Martinis group at UCSB have demonstrated operations on a quantum bit with 5 levels (qudit with d=5) instead of the usual 2 (qubit):

**“Emulation of a Quantum Spin with a Superconducting Phase Qudit”**

Matthew Neeley,1 Markus Ansmann,1 Radoslaw C. Bialczak,1 Max Hofheinz,1 Erik Lucero,1 Aaron D. O’Connell,1 Daniel Sank,1 Haohua Wang,1 James Wenner,1 Andrew N. Cleland,1 Michael R. Geller,2 John M. Martinis1,

They use a standard type of phase qubit experiment in which the quantum states are defiined by a ladder of energy levels in a single potential well, rather than the more common flux qubit where the energy levels arise from the degeneracy between two adjacent wells. The qubits/qudits are controlled by applying very careful timed and shaped pulses of microwaves to excite the quantum states between levels and to allow the levels to interact with one another. The energy between each level is very slightly different due to the anharmonicity of the Josephson junction’s energy landscape, so each level transition has a unique ‘frequency signature’. (This scheme wouldn’t work if the quantum states were in a harmonic oscillator, as all the levels would be equally spaced.)

The group demonstrate a shift in the Ramsey fringes which equates to the expected Berry phase produced by the rotation of the quantum state around the Bloch Sphere. They also demonstrate robust Rabi oscillations and the swapping of quantum information between states. The relaxation times of the states are all in the 100’s of ns, but are smaller for the higher states.

I can’t really stress how exciting this result is for experimental quantum computation with superconducting circuits – it opens up new possibilities for implementation of algorithms and quantum simulation. The group focus on the potential of the technique for emulating quantum spin systems.

I wonder what algorithms have been developed that require multi-dimensional Hilbert spaces for their implementation? I know that higher dimensional quantum bits can help make quantum cryptography more secure. I find a sudden renewed interest in learning about qudits…

I’m also slightly smug in my opinion that this once again puts Josephson SC qubits marginally ahead in the awesomeness stakes. (Those ion trap guys were really giving us a run for our money). Qutrit systems (3 levels) have been realised in NMR and Ion trap QC but I believe that experiments like this really open up the door for more complex QIP realizations.

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The “Emulation of a Quantum Spin with a Superconducting Phase Qudit” story has the direction I think of as perfect. Focusing on the most modern concepts; nanostructures with discrete quantum states may be gradually defined until a clear mathematical model for the atomic/molecular/wave object is deciphered. That will produce the algorithm for all cases of that object, the topological wavefunction of that particle or wave.

Careful applications of highly timed, controlled force to targets seems like the future, and should lead to advances in material and energy appliances which are far more efficient and versatile.

The equation for one atom builds algorithms for polypsi molecules. Calculations for molecular modeling have bases which stem from the wavefunctions of quantum mechanics, and have some semiformal nanoscale arguments. These quantum tasks need a new approach to develop more comprehensive practices. The fact is that without a mathematical model of the atom there is no satisfactory molecular definition either.

One way to set up the math model is to write a wavefunction for an atom, psi (Z), which defines the data point map for all of it’s mass and energy, atopologiacal psi function. That may only be done by relative quantum rules, since the Lorenz-Einstein transform functions for time, mass, and energy must be applied to the workon quantum wavefunction rules for frequency and wavelength to model the pico and femtometric atomic features accurately.

When the atom is defined by rates of nuclear emission of positrons and gravity the core mass may be represented as transforming to forcons with valid joule values by {e=m(c^2)} radiation. Four forcons animate atoms: time, probability, magnetism, gravity.

The psi pulsates at the fequency {Nhu=e/h} by a cycle of alternate emission and absorption of force within spacetime boundaries represented by {gravity-time}. Next, the rate of nuclear radiation is expanded as a series of orders to model output of the spectrum of force fields along a cycle. That sets up the unified field GT integral atomic topofunc.

In brief, when the psi’s internal momentum function is written, rearranged to give the photon gain rule, and integrated for GT limits, the result is a series of 26 topological wavefunctions for the energy intermedon particles of the atom’s outer cloud of 5/2 kT J heat capacity energy. Those intermedon sizes intersect the values for the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton, k, 5/2 k, 3/2 k.

This model projects an accurate 3D atomic video image of picoyotechnical detail, with exact topological images for the five classes of intermedons as well: positrons, workons, thermons, electromagnetons, magnemedons. Femtotechnical electron imaging follows.

Images of the h-bar magneparticle of ~175 picoyoctometers are available online at http://www.symmecon.com along with discussions, graphics, essays, and infotools for MAVCAM (molecular or material animated video computer assisted modeling) build projects.