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Science

Fingerprinting Spin Qubits

J. Carlos Egues

Published Jul 22, 2005• 6 citations
Publisher

Abstract

Electrons not only have mass and charge, they also have magnetic properties directly related to their intrinsic spin. These spins can combine into quantum states of different spin parity, and such states may be useful as qubits in future quantum computers. As [Egues][1] discusses in his Perspective, [Engel and Loss][2] report in this issue a method for fingerprinting the spin states of electrons contained in quantum dot structures. By allowing the electrons to leak from one dot to another, and then using a nanowire to sense the presence of the spin states, the authors were able to perform a nondestructive spin-parity measurement. Such a spin-parity detector should permit the manipulation of quantum dot qubits for quantum computation. [1]: http://www.sciencemag.org/cgi/content/full/309/5734/565 [2]: http://www.sciencemag.org/cgi/content/short/309/5734/586

DOI
10.1126/science.1115256

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Electrons not only have mass and charge, they also have magnetic properties directly related to their intrinsic spin. These spins can combine into quantum states of different spin parity, and such states may be useful as qubits in future quantum computers. As Egues discusses in his Perspective, Engel and Loss report in this issue a method for fingerprinting the spin states of electrons contained in quantum dot structures. By allowing the electrons to leak from one dot to another, and then using a nanowire to sense the presence of the spin states, the authors were able to perform a nondestructive spin-parity measurement. Such a spin-parity detector should permit the manipulation of quantum dot qubits for quantum computation.
Quantum dots are microscopic structures that can trap single electrons for study and manipulation. Such devices are of interest as potential logic elements in a future quantum computer in which electron spins are used as quantum bits. The problem is that the spins on the nuclei of the device material itself can interfere with the electron spins. In his Perspective, [DiVincenzo][1] discusses results reported in the same issue by [ Petta et al. ][2] in which a double quantum dot structure was used to avoid the effect of the background spins. By swapping the quantum spin states back and forth between the dots, the researchers were able to greatly increase the quantum coherence time of the stored states. The results show that fully electric (as opposed to magnetic) control of the spin states offers the possibility of using such double dots in a quantum computer. [1]: http://www.sciencemag.org/cgi/content/full/309/5744/2173 [2]: http://www.sciencemag.org/cgi/content/short/309/5744/2180
There is great interest in exploiting the unique behavior of quantum systems for computation, but building real devices has proved difficult. One approach is to use electron spin to represent the qubits (quantum bits) in a computational device. In their Perspective, [Glazman and Ashoori][1] discuss results reported in the same issue by [ Craig et al .][2] on using quantum dots as quantum logic elements. The dots act as artificial atoms, with the number of electrons on each subject to control. The electron spins in a pair of quantum dots interact with each other, and the Kondo effect enables detection of the state of the spin pair. This ability to control and detect the interaction between the spins may one day find use in quantum computation. [1]: http://www.sciencemag.org/cgi/content/full/304/5670/524 [2]: http://www.sciencemag.org/cgi/content/short/304/5670/565
A two-level quantum system is the building block of a quantum computer. This pair of quantum states defines the computational unit of a quantum computer, and it is called a quantum bit or qubit in analogy to the bit that is the binary unit of a classical computer. The spin of a single electron naturally defines such a two-level quantum system. A quantum dot can be tuned to the single-electron regime, and an array of singly occupied quantum dots provides a multi-qubit register. This thesis describes the multielectron encoding of a spin qubit using a pair or a trio of quantum dots, and it analyzes the coherence properties and manipulation protocols of this system. The singlet-triplet qubit, coded using the singlet state and the spinless triplet state of a pair of singly occupied quantum dots, can be controlled all electrically when applying voltages to gates close to the quantum dot structure. Rapid, subnanosecond modifications of the double quantum dot's charge configuration have been realized successfully. A small magnetic field gradient across the double quantum dot enables universal qubit control. Two modifications of the normal singlet-triplet encoding are introduced. (1) The six-electron configuration of a double quantum dot encodes a singlet-triplet qubit in the same way as for the two-electron double quantum dot. Two electrons at each quantum dot are irrelevant for the qubit manipulations because they are paired in a singlet state; the remaining two electrons encode the qubit. The qubit's wave function is immune to charge noise at moderate out-of-plane magnetic fields. (2) A singlet-triplet qubit encoded using two quantum dots of different sizes has an orbital state degeneracy of the singlet state and the spinless triplet state at finite out-of-plane magnetic fields. Spin-orbit interactions lift this state degeneracy, while the magnitude of the state coupling is determined by the size difference of the QDs. This setup enables the manipulations of singlet-triplet qubits without the need for magnetic field gradients. Finally, two-qubit gates between singlet-triplet qubits are proposed that use mediated exchange interactions via one quantum state. These operations are well controlled and highly noise insensitive. Orbital interactions alone can control spin qubits coded in a three electron Hilbert space. For example, the exchange-only qubit is encoded using three singly occupied quantum dots. The exchange interactions of two quantum dot pairs need to be modified to manipulate this qubit. The noise sensitivity of the exchange-only qubit is discussed. Alternatively, a three-electron qubit at a double quantum dot can be operated when single electrons are transferred between the quantum dots. Fast, subnanosecond manipulations of the double quantum dot's charge configuration are required to realize single-qubit gates. A novel two-qubit pulse gate for the three-electron double quantum dot qubit is proposed.
The interaction of electrons and photons lies at the heart of quantum physics. The \nmost notable phenomena which are described by quantum physics but which obviously \ninvalidate a classical description of the electromagnetic field - the photoelectric \neffect, the Compton effect, or the antibunching of photons emitted from a single atom, \nto mention a few - are intimately related to the interaction of electrons and photons. \nElectrons possess an internal degree of freedom, the spin. The spin S of an electron \ncan be described as an internal angular momentum, leading to a magnetic moment \nm due to the electric charge of the electron. Stern and Gerlach have shown that \nthe projection of m onto a quantization axis (defined by an external magnetic field \nin their experiment), e.g., along the z axis, is either mz = g�μB/2 (\\spin up") or \nmz = g�μB=2 (\\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton \nand g is the g-factor of the electron (g = 2 for free electrons). \n \n An electron spin \nis therefore usually referred to as a two-level system. Due to this property, the \nspin of electrons which are localized in semiconductor quantum dots has recently \nattracted significant attention regarding the implementation of quantum information \nprocessing: Electron spins can be used as carriers of quantum information. One \ncan define that the spin pointing "up" corresponds to the logical value "0" and \nthe spin pointing "down" corresponds to "1". Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. Moreover, because the electron spin \nis a quantum mechanical property one can form arbitrary coherent superpositions of \n"up" and "down" with a single spin. A system with this property is called a quantum \nbit (qubit). The additional possibilities due to quantum superpositions of qubits are \nexploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks \nmuch more efficiently than with a classical computer (i.e., the prime factorization of \nlarge numbers for Shor's algorithm and the search within an unstructured database for \nGrover's algorithm). While quantum computation has presently only been achieved \nin prototypical experiments with few qubits, the implementation of efficient largescale \nquantum computation with many qubits still remains an extremely demanding \ntask. Yet, other quantum mechanical properties of qubits, such as entanglement, \nhave already been exploited experimentally with photons in quantum communication \nschemes, for example, quantum teleportation and quantum data compression. \nIn this thesis, we investigate the interaction of electrons and photons in semiconductor \nquantum dots. Optical transitions in quantum dots enable a direct link between \nelectron spins and photon polarizations due to conservation laws. We show that \n \nentanglement can be transferred from electron spin qubits to qubits defined by the \nphoton polarization, enabling the measurement of entangled spin states via photons. \nThe mechanism under study can also be used for the production of entangled photons, \nfor instance for the implementation of quantum communication protocols. In contrast \nto the presently used sources of entangled photons, the photon source we propose here \nis deterministic, providing entangled photons on demand. It has been demonstrated \nin several recent experiments that the most obvious way to achieve such a transfer of \nentanglement - using the recombination of biexcitons in a single quantum dot - fails \nin the presently available quantum dot structures. We have analyzed the problems \nof this approach. As a solution, we propose schemes based on charged excitons in \nsingle or coupled quantum dots. We discuss the generation of entangled two- and \nfour-photon states. \nIn addition to the transfer of quantum states, photons can also be used to probe \nelectron spin states. We investigate in detail different methods to optically measure \nthe decoherence time of a single electron spin in a quantum dot. The decoherence time \nof a spin establishes the time scale during which coherent manipulation is possible. \nMeasurements of the electron spin decoherence time are therefore highly desirable \nin view of the implementation of spin-based quantum information processing. We \nshow that the schemes we propose can be implemented with current experimental \ntechniques. \nWe then study the magneto-optical effect called Faraday rotation. Using the technique \nof time-resolved Faraday rotation, a recent experiment has demonstrated the \ncoherent transfer of spin between quantum dots coupled by molecules. We calculate \nthe Faraday rotation signal for a coupled dot system and show that a two-site \nHamiltonian with a transfer term captures the essential features observed in this experiment. \nWe also present results for a system of two coupled dots doped with a \nsingle electron. \nWe finally show that the coupled states of two qubits can be detected via the optical \ninteraction with a cavity in the dispersive regime. We present a Schrieffer-Wolff \ntransformation which removes the coupling of the two qubits to the cavity in leading \norder. The different two-qubit states lead to a different spectral shift of the cavity \nline. For a sufficiently low cavity linewidth, this enables the direct readout of a \ntwo-qubit system.
Quantum Devices To date, the most promising solid-state approaches for developing quantum information-processing systems have been based on the circulating supercurrents of superconducting circuits and manipulating the spin properties of electrons in semiconductor quantum dots. Hays et al. combined the desirable aspects of both approaches, the scalability of the superconducting circuits and the compact footprint of the quantum dots, to design and fabricate a superconducting spin qubit (see the Perspective by Wendin and Shumeiko). This so-called Andreev spin qubit provides the opportunity to develop a new quantum information processing platform. Science , abf0345, this issue p. [430][1]; see also abk0929, p. [390][2] [1]: /lookup/doi/10.1126/science.abf0345 [2]: /lookup/doi/10.1126/science.abk0929