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The construction of two-qubit gates appropriate for universal quantum computation is of enormous importance to quantum information processing. Building such gates is dependent on accurate knowledge of the interaction dynamics between two…
Electron spins in semiconductor quantum dots are promising candidates for the experimental realization of solid-state qubits. We analyze the dynamics of a system of three qubits arranged in a linear geometry and a system of four qubits…
We show that two electrons confined in a square semiconductor quantum dot have two isolated low-lying energy eigenstates, which have the potential to form the basis of scalable computing elements (qubits). Initialisation, one-qubit and…
We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one…
We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, trapped within an optical lattice. The qubit states are encoded by the scattering state and the bound…
We review a recent theoretical proposal for a universal quantum computing platform based on tunable nonlinear electromechanical nano-oscillators, in which qubits are encoded in the anharmonic vibrational modes of mechanical resonators…
Quantized integrable systems can be made to perform universal quantum computation by the application of a global time-varying control. The action-angle variables of the integrable system function as qubits or qudits, which can be coupled…
A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and…
In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian…
Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward…
We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be…
Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…
The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are…
We describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial…
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of…
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast,…
We study the computation power of lattices composed of two dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of 6 global two qubit gates can be performed,…