Solid State Quantum Computer

Rajan Sharma, Leeds, UK


Introduction

Physical realization of Quantum computers (QC) have been demonstrated using spins on a molecules in a NMR experiment, polarization of light in a laser or the energy of atoms in a trap. But the main problem with these techniques lies either in scaling the number of qubits to a useful value without losing the purity of quantum state (decoherence time), or, complexity involved in the setup to address and manipulate many qubits, optical implantation for example [1].

In solid state systems, the spin states of either electron or nuclei, form two-level systems which can be represented as qubits. Quantum computer realizations rely on interaction between spins. Also, localised spins are available via confinement to quantum dots or impurity atoms. Fabrication techniques for Quantum dots (QDs) are available down to the single-electron spin but not has been implemented with impurity atoms [1]. The basic idea was given by Loss and DiVincenzo (QDs), which were later adapted to impurity spins by Kane, and now have been extended to optically driven spin based system by Rossi and Zoller and Sham et al [2]. All three approaches have been briefly described here. Solid state QC: The Vincenzo criteria According to DiVincenzo criteria for a system to be a candidate for implementation of quantum computer [2], it should: 1. Be a scalable system with well-characterized qubits. 2. Be initializable to a simple fiducial state: Includes how well the qubits can be initialized, how quickly they can be reset and how long the initialization takes place. 3. Have much longer decoherence times: Longer than gate operation time. 4. Have a universal set of quantum gates: Ability to perform rotations of single qubits together with two qubit coupling to perform all universal gate operations. 31P system as the best candidate for its implementation. Also it has been found out that for this system at T=1.5K, the electron spin relaxation time of Si is thousand of seconds (1 ms) and the nuclear spin relaxation time for the donor 31P atom is 10 hr [5-7].

II) Electron spins in GaAs QDs: Gated Qubits

DiVincenzo et al, proposed spin of a excess single electron confined to a quantum dot as a qubit that can be manipulated for quantum computations [8].

Coherent interaction between pair of qubits represents the basic quantum computation. This can be manipulated by the gating of the tunneling barrier between neighbouring dots i.e. pair of qubits. If the barrier potential is high the tunneling between the two dot is forbidden and no change in qubit state is performed. However if the potential is lowered down, spin gets subjected coupling given by

Hs(t) =J(t) S1. S2 (1) Where J(t) is the exchange coupling constant and Si is the spin-1/2 operator for the dot i.

In the proposed method spin rotation is achieved by exciting a pulsed magnetic field onto spin Si by a scanning probe tip or alternatively fabricating an auxillary dot (among the two dot pairs) made of insulating ferromagnetic material. Lowering of potential causes electronic wave-function overlaps for a fixed time thereby causing the rotation of spins.

Two scheme for qubit measurement was given: First involves switchable tunneling into supercooled paramagnetic (PM) dot. For performing measurements electron tunnels to PM dot, nucleating from a metastable state to a ferromagnetic domain whose magnetization can be measured by conventional means. Other includes spin dependent switchable ‘spin-valve (SV)’ tunnel barrier. When measurement needs to be performed the spin valve is switched so that only the up-spin electron passes into a third QD. The presence of electron on third dot can be measured externally and gives indication that spin had been up.

of ground state exciton phonon is approximately 1ns limited by excitonic life-time. Figure 3 below shows the proposed device. s

Fig. 3. Quantum dots and energy level scheme. Left: the excess electron is in state | - 1/2> = |0> and the transition induced by a polarized light is blocked. Right: the excess [6] Wilson, D.K. et al; Phys. Rev. 124, 1068–1083 (1961). electron is in | + 1/2> = |1> and the exciton can be excited. (from Ref 9) Conclusion

Although semiconductor QC system offer inherent scalability apart from offering compatibility with present microelectronics industry and a well defined two-level system, but the approach however suffers from background impurity levels problems, single spin read-write operations and extension to 2-D arrays via gate techniques is challenging. Further work is being done and is required to address these issues in detail.

[9] Pazy, E., E.Biolatti, T.Calarco, I.D'Amico, P.Zanardi F.Rossi, and P.Zoller “Spin-based optical quantum gates via Pauli blocking in semiconductor quantum dots,” (19-Sep-2001) preprint cond-mat/0109337. Contibutor: "Rajan Sharma is doing a PhD in Nanobioelectronics at School of Electrical and Electronics Engineering. He completed MS in Nanoelectronics with distinction from University of Leeds. He graduated from NIT Jalandhar, India with a first class degree and distinction in Instrumentation and Control Engineering. Currently he is working on his PhD project of nanowire self assembly of nanowires with biomolecules at Nanobioelectronics lab."



References:

[1] Nielsen, M. A. & Chuang, I. J. Quantum Computation and Quantum Information; Cambridge Univ. Press, Cambridge, 2000.

 

5. Permit high qubit-specific measurements capability: Read out the state of a specific qubit with high accuracy.
6. Have the ability to interconvert stationary and flying qubits: This can allow connection of different parts of quantum computer and act as a bus. 7. Have the ability to faithfully transmit the flying qubits between specified location.

I) Realization using nuclear spin of 31P donors in Si

Kane proposed of building a solid-state quantum computer by manipulating array of nuclear spin located on the donor 31phosphorous atoms in silicon [3]. In his proposal the nuclear spins of the 31phosphorus nuclei constitutes the qubits; which is manipulated using a combination of static magnetic, static electric and oscillating radio-frequency magnetic fields. As shown in figure single spin operation is performed by changing the voltage on the metallic gate electrode (‘A’ gate) located each above the 31phosphorous nuclei. Spin-flips or electron-mediated interaction between the two nuclei is carried out by pulsed rf field i.e. by applying voltage to metallic electrode placed between them (‘J’ gate).

s

Measurements can be done by transferring the nuclear spin polarization to the electrons and determining the electron spin state by its effect on the orbital wave function, which can be done by capacitance measurements between adjacent gates. Requirement of donor nuclear spin state I=0 and shallow donor with nuclear spin state I=1/2 made Si: sd

Fig 2: Two coupled quantum dots 1 and 2, containing one single excess electron (e) with spin 1/2 (from Ref 4). Also, for the preparation of the initial state of the system is, a simple initial state like all spins up can be created if the system is cooled in a uniform magnetic field; where acceptable spin polarization of electrons are achievable at cryogenic temperatures. Minimum decoherence time for systems are found to be atleast 1µs for electrons in GaAs [4].

III) Optically Measured QD qubits

Zoller et al have proposed a spin based optical quantum computation via Pauli blocking in QDs [9]. The device is based on the spin of electrons confined on to a semiconductor quantum dots. The qubit of the system is represented by the excess electron spin in a quantum dot defining |0> and |1>. Two qubit gate quantum operations by the spin were mediated by exciton interactions. Quantum registers in the proposed scheme consisted of arrays of GaAs based QDs each containing an excess electron for conduction.

Quantum operations are performed based on Pauli’s blocking mechanism in quantum dots. Quantum dots can be individually addressed and the Coulomb interactions are obtained by shining a polarized laser pulse on the quantum dot. Due to Pauli’s exclusion principle a heavy electron pair is created in the s-shell only if the excess electron present in the QD has a spin projection of 1/2. Thus precise spin control of the switching on and off of further Coulomb interactions is made possible. Presence of photo generated electron pair is required only during the gating, after which latter is annihilated via a second laser pulse. Thus switching on and off the exciton interactions. The dephasing times

[2] Solid State Approaches to Quantum Information Processing and Quantum Computing: A Quantum Information Science and Technology Roadmap April 2004. URL: http://qist.lanl.gov

[3] Kane, B.E.,“A silicon-based nuclear spin quantum computer,” Nature 393, 133–137 (1998).

[4] URL: < http://www.physics.ohio-state.edu/~ hammel/ ssqc.html >

[5] Feher, G. Phys. Rev. 114, 1219–1244 (1959).

[6] Wilson, D.K. et al; Phys. Rev. 124, 1068–1083 (1961).

[7] Waugh, J. S. et al; Phys. Rev. B 37, 4337–4339 (1988).

[8] Loss, D. and D.P.DiVincenzo, “Quantum computation with quantum dots,” PhysicalReview A 57, 120–126 (1998).

[9] Pazy, E., E.Biolatti, T.Calarco, I.D'Amico, P.Zanardi F.Rossi, and P.Zoller “Spin-based optical quantum gates via Pauli blocking in semiconductor quantum dots,” (19-Sep-2001) preprint cond-mat/0109337.

Contibutor: "Rajan Sharma is doing a PhD in Nanobioelectronics at School of Electrical and Electronics Engineering. He completed MS in Nanoelectronics with distinction from University of Leeds. He graduated from NIT Jalandhar, India with a first class degree and distinction in Instrumentation and Control Engineering. Currently he is working on his PhD project of nanowire self assembly of nanowires with biomolecules at Nanobioelectronics lab."



 

 

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