Molecular Magnets in the Field of Quantum Computing By Richard Cresswell Addison Huegel Contents Introduction Methods of Using Molecular Magnets as Qubits Improved Data Storage with Grover s Algorithm Di Vincenzo Evaluation Criticism Criteria for Molecular Magnets Large Molecules Little intermolecular interaction High total spin S High magnetic anisotropy directional dependence Fe8 Mn12 are both S 10 Fig 1 View of the structure of the Fe8 molecular cluster The iron atoms yellow carry the magnetic moments that in the ground state are arranged to give S 10 R Sessoli Europhysics News 34 2 2003 Using MM s as Qubits Case 1 Suppressed Spin Tunneling Fig 2 0 is the ground state in one of the wells and 1 is the first excited state separated by an energy gap set by the ferromagnetic resonance frequency J Tejada et al Nanotechnology 12 181 186 2001 Using MM s as Qubits Case 2 Spin Tunneling High magnetic anisotropy Sz Applying a longitudinal magnetic field Bz in the easy axis will result in a shift in the potential wells Bz Fig 3 Application of a longitudinal magnetic field causes a shift in the potential wells Spin Tunneling Additionally we apply a transverse magnetic field Bx For molecules like Mn12 and Fe8 the spin Hamiltonian at low temperatures is Spin Tunneling H H a H Z H Where 2 z H a AS BS 4 z H Z g B Bz S z Longitudinal Field H g B Bx S x Transverse Field J Tejada et al Nanotechnology 12 181 186 2001 Fig 4 The qubit states are the symmetric 0 and anti symmetric 1 combinations of the twofold degenerate ground state Sz S The energy splitting between the qubit states depends on the spin tunnelling frequency and can be tuned using an external magnetic field perpendicular to the easy axis of the molecular cluster Fig 5 Magnetisation of Mn12 as a function of magnetic field at six different temperatures R Friedman et al Phys Rev Let 76 20 1996 Review of Grover s Algorithm Improves on classical database search O N to O N1 2 UsU s Algorithm iterated until s system vector lies near to 2 desired state Probability of measuring state close to unity U Molecular Magnets As A Quantum Memory Device Utilize the spin eigenstates as qubits Each eigenstate represents a different binary unit i e 20 21 22 Apply a strong magnetic field along Z axis to initialise then decrease to bias strength Use modified Grover scheme as descibed by Ahn Weinacht and Bucksbaum Science 287 463 465 2000 and Grover Phys Rev Letters 79 4709 4712 1997 Potential Well and Spin Eigenstates Leuenberger and Loss Nature 410 789 793 2001 Superposition of States Apply two magnetic fields to induce transitions between eigenstates H m t cos m t m SX sin m t m SY g B H 0 t cos 0 t SZ Perturbation theory determines field frequencies and strengths Non equidistant energy level spacing means individual frequencies do not interact transitions and transitions populate all levels coherently with equal transition amplitudes as required by Grover s algorithm Transitions Between Spin Eigenstates Leuenberger and Loss Nature 410 789 793 2001 Data Read in Circularly polarised field adds individual phases to each transition amplitude 0 or 1310 11012 requires phases 9 8 7 0 6 5 as different states require different numbers of photons Transition amplitudes are then and form the basis of a s am m m m quantum data register 0 Decoding Data Magnetic pulses similar to the encoding process are applied but with different phases Phases are independent of stored data as the pulse acts as a unitary transform on the system So for previous example 9 7 5 0 and 6 8 Transform amplifies flipped bits other bits are suppressed marking up the state Transforms amplitude of states by Data Read out Irradiate system with pulse containing frequencies m 1 m Induce transitions between populated levels and neighbouring states Non equidistant energy levels give characteristic spectrum The Capabilities of This Device Capable of storing numbers as large as 22s 2 if both wells are utilised Even as high as M2s 2 if M phases are distinguishable Read in decode read out time of 10 10 s Measurement of spins made easier by ensemble nature of molecular crystals Crystals of length 10 m easily grown naturally Limitations Cannot scale to arbitrarily high spins decoheres to classical physics Hence limited number storage Requires the control of logMN frequencies Di Vincenzo Evaluation 1 Identifiable Qubits Case 1 In the suppressed tunneling method GS and 1st excited state are seperated by an energy equivalent to the ferromagnetic resonance frequency Case 2 Must be arranged in a controlled manner Di Vincenzo Evaluation 2 State Preparation Case 1 T much less than the energy gap 4K Case 2 Equilibrium at very low temperature mK in a transverse field Di Vincenzo Evaluation 3 Decoherence Resonance experiments have shown that quantum coherence can be maintained for at least 10ns Corresponding quality factor Q of 10 6 Note that the decay of an excited state cannot come through the spontaneous emission of a photon Di Vincenzo Evaluation 4 Quantum Gates Realisation of single qubit gates can be done by achieving Rabi oscillations between the GS and the 1st excited state Two qubit gates can be achieved by coupling neighbouring qubits through superconducting loops possibly with Josephson switches J Tejada et al Nanotechnology 12 181 186 2001 Fig 6 A schematic example of the coupled controlled qubit realization The magnetic qubits clusters particles yellow are arranged in a one dimensional lattice and coupled to the superconducting loops of micro SQUID red circuits as shown The coupling circuits blue contain Josephson switches green Di Vincenzo Evaluation 5 Measurement Individual microSQUIDs are needed to measure the spin state of the system Limitation of technology S 10 000 Criticism T dependence Individual system isolation Very low noise Thanks for Listening