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Josephson junction persistent current elements for quantum computation
Microelectronic Engineering 47 (1999) 3-5
Josephson Junction Persistent Current Elements for Quantum Computation J.E. Mooij Department of Applied Physics and DIMES Institute Delft University of Technology, P.O. Box 5046,260O GA Delft [email protected] Quantum computers, if realized, could perform certain calculations that are beyond the potential of classical computers [ 11. The basic elements for quantum computers are qubits. These can exist in a general superposition of two well-defined quantum states. Qubits are made to interact; the so-called controlled-not gate is a particularly useful example that can entangle the information between qubits. The quantum state of the whole quantum computer is transformed by unitary transformations; any of those transformations can be obtained by a succession of single qubit operations and controlled-not actions. If realized with sufficient size, a quantum computer can perform certain operations (e.g. the factorization of a very large number) that cannot be performed by a conventional computer. For a computation, the quantum computer is first prepared in a well-defined state, transformations are performed whereby no interaction is allowed with uncontrolled degrees of freedom outside the system, and finally the resulting state is measured. The measurement constitutes a collapse onto classical variables that destroys the quantum state. Error correction is possible during computation for low error probabilities. Hardware realisations of quantum computers are developed with trapped atoms or ions combined with single photon laser pulses [2] and with NMR on interacting spins in a large number of identical molecules.[3] In such systems the necessary experience already exists to perform controlled Rabi oscillations (rc, n/2, n/4 pulses) on two-level states and to manipulate the coupling between such qubits. The prospects for integration into large quantum computers that could be of practical value are poor, however. Solid state systems have the disadvantage of a large number of degrees of freedom that can easily lead to decoherence. Energy values may also vary with the individual dimensions of samples or with the presence of charged impurities. On the other hand, lithographically fabricated solid state sitemaps lend themselves easily to controlled large-scale integration. Various proposals have been put forward for semiconductor realizations gates for quantum computations. Spin polarized states in semiconductor are expected to have a relatively long coherence time.[4] Such states of artificial atoms may provide a qubit, coupling by tunneling the required 0167-9317/99/$ - see front matter PII: SO167-9317(99)000131-8
0
1999 Elsevier Science B.V. All rights reserved.
of qubits and quantum dots one-electron controlled-not
J.E. Moo{
4
I Microelectronic
Engineering 47 (1999) 3-5
gate. It has also been suggested that atoms with particular nuclear spin may be located at precisely determined positions in a semiconductor lattice.[5] The nuclear spin interacts with the electron spin through the hyperfine coupling. With gates, the electron cloud could be displaced, thereby altering the interaction with the nuclear spin. This scheme could be used for single qubits as well as controlled-not gates. Superconducting tunnel junction circuits, where all electrons in an isolated metallic region share the same quantum state separated by a gap from the continuum of quasiparticles, have a strong advantage.[6] In these circuits, two energy scales are relevant: the Josephson coupling energy and the Coulomb charging energy for single Cooper pairs. In circuits where the charging energy dominates, the numbers of Cooper pairs on superconducting island are strongly fixed. On the other hand, when Josephson tunneling is strong, linking the quantum phases on either side of the barrier, the Cooper pair numbers are undetermined. In fact, number and phase are non-commuting quantum variables. In fabrication, the ratio between charging energy and Josephson energy can be varied over a wide range. We favour the other regime, where the Josephson energy is larger, because practical charging circuits are susceptible to noise due to moving charged defects. We have designed a new type of qubit that consists of a closed loop with three Josephson junctions, without connecting leads.[7] The applied flux through the loop is close to half a flux quantum. The states are clockwise and anti-clockwise persistent current states. In loops of size 1 to 2 urn, these currents have a small but measurable flux associated with them of order 10” flux quanta. One of the three junctions is smaller than the others. Tunneling between the two states is possible if the capacitance (the mass) is small enough, the value of the tunneling matrix element can be adjusted by the choice of the ratio of charging energy to Josephson energy. The barrier height is determined by the ratio of the Josephson energy of the junctions. Through a suitable choice of these two ratios, it is possible to make the device insensitive to gate voltages and offset charges.
EJ >
Design of the basic qubit. Left: principle of the three-junction loop; a is about 0.75. For the flux in the loop equal to half a flux quantum @‘,,the clockwise and anticlockwise persistent current states have equal energy, offset from 0.5 sets the energy differ-
J.E. Mooij I Microelectronic Engineering 47 (1999) 3-5
ence between the qubit states. Right: arrangement where the top junction is made into a SQUID, with enclosed flux a’,. Time-dependent change of cxleads to Rabi oscillations.
The qubit can be operated by modulation of the tunneling barrier. For this purpose, the top junction is made into a SQUID. The flux in the SQUID, that can be independently changed, is modulated at the frequency of the energy difference. In this way, Rabi oscillations are induced. Qubits can be coupled through coupling loops on a second lithography level, and controlled-not gates can be designed in this way. Prototype qubits will be tested in the near future. Acknowledgements: T.P. Orlando, L. Levitov, L. Tian, C. van der Wal and S. Lloyd are collaborators in the project, performed together with Massachusetts Institute of Technology. I thank FOM, US Army Research Office and NED0 for support. References 1. e.g. D.P. Divincenzo, Science 270,255 (1995) 2. C. Monroe, D.M. Meekhof, B.E. Ring, W.M. Itano and D.J. Wineland, Phys.Rev.Lett. 75,4714 (1995) 3. N.A. Gershenfeld, I.L. Chuang, Science 277,1688 (1997) 4. D. Loss , D.P. Divincenzo, Cond-Mat 9701055 5. B.E. Kane, Nature 393,133 (1998) 6. A. Shnirman, G. Schoen, Z. Hermon, Phys.Rev.Lett. 79,2371(1997) 7. J.E. Mooij, T.P. Orlando, L. Levitov, L. Tian, C.H. van der Wal, S. Lloyd, submitted to Science
5
Josephson Junction Persistent Current Elements for Quantum Computation J.E. Mooij Department of Applied Physics and DIMES Institute Delft University of Technology, P.O. Box 5046,260O GA Delft [email protected] Quantum computers, if realized, could perform certain calculations that are beyond the potential of classical computers [ 11. The basic elements for quantum computers are qubits. These can exist in a general superposition of two well-defined quantum states. Qubits are made to interact; the so-called controlled-not gate is a particularly useful example that can entangle the information between qubits. The quantum state of the whole quantum computer is transformed by unitary transformations; any of those transformations can be obtained by a succession of single qubit operations and controlled-not actions. If realized with sufficient size, a quantum computer can perform certain operations (e.g. the factorization of a very large number) that cannot be performed by a conventional computer. For a computation, the quantum computer is first prepared in a well-defined state, transformations are performed whereby no interaction is allowed with uncontrolled degrees of freedom outside the system, and finally the resulting state is measured. The measurement constitutes a collapse onto classical variables that destroys the quantum state. Error correction is possible during computation for low error probabilities. Hardware realisations of quantum computers are developed with trapped atoms or ions combined with single photon laser pulses [2] and with NMR on interacting spins in a large number of identical molecules.[3] In such systems the necessary experience already exists to perform controlled Rabi oscillations (rc, n/2, n/4 pulses) on two-level states and to manipulate the coupling between such qubits. The prospects for integration into large quantum computers that could be of practical value are poor, however. Solid state systems have the disadvantage of a large number of degrees of freedom that can easily lead to decoherence. Energy values may also vary with the individual dimensions of samples or with the presence of charged impurities. On the other hand, lithographically fabricated solid state sitemaps lend themselves easily to controlled large-scale integration. Various proposals have been put forward for semiconductor realizations gates for quantum computations. Spin polarized states in semiconductor are expected to have a relatively long coherence time.[4] Such states of artificial atoms may provide a qubit, coupling by tunneling the required 0167-9317/99/$ - see front matter PII: SO167-9317(99)000131-8
0
1999 Elsevier Science B.V. All rights reserved.
of qubits and quantum dots one-electron controlled-not
J.E. Moo{
4
I Microelectronic
Engineering 47 (1999) 3-5
gate. It has also been suggested that atoms with particular nuclear spin may be located at precisely determined positions in a semiconductor lattice.[5] The nuclear spin interacts with the electron spin through the hyperfine coupling. With gates, the electron cloud could be displaced, thereby altering the interaction with the nuclear spin. This scheme could be used for single qubits as well as controlled-not gates. Superconducting tunnel junction circuits, where all electrons in an isolated metallic region share the same quantum state separated by a gap from the continuum of quasiparticles, have a strong advantage.[6] In these circuits, two energy scales are relevant: the Josephson coupling energy and the Coulomb charging energy for single Cooper pairs. In circuits where the charging energy dominates, the numbers of Cooper pairs on superconducting island are strongly fixed. On the other hand, when Josephson tunneling is strong, linking the quantum phases on either side of the barrier, the Cooper pair numbers are undetermined. In fact, number and phase are non-commuting quantum variables. In fabrication, the ratio between charging energy and Josephson energy can be varied over a wide range. We favour the other regime, where the Josephson energy is larger, because practical charging circuits are susceptible to noise due to moving charged defects. We have designed a new type of qubit that consists of a closed loop with three Josephson junctions, without connecting leads.[7] The applied flux through the loop is close to half a flux quantum. The states are clockwise and anti-clockwise persistent current states. In loops of size 1 to 2 urn, these currents have a small but measurable flux associated with them of order 10” flux quanta. One of the three junctions is smaller than the others. Tunneling between the two states is possible if the capacitance (the mass) is small enough, the value of the tunneling matrix element can be adjusted by the choice of the ratio of charging energy to Josephson energy. The barrier height is determined by the ratio of the Josephson energy of the junctions. Through a suitable choice of these two ratios, it is possible to make the device insensitive to gate voltages and offset charges.
EJ >
Design of the basic qubit. Left: principle of the three-junction loop; a is about 0.75. For the flux in the loop equal to half a flux quantum @‘,,the clockwise and anticlockwise persistent current states have equal energy, offset from 0.5 sets the energy differ-
J.E. Mooij I Microelectronic Engineering 47 (1999) 3-5
ence between the qubit states. Right: arrangement where the top junction is made into a SQUID, with enclosed flux a’,. Time-dependent change of cxleads to Rabi oscillations.
The qubit can be operated by modulation of the tunneling barrier. For this purpose, the top junction is made into a SQUID. The flux in the SQUID, that can be independently changed, is modulated at the frequency of the energy difference. In this way, Rabi oscillations are induced. Qubits can be coupled through coupling loops on a second lithography level, and controlled-not gates can be designed in this way. Prototype qubits will be tested in the near future. Acknowledgements: T.P. Orlando, L. Levitov, L. Tian, C. van der Wal and S. Lloyd are collaborators in the project, performed together with Massachusetts Institute of Technology. I thank FOM, US Army Research Office and NED0 for support. References 1. e.g. D.P. Divincenzo, Science 270,255 (1995) 2. C. Monroe, D.M. Meekhof, B.E. Ring, W.M. Itano and D.J. Wineland, Phys.Rev.Lett. 75,4714 (1995) 3. N.A. Gershenfeld, I.L. Chuang, Science 277,1688 (1997) 4. D. Loss , D.P. Divincenzo, Cond-Mat 9701055 5. B.E. Kane, Nature 393,133 (1998) 6. A. Shnirman, G. Schoen, Z. Hermon, Phys.Rev.Lett. 79,2371(1997) 7. J.E. Mooij, T.P. Orlando, L. Levitov, L. Tian, C.H. van der Wal, S. Lloyd, submitted to Science
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