A variational quantum algorithm for Hamiltonian diagonalization

3 A Diagonalization Algorithm

A Quantum Algorithm for the Hamiltonian NAND Tree

The NAND trees in this paper are perfectly bifurcating trees with N leaves at the top and depth n = log2(N). Each leaf is assigned a value of 0 or 1 and the value of any other node is the NAND of the two connected nodes just above. The goal is to evaluate the value at the root of the tree. An example is shown in figure (1). Classically there is a randomized algorithm that succeeds after evaluat...

Quantum Algorithm Processors to Reveal Hamiltonian Cycles

Professor J. R. Burger Summary – Quantum computer versus quantum algorithm processor in CMOS are compared to find (in parallel) all Hamiltonian cycles in a graph with m edges and n vertices, each represented by k bits. A quantum computer uses quantum states analogous to CMOS registers. With efficient initialization, number of CMOS registers is proportional to (n-1)! Number of qubits in a quantu...

A Hamiltonian for Quantum Copying

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system—a qubit—onto n " copy " qubits (n ≥ 1) initially all prepared in the down state. In terms of spin components , for spin-1 2 particle spin states, the resulting Hamiltonian involves n-and (n + 1)-spin interactions. The case n = 1 also corresponds to a quantum-computing controlled-NOT gate.

Diagonalization of the Hamiltonian in a Chromomagnetic Field

We demonstrate how to find both the color diagonal form of the squared Dirac equation in the axial color background and the transformation of the color space, which makes this equation diagonal.