1.1.2 Quantum Computation

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Classical physics is at the root of present-day information processing: strings of bits (discrete digital states) are represented and processed in electronic devices (registers, logic gates etc.) through quantities such as charges, voltages, or currents. In Quantum Computing and more generally in Quantum Information Processing (QIP), one makes instead use of the laws of quantum mechanics replacing bits with qubits, two-state quantum systems that do not possess in general the definite values of 0 or 1 of classical bits, but rather are in a so-called ‘coherent superposition’ of the two. Full exploitation of this additional freedom implies that new processing devices (quantum registers, quantum logic gates etc.) need to be designed and implemented. As several sets of universal quantum gates acting on one and two qubits are known, a large scale quantum computer can in principle be built, provided the quantum physical system used meets some basic requirements (the so-called DiVincenzo criteria) on scalability, faithful initialization, manipulation, transmission and readout of qubits, and long coherence times with respect to the gate operation time. At present, a number of physical systems are under investigations for their suitability to implement a quantum computer. These include trapped ions and neutral atoms, cavity quantum electrodynamics (CQED), solid state devices (such as superconducting qubits, possibly in combination with circuit CQED, and spin qubits), all-optical devices, as well as impurity spins in solids, single molecular magnets etc.. During the last few years remarkable progress, measured in terms of the aforementioned DiVincenzo criteria, towards demonstrating the basic building blocks of a quantum computer have been reported in these systems. At present no fundamental physical roadblocks seem in sight for building a scalable quantum computer including error correction. However, a mixture of significant technological challenges and some open physical questions remain to be answered. At the same time it is premature to select a winner, rather research should progress on a broad front across all physical disciplines which studies these systems in view of scalability, coherence and speed of QIP, in particular also concerning their reliability, fault tolerance and use of error correction. Finally, development of a computer architecture must be complemented by interfacing with quantum communication to allow building of quantum networks. Ultimately, the goal must be to transfer this academic knowledge about the control and measurement of quantum systems to industry. Major international companies have shown interest and support for developing and providing systems suitable for quantum manipulation.

Few-qubit applications. A first short range goal is the realization of a few-qubit general purpose quantum computer including error correction, as a test bed for demonstrating operation of a quantum computer. In parallel, however, special effort must be made to further develop few qubit applications which range from quantum information processing and quantum communication all the way to quantum assisted precision measurements.

Many-qubit specialized applications. As a second short range goal, special purpose quantum computers with a large number of qubits should be developed. A highly relevant example is provided by quantum simulators, programmable quantum systems whose dynamics can be engineered such that it reproduces the dynamics of other many body quantum systems of interest, e.g., atoms in optical lattices simulating high temperature superconducting systems and/or quantum phase transitions. Full simulation of a quantum mechanical system consisting only of a few hundred particles (spins) requires in fact classical computing resources in terms of memory of the order of the number of atoms in the visible universe – clearly demonstrating the inadequacy of any classical computer for this task. Quantum simulators could be the first nontrivial applications of quantum information, providing answers to problems which are fundamentally beyond classical computing capacities, such as the study of microscopic properties of materials permitting free variation of system parameters, an accurate description of chemical compounds and reactions, or find out the reason why free quarks are not found in Nature.

Quantum interfaces. In the long term a first goal is the development of hybrid technologies and architectures for quantum computation, including interfaces between them. This will stretch the theoretical and experimental resources of many branches of physics, from quantum optics and atomic physics to solid state devices. It is likely that there will not be a single winner in this search, but rather a number of different technologies complementing each other: some will be more suitable for quantum memories, some for quantum processing, and some for quantum communication and so on. Therefore, in addition to developing individual technologies, interfaces between the latter are also needed, so that different qubit ‘memories’ (atoms/ions, quantum-dots, squids) and carriers of quantum information (atoms/ions, photons, phonons, electrons) can be interconnected.

Fault-tolerant gates and architectures. A second long range goal is the demonstration of fault-tolerant quantum logic gates, by the engineering of sub-microscopic systems in which qubits affect each other in a controllable way, while avoiding at the same time undesired couplings with the environment leading to decoherence. Applying to quantum computers the traditional network model, simple quantum logic gates would be connected up into quantum networks. However, the more interacting qubits are involved, the harder it tends to be to engineer the interaction that would display the quantum behaviour, and the more components there are, the more likely it is that quantum information will spread outside the quantum computer and be lost into the environment, thus spoiling the computation. It has been proven that if decoherence-induced errors are small (and satisfy certain other achievable conditions), they can be corrected faster than they occur, even if the error correction machinery itself is error-prone. The requirements for the physical implementation of quantum fault tolerance are, however, very stringent, and can be met either by improving technology or by going beyond the network model of computation and designing new, inherently fault-tolerant, architectures for quantum computation. One candidate for such an alternative architecture, e.g., might be the one-way quantum computer model, in which errors can classically be fed-forward and corrected. At the end however, a fault-tolerant quantum computer will most likely be achieved by an optimized combination of both strategies.

Implementation theory. Theory must continue to play a leading role in guiding and supporting experimental developments. Aside from finding and investigating fundamentally new algorithms especially suited for quantum computing, the various implementations require continuous theoretical work especially finding physical solutions where mere technology is yet too cumbersome. For example, operations in specially designed “decoherence free subspaces”, i.e., physically tailored systems less susceptible to technical errors, will be an important feature in finding an optimum system and optimized algorithms. Therefore, the theoretical work will have to cover a wide range of physical systems and technologies.