Related papers: Quantum Circuits and Spin(3n) Groups
Spin qubits offer one of the most promising routes to the implementation of quantum computers. Very recent results in semiconductor quantum dots show that electrically-controlled gating schemes are particularly well-suited for the…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin…
Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group…
In quantum computation, series of quantum gates have to be arranged in a predefined sequence that led to a quantum circuit in order to solve a particular problem. What if the sequence of quantum gates is known but both the problem to be…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…
We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier…
The implementation of a universal quantum processor still poses fundamental issues related to error mitigation and correction, which demand to investigate also platforms and computing schemes alternative to the main stream. A possibility is…
We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed…
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…
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…
In this paper, we present the experimental realization of multi-qubit gates $% \Lambda_n(not) $ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the…
The faster speed and operational convenience of two-qubit gate with flux bias control makes it an important candidate for future large-scale quantum computers based on high coherence flux qubits. Based on a properly designed two-spin gadget…
Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…
To realize large-scale quantum information processes, an ideal scheme for two-qubit operations should enable diverse operations with given hardware and physical interaction. However, for spin qubits in semiconductor quantum dots, the common…
The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our…
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
In this paper, we design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates. A key result we derive is that any two Pauli-string operators composed of…
Some physical implementation schemes of quantum computing can apply two-qubit gates only on certain pairs of qubits. These connectivity constraints are commonly viewed as a significant disadvantage. For example, compiling an unrestricted…