385 citations · 429 across the 11 of their papers we have counts for
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Quantum Heat Engines, the Second Law and Maxwell's Daemon
Tien D. Kieu
We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and…
Quantum adiabatic algorithm for Hilbert's tenth problem: I. The algorithm
Tien D. Kieu
We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for…
The Diagonal Method and Hypercomputation
Toby Ord, Tien D. Kieu
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes…
Representations of Omega in Number Theory: Finitude Versus Parity
Toby Ord, Tien D. Kieu
We present a new method for expressing Chaitin's random real, Omega, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Omega…
On the existence of a new family of Diophantine equations for
Toby Ord, Tien D. Kieu
We show how to determine the -th bit of Chaitin's algorithmically random real number by solving instances of the halting problem. From this we then reduce the problem of…