Imagine a toroidal tank of water with the approximate volume of the Earth's oceans. In this tank currents keep some regions partially isolated from others and nutrients-sugars, lipids, amino acids, the ingredients for new life (Szostak et al. 2001)-seep in from the bottom. If we could write down the coordinates and composition of every "dry" molecule-dissolved in the water-we would have a real version of the proposed QVM. Even with fault-tolerant, biomolecular, quantum proto-cells we would lose, however, our unique ability to keep track of the history of quantum operations. In the Quantum Coreworld the possibility of writing down a classical description of the QVM at every fluctuation is quite remarkable. In part, I believe that the line of research described here is scientifically interesting because a classical description of a real quantum mechanical ecology is essentially impossible
Physics and computer-science are increasingly recognized as intertwined. A striking example is that (most) non-linear versions of quantum mechanics would render thousands of intractable computer science problems tractable (Abrams and Lloyd, 1998) . It is my hope that in studying QVMs an equally startling connection could be made between evolution and physics or evolution and computer science. To me, the idea that an "objective" quantity like entropy can differ, for an agent "simulating the universe" and an agent "in the universe", is already startling; I call these actual entropy and apparent entropy, respectively. Finding a simple concrete example of the divergence of actual and apparent entropy seems to be very worthwhile. Zuse (1969) concluded that there is a kind of continuum between classical physics, quantum physics and digital physics ("calculating space"); to my knowledge, this continuum remains mostly unexplored.
Some considerations: 1) as desired, the coreworld equivalent of a "flame" will have low actual entropy, they have high apparent entropy, but don't manipulate coherent quantum information; 2) as desired, the coreworld equivalent of a "mule" will have high actual entropy, since they manipulate coherent quantum information, it doesn't matter that they don't replicate because all their parts are shared with other replicating things; 3) pure speculation - large contributions to actual entropy, from quantum histories, can only be generated by a process of Natural selection if the history is evidence for the sort of complexity we want in a complexity measure. In some sense this turns the argument against biological quantum information processing on its head. If Natural selection can generate and manipulate coherent quantum information (i.e. it is capable of evolving quantum error correction and fault tolerant QIP techniques) then when it does so it is due to a strong selective pressure and is strong evidence for high complexity.
This project was undertaken with an intent to leverage the diverse "ecologies" of the game Corewar. Thousands of programs, using a dizzying variety of strategies, have been engineered by an international community of Corewar enthusiasts. No one strategy dominates all others. Instead, a scenario similar to the children's game of rock-paper-scissors emerges: rock blunts scissors, scissors cuts paper, but paper wraps rock. Diversity in the coreworld, however, is not a given because all motifs must replicate-or be replicated-to persist in the long-term. Perhaps there is simply one best way to survive.
Furthermore, the hypothesis that QIP provides a selective advantage in the QVM might be false; and it can be false in several ways (by no means an exhaustive list):
One way or the other, furthers experiments will help clarify these matters.
The entire universe has performed, at most, 10120 ≈ 2400 operations on 1090 ≈ 2300 bits (Lloyd 2002). Practically, a QVM with ≈ 2100 molecules is as out of reach as a QVM with ≈ 2300 molecules but it should still be possible to prove things about QVMs of that size. We know, for example, they cannot do anything super-Turing. On the positive side we know-if a real quantum computer was available to act as an oracle-they could be used for factoring large integers. If experiments for the small QVM prove fruitful then theoretical techniques could be used to make precise the intuitive idea of equating complexity with the actual-as opposed to apparent-entropy of an evolving system. For classical entities this is a distinction without a difference but for quantum entities it could still be the case that a motif's high actual entropy in the Quantum Coreworld might not mean we should consider it especially complex.
Necessarily, an abstract ecology with any claim to being called natural is significantly more complicated than is considered practical or desirable by most theoreticians. An approach combining both theory and experiment may remain prudent for the foreseeable future. If experimental evidence in favor of the complexity measure described here accumulates then further theoretical investigation is probably warranted.