Qudit quantum computation in the Jaynes-Cummings model

Abstract

We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one-and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme [1]. The second method replaces some of the analytical pulse sequences with more rapid numerically optimized sequences. In our third approach, we directly optimize the evolution of the system, without making use of any analytic techniques. While limited to smaller dimensional qudits, the third approach finds pulse sequences which carry out the desired gates in a time which is much shorter than either of the other two approaches. * brianm@phys.au.dk 1 arXiv:1210.4488v1 [quant-ph]

Quantum computation mediated by ancillary qudits and spin coherent states

“…Qudits have been demonstrated in various physical systems, including superconducting [46], atomic [47], and photonic systems, where in the latter the qudit is encoded in the linear [48,49] or orbital angular momentum [50] of a single photon. A further possible realization of a qudit is in the Fock states of a field mode which can be coupled to individual qubits via the Jaynes-Cummings model [51]. The dispersive limit of the Jaynes-Cummings model results in an effective coupling of the form,…”

Phonon-to-spin mapping in a system of a trapped ion via optimal control

“…However, this is a very interesting problem not only because it requires less complexity when implemented in an experiment, but also since it corresponds to the systems analyzed e.g. by [11,[14][15][16]. Figure 6 compares the resulting fidelity F (m, 10) three driving fields (black squares), with scenarios using the carrier and the blue sideband transition (blue circles) and using the carrier and the red sideband transition (red crosses).…”

“…This requires a map that acts in a desired way only on |ψ n n=0,1,2 and can be achieved by maximizing F (m, N = 3), thus considering the time evolution of only N = 3 basis functions. As presented in [16], the control task dramatically simplifies if fewer levels are included in the control functional. Fig.…”

“…In the following we consider one field resonant to the carrier and one field resonant to the red sideband transition since it is closer to the systems in Ref. [11,[14][15][16]. So far we had U m operating in the desired way on the subspace of N = 10, thus for up to 9 vibrational quanta.…”

“…The controllability of the problem has been analyzed by [14], and the control problem has been tackled for state-to-state transfer [11] and gate optimization [15,16]. This work is an example for incomplete control : We seek…”