Project Description
Quantum Gates
An important and crucial point in our research plan is the construction of quantum gates.
In order to perform arbitrary quantum computations, it must be possible to realisea universal set of gates. It is known that
- arbitrary single qubit operations, and
- two-qubit gate capable of generating maximal entanglement from a product state
form a universal set. Such gates can be performed with magnetic qubits. This requires
- controlled coupling of external sources to qubits, and
- controlled interaction between qubits.
In our research project we aim the realisation of single magnetic qubit gates by effectively producing Rabi oscillations between the ground state and the first excited state for the two cases (1) and (2).
As was mentioned above, we may use two different frequency ranges:
- one associated with the energy gap that corresponds to the ferrimagnetic resonance of a single domain particle, and
- the other associated with the gap that corresponds to the quantum splitting in the presence of tunneling, which can be varied by the external field.
Current technology allows the feasibility of
- these two frequency ranges,
- the time interval between pulses, and
- the control of the whole system.
In more detail, magnetic qubits can be manipulated in an analogous manner to themanipulation of spins in ensemble NMR quantum computation.
Application of a resonant pulse effects a rotation (proportional to the time-field product) about an axis in the x-y plane. (Rotations about the z-axis can be achieved through combination of x- and y- rotations.)
That is, the verification of one-qubit gate using magnetic qubits would require thefitting of the energy gap between the two lowest levels to the natural frequency of the SQUID detector. This should not be very difficult as
- the energy gap in the case of clusters may be tuned to the external transverse field, and
- in the case of particles, the precession frequency depends on the anisotropyand total spin of the particles and both parameters may be varied.
In an ideal system, a two-bit operation on qubits 1 and 2 can be achieved by turning on the interaction
Hint = J S1 . S2
between the clusters for a certain length of time. Denoting (for example) spin up as the logical state |0> and spin down as the logical state |1>, it is possible to achieve a“square root of swap” gate,
Usw1/2 = exp(-i π/8) exp(i π/2 S1 . S2),
by turning on the coupling J for a time so that its integrated effect generates the appropriate phase in the second exponential.
Along with single qubit rotations, this gate Usw1/2 forms a universal set for quantum computation.
If twice the phase is generated, this is the familiar “swap” operation
Usw = exp(-i π/4) exp(i π S1 . S2),
which generates
- |0102> → |0102>
- |1102> → |0112>
- |0112> → |1102>
- |1112> → |1112> .
We note that this is not a universal gate: Usw1/2 as defined above is needed for universality, so it is important to have control over Hint.
