Related papers: Geometric Quantum Computation
The geometric measure of entanglement of variational quantum states is studied on the basis of its relation with the mean value of spin. We examine n-qubit quantum states prepared by a variational circuit with a layer formed by the…
We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and $R_z$ rotations can be implemented in…
We present quantum algorithms to realize geometric transformations (two-point swappings, symmetric flips, local flips, orthogonal rotations, and translations) based on an $n$-qubit normal arbitrary superposition state (NASS). These…
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically…
Geometric phases, accumulated when a quantum system traces a cycle in quantum state space, do not depend on the parametrization of the cyclic path, but do depend on the path itself. In the presence of noise that deforms the path, the phase…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…
Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state…
We propose a universal set of single- and two-qubit quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit to a $\mathbb{Z}_{2m}$ parafermion qubit with arbitrary integer $m$. The special case $m=1$ reproduces…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground state is a universal resource for measurement based quantum…
Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…
Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: There is a basic conflict between nanometre separation desired for qubit-qubit interactions, and…
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…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface…
Quantum gates are the building blocks of quantum circuits, which in turn are the cornerstones of quantum information processing. In this work, we theoretically investigate a single-step implementation of both a universal two- (CNOT) and…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…