How to associate quantum computation to classical computation

How could a classical computer become a conscious and living system? The tentative answer to this question, discussed in \cite{btart/QCs}, is that something analogous to a fusion of classical and quantum computer takes place.

In zero energy ontology (ZEO) one can say, the quantum computation would be a superposition of all possible computations with fixed initial values. This is made possible by the fact that classical physics as Bohr orbitology is an exact part of quantum physics in TGD and by the predicted slight violation of classical determinism. The computation in the usual sense would correspond to the most probable computation in the superposition.

In the sequel I consider the above question in detail.

1. Basic input from Quantum TGD

What are the basic pieces from the TGD side?

1. Zero energy ontology (ZEO) defining new quantum ontology, solving the basic problem of quantum measurement theory, is necessary. General coordinate invariance requires holography and it is not quite deterministic so that space-time surfaces are analogous to almost deterministic Bohr orbits and Bohr orbitology becomes an exact part of quantum TGD.
2. Classical non-determinism corresponds to the non-determinism of minimal surfaces: already for 2-D soap films as minimal surfaces the frames do not define the soap film uniquely. In ZEO this non-determinism makes possible a sequence of small state function reductions (SSFRs) as a counter for a sequence of measurements of the same observables which in standard QM does not change the state. In TGD the second member of the zero energy state at the passive boundary of the causal diamond (CD) is unaffected by the second member at the active boundary is affected.This gives rise to a conscious entity, self. In "big" SFR (BSFR) the self "dies" and reincarnates with a reversed arrow of geometric time.
3. Each pulse of the computer clock is associated with the possibility of classical non-determinism of a 4-D minimal surface. Classical non-determinism would produce a superposition of 4-surfaces corresponding to different values of bit and associated qubit. Protons are also involved: protons are either ordinary or dark and located at the gravitational magnetic body. Pollack effect induces the transfer of the proton to the magnetic body and its reversal occurring spontaneously its transfer back.
4. OH-O^- qubits are an essential part of the system. For the O^- qubit, the proton of OH is at the gravitational magnetic body. Under certain conditions the gravitational magnetic body should be able to control the ordinary bits. Quantum entanglement of the ordinary and OH-O^- qubit and quantum criticality is required and would be induced by the classical non-determinism.

   If the bit's reversal energy corresponds to the thermal energy, the situation is quantum critical. This is the case also when the energies for the reversal of qubit and bit are nearly identical. This quantum criticality is controlled by the difference in the bit's reversal energies. Small energy difference corresponds to quantum criticality.

   The reversal of the second qubit reverses the bit: one can interpret the reversal for bit and qubit as an exchange of energy between the qubit and the bit. The farther away the probability for a given value of bit is from the value 1/2 the higher the determinism of the program is.

5. The magnitudes of the classical electric and magnetic fields control the energy of the bit and qubit. These are determined by classical physics for the classical space-time surface, which can be non-deterministic.

2. Concrete model for classical-to-quantum tranformation

2.1 What happens in ordinary computing?

The standard model of classical computer can be formulated as follows.

1. The first model: A tape containing program instructions is fed into a Turing machine. Depending on the command, the state of the computing unit changes. The transition of the tape corresponds to a clock pulse.
2. The second model: The program is implemented as a 1-D conveyor belt and the incoming bit configuration enters the tape and progresses along it, changing with each step. The output of the program comes out. DNA replication, transcription and mRNA translation correspond to this analogy.

2.2 Classical non-determinism

Classical non-determinism, which is the new element, can be assigned to the periods between clock pulses.

1. Thanks to classical non-determinism, the output produced by a program instruction would be a superposition of two space-time surfaces as analogs of Bohr orbits.
2. In the transition corresponding to a clock pulse, the state would be transformed to an unentangled state by a non-deterministic SSFR or a pair of BSFRs. A quantum measurement of bits would be thus performed on the outgoing superposition of bit-qubit configurations.

2.3 A concrete model

Consider now a concrete model for how aclassical computer could transform to quantum computer-like system.

1. The network performing the computation consists of gates. A gate connects a small number of input bits to the output bits, the number of which cannot be greater than the number of input bits. This operation is statistically deterministic.

   When the input bits are fixed, the output bits are determined by dynamics as non-equilibrium thermodynamic state.

2. The clock pulse triggers the next operation. The failure of the exact classical determinism must relate to this and produce a superposition of space-time surfaces as the resulting qubit because OH and O^- correspond to different space-time surfaces, even topologically.
3. What is essential is the entanglement of the OH-O^- qubit and the ordinary bit and the measurement of the qubit in the beginning of the nex clock pulse. The outcome is not deterministic.
4. The classical bit corresponds to a voltage or current that is determined through statistical determinism in the gate. On the other hand, it corresponds to a classical electric field in a transistor or a magnetic field in a memory bit.

   The direction of this classical field is classically non-deterministic and correlates with the OH-O^- qubit. When the field changes direction, the OH-bit becomes an O^-bit or vice versa. A dark proton is transferred between the system and its gravitational magnetic body.

5. Classical non-determinism creates a superposition of OH and O^- bits. The proton resides both at the gravitational magnetic body and in OH molecules, being analogous to Schr dinger's cat.

   This induces the formation of a quantum entangled state between ordinary qubit and OH-O^- qubits. If the OH-O^- qubit and the bit are quantum entangled before the clock pulse, the quantum measurement of OH-O^- qubit or of ordinary qubit recues the entanglement and leads to a fixed bit.

2.4 Some questions

One can raise critical questions:

1. The energy transfer between a bit and a qubit resembles quantum tunnelling. I have proposed that a pair of BSFRs correspond to quantum tunnelling. It is not clear whether a single SSFR can have an interpretation as quantum tunnelling. Could the measurement of a qubit correspond to a single SSFR or to two BSFRs?
2. What could be the energetic role of the clock pulse? The system under consideration would be a clock photon + bit + qubit and the total energy would be conserved.
   1. Could the clock pulse have a role of a catalyst, providing the energy needed for quantum tunnelling. In a qubit measurement, energy can be transferred between the bit and the qubit, but the total energy is conserved. The clock photon would kick the system over the potential barrier and then be emitted back into the field.
   2. Or does the clock photon transfer energy to or from the bit + qubit system? Could the energy of the photon associated with the pulse frequency correspond to the energy difference for a bit and a qubit. The typical frequency of computer clock is few GHz. 1 GHz would correspond to an energy E=.4× 10^-5 eV and wavelength λ ∼ .75 m. At the surface of the Earth, the gravitational binding energy of a proton is about 1 eV. The energy E eV can raise the proton to the height h ≈ .4× 10^-5R_E≈ 25.6 m.

See the article Quartz crystals as a life form and ordinary computers as an interface between quartz life and ordinary life? or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.