Quantum Information:
Entanglement, Quantum Phase Transitions, Solid-State Processing
➤ The excitonic quantum computer
Processing information in a quantum mechanical fashion can provide, in some cases, a huge computational speed-up with respect to any classical device. From the fundamental point of view, this novel computational power relies on two basic quantum features: (i) superposition of states and (ii) quantum entanglement. These two ingredients, along with the unitary character of quantum dynamics, lie at the heart of the additional capability provided by quantum information/computation (QIC) processing.
We have proposed the first all-optical implementation of QIC with semiconductor macroatoms. Our quantum hardware consists of an array of quantum dots and the computational degrees of freedom are energy-selected interband optical transitions. The quantum-computing strategy exploits exciton-exciton interactions driven by ultrafast multicolor laser pulses. Contrary to existing proposals based on charge excitations, our
approach does not require time-dependent electric fields, thus allowing for a subpicosecond, decoherence-free, operation time scale in realistic semiconductor nanostructures.
References
E. Biolatti, R.C. Iotti, P. Zanardi, and F. Rossi, Quantum Information Processing with Semiconductor Macroatoms, Phys. Rev. Lett. 85, 5647 (2000).
E. Biolatti, R.C. Iotti, P. Zanardi, and F. Rossi, Optical quantum gates with semiconductor nanostructures, Int. J. Circ. Theor. Appl. 29, 137 (2001).
I. D’Amico, S. De Rinaldis, E. Biolatti, E. Pazy, R.C. Iotti, P. Zanardi, and F. Rossi, The excitonic quantum computer, phys. stat. sol (b) 234, 58 (2002).
➤ Spin-based architectures for Quantum Information Processing
In the past years, we have also proposed an alternative all-optical QIP implementation scheme, based on charge-plus-spin degrees of freedom in semiconductor quantum dots. In this scheme, while the qubit is the spin of an excess electron in a dot, quantum-information/computation operations rely on swapping spin superpositions via short laser pulses to charged excitonic states.
References
E. Pazy, 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 dot, Europhys. Lett. 62, 175 (2003).
This strategy merges ideas from both the fields of spintronics and optoelectronics: using spin as quantum memory and charge for the interaction between qubits, we can benefit
(i) from the relatively low spin decoherence rates of conduction electrons;
(ii) from ultrafast (sub-picosecond) optical gating of charge excitations. Indeed, coherent optical control of electronic spins as well as of excitonic state together with a proper tailoring of exciton-exciton Coulomb coupling, may allow for the implementation of single- as well as two-qubit gates, i.e., the full set of basic operations to implement quantum computing.
In the past years, the characterization of complex quantum phenomena has received a strong boost by the recent developments in quantum information theory. In particular, the notion of entanglement has been used to better characterize the critical behavior of different many-body quantum systems undergoing a quantum phase transition (QPT). The peculiarity of using entanglement in this field is that, being a single direct measure of quantum correlations, it should allow for a unified treatment of QPTs.
➤ Entanglement and Quantum Phase Transitions
References
M. Allegra, P. Giorda, and A. Montorsi, Quantum discord and classical correlations in the bond-charge Hubbard model: Quantum phase transitions, off-diagonal long-range order, and violation of the monogramy property for discord, Phys. Rev. B 84, 245133 (2011).
A. Anfossi, P. Giorda, and A. Montorsi, Momentum-space analysis of multipartite entanglement at quantum phase transitions, Phys. Rev. B 78, 144519 (2008).
P. Giorda and A. Anfossi, Structure of quantum correlations in momentum space and off-diagonal long range order in eta pairing and BCS states, Phys. Rev. A 78, 012106 (2008)
A. Anfossi, P.Giorda, and A. Montorsi, Entanglement in extended Hubbard model and quantum phase transitions, Phys. Rev. B 75, 165106 (2007)
A. Anfossi, P. Giorda, A. Montorsi, and F. Traversa, Two-point versus Multipartite entanglement at Quantum Phase Transitions, Phys. Rev. Lett. 95, 025114 (2005).
For several models in condensed matter physics, it has been shown that partial derivatives of appropriate measures of entanglement with respect to the field driving the QPT develop a singularity in correspondence with the critical points. Moreover, a study of QPTs through entanglement measures can enlighten the structure of the correlations involved.
We have shown that a comparison of the single-site Von Neumann entropy (a measure of the quantum correlation between a site and the rest of the system) with the quantum mutual information (measuring the total correlations between pairs of sites) allows one to infer which kind of correlation plays the prominent role at a given transition. One is thus led to distinguish between the QPTs where the quantum correlations between pairs of sites are more relevant (“two-point QPTs”) from those where the multipartite correlations are important (“multipartite QPTs”).
We believe that the application of the above scheme at nonzero temperature could better characterize the quantum to classical crossover.
➤ Quantum Computation
We have constructed, from a theoretical point of view, logical states (codewords) and logical operators (gates) for the class of Josephson-like systems, whose Hamiltonian is characterized by a cos θ interaction term, where θ is the phase operator. Among such systems we mention the superconducting Josephson junctions, one of the more promising candidates for the physical implementation of a quantum computer.
We have shown that the codewords, i.e., the states of the computations basis, are related to the coherent states of the underlying k-boson algebra (generalization of the Weyl-Heisenberg algebra) where k is the dimension of the computational scheme, while the gates are expressed in terms of operators in the same algebra. For k = 2 and k = 3 this approach has led to the construction of qubit/qutrit computational bases and bit flip and phase flip operators; the expression of the quantum controlled NOT gate (CNOT) is also given. The whole procedure has been extended to general values of k.
References
F. A. Raffa, M. Rasetti, Two-boson algebra and quantum computing with Josephson-like systems, J. Opt. B: Quantum Semiclass. Opt. 7, S539 (2005).
F. A. Raffa, L. Faoro, M. Rasetti, Quantum logical states and operators for Josephson-like systems, J. Phys. A: Math. Gen. 39, L111 (2006).
F. A. Raffa, M. Rasetti, Multibosons in quantum computation, Laser Phys. 16, 1486 (2006).
F. A. Raffa, M. Rasetti, Quantum computational schemes generated by k-boson algebras, Int. J. Quantum Inf. 5, 229 (2007).
It has been recently recognized that processing information in a quantum mechanical fashion can provide, in some cases, a huge computational speed-up with respect to "any" classical device; from the fundamental point of view, the novel computational power owned by such devices relies on two basic quantum features: (i) superposition of states and (ii) quantum entanglement.
Even though from a theoretical point of view quantum information processing can be already considered as a well-established field, two key issues are still subject of intense investigation: (i) the intimate link between quantum entanglement and quantum phase transitions, and (ii) the design and realization of concrete solid-state implementation protocols.
Nanophysics and Quantum Systems