-level quantum bits (qubits), multilevel systems, so-called qudits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum computation algorithms. This has…

We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum…

The physics of interacting nuclear spins arranged in a crystalline lattice is typically described using a thermodynamic framework: a variety of experimental studies in bulk solid-state systems have proven the concept of a spin temperature…

Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and in quantum information processing. Here we review our proposal for quantum computing with…

We report the implementation of the central building block of the Schulman-Vazirani procedure for fully polarizing a subset of two-level quantum systems which are initially only partially polarized. This procedure consists of a sequence of…