15,637 research outputs found
Fault-tolerant quantum computation
The discovery of quantum error correction has greatly improved the long-term
prospects for quantum computing technology. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment, or due to imperfect implementations of quantum logical operations.
Recovery from errors can work effectively even if occasional mistakes occur
during the recovery procedure. Furthermore, encoded quantum information can be
processed without serious propagation of errors. In principle, an arbitrarily
long quantum computation can be performed reliably, provided that the average
probability of error per gate is less than a certain critical value, the
accuracy threshold. It may be possible to incorporate intrinsic fault tolerance
into the design of quantum computing hardware, perhaps by invoking topological
Aharonov-Bohm interactions to process quantum information.Comment: 58 pages with 7 PostScript figures, LaTeX, uses sprocl.sty and psfig,
to appear in "Introduction to Quantum Computation," edited by H.-K. Lo, S.
Popescu, and T. P. Spille
Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games
Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically
Reliable Quantum Computers
The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)Comment: 24 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor
correction
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