The Pleasures on the Road to a Quantum Computer

Bernd Braunecker and Daniel Loss, Departement für Physik und Astronomie, Universität Basel

 

Quantum computing has a variety of properties that make it attractive for tasks that are particularly hard for classical computers. The most popular ones are perhaps their efficiency in factoring large numbers and thus in code breaking, or fast database searching algorithms. As important for physicists may be the intriguing possibility of simulating quantum systems per se in a controlled way.

Figure 1: A double quantum dot. Top gates confine electrons in the two-dimensional electron gas to the circular regions. A negative voltage on the backgate depletes the dots until they contain a single electron with a spin ½ described by SL and SR. The corresponding |↑⟩ and |↓⟩ states form the qubit basis.

Yet a quantum computer can only become really useful if it can be fabricated at large scale, at low cost, and if its constituents, the qubits (energetically degenerate 2-level systems with states |0⟩ and |1⟩), allow a reliable initialization, operation, and readout. With the expertise of the semiconductor industry, acquired over the last decades as the basis of the triumphant success of classical computers, it is suggestive to rely on the same technology for a quantum computer. If we take this as our starting point (there are many other propositions though), the challenge for a quantum engineer is then to produce a viable semiconductor qubit. Interestingly, however, this turns out not to be an engineering task but a problem of fundamental physics. It requires the understanding of the physical processes from the foundations of quantum mechanics to many-body physics, and the full set of methods of modern physics at our disposition.

As an illustration, we give here one specific example from our theory group at the University of Basel. The basic qubit is the spin of an electron confined to a semiconductor quantum dot (see Figure 1). It forms a natural 2-level basis, |0⟩=|↑⟩ and |1⟩=|↓⟩. Scalability as well as operability can be granted through local, all-electronic control (gating) of the exchange interactions between neighboring quantum dots [1]. The qubit operates through quantum superpositions of its basis states, |ψ⟩=a|0⟩+b|1⟩.

Here the main source of errors of a quantum computer becomes visible: The quantum algorithm strongly depends on the fixed ratio of the amplitudes a and b. This ratio is distorted by any uncontrolled interaction with the rest of the universe. This is known as decoherence. In order to devise a plan to protect the qubit from decoherence, we must, therefore, understand how it interacts with its environment. In a GaAs semiconductor environment the main two sources of decoherence for a spin qubit are spin-orbit coupling and the hyperfine interaction with the nuclear spins. This is many-body physics.

Figure 2: Illustration of the hyperfine interaction of the electron spin in the quantum dot with nearby nuclear spins. Disorder of the nuclear spins is an important source of decoherence (left). It can be largely reduced by polarization of the nuclear spins (right) as, for instance, achieved through a ferromagnetic phase transition triggered by many-body interactions.

Let us focus on the hyperfine interaction only. Decoherence is mainly due to interaction with a disordered ensemble of nuclear spins. The decoherence time can be largely extended, however, if the nuclear spins are fully polarized [2] (see Figure 2). This usually would require a very strong external field, but interestingly can also be achieved differently. One possibility is described in [3]: The nuclear spins are well separated on the crystalline lattice and their direct interaction is weak. More significant, however, is their indirect interaction through the electron spins. As shown in [3] this interaction can induce a phase transition to a nuclear ferromagnet. If the electrons were not interacting, the transition temperature would lie at Tc = 0K, but electron-electron interactions and the resulting non-Fermi-liquid behavior drive it up to the millikelvin range for typical confined two-dimensional electron gases in semiconductors. This temperature lies within the reach of state-of-the-art experimental setups. A full polarization and so the elimination of a major source for decoherence can thus be achieved by cooling the system down through the transition temperature. The polarization persists upon subsequent reheating. The precise understanding of such processes is thus an essential ingredient in the prospect of implementing a fully controllable quantum computer.

With this specific example we have shown that the design of a quantum computer is intimately connected to the solution of problems of fundamental research. The above example, for instance, can be formulated as a Kondo lattice problem, a typical representative of strong correlation physics. Such problems are challenging, modern, and, last but not least, pleasurable for the active researchers.

 

[1] D. Loss and D. P. Di Vincenzo, Quantum computing with quantum dots, Phys. Rev. A 57, 120 (1998); V. Cerletti, W. A. Coish, O. Gywat, and D. Loss, Recipes for spin-based quantum computing, Nanotechnology 16, R27 (2005) [http://arxiv.org/abs/cond-mat/0412028]; W. A. Coish and D. Loss, Quantum computing with spins in solids, http://arxiv.org/abs/cond-mat/0606550 (2006).
[2] A. V. Khaetskii, D. Loss, and L. Glazman, Electron spin decoherence due to interaction with nuclei, Phys. Rev. Lett. 88, 186802 (2002); W. A. Coish and D. Loss, Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics, Phys. Rev. B 70, 195340 (2004).
[3] P. Simon and D. Loss, Nuclear spin ferromagnetic phase transition in an interacting two dimensional electron gas, Phys. Rev. Lett. 98, 156401 (2007) [http://arxiv.org/abs/cond-mat/0611292].

 

The main research focus in the Condensed Matter Theory group of Prof. D. Loss at the University of Basel is on Spintronics and Quantum Computing. Much emphasis is put on understanding and proposing realistic implementations of a quantum computer. Indispensable here is the close contact with experimental groups. With the Center of Excellence in Quantum Computing and Quantum Coherence (QC2) and the NCCR Nanoscale Science program, combining experimental and theoretical groups, Basel offers an ideal environment for this activity, and allows us to keep an international high scientific standard. [More information]

 

[Released: April 2007]