# Long-Term Memory, Simulated Qubits, Physical Qubits

## Abstract

Developed below are circuits for elements of long-term memory suitable for a brain system. Three types of elements are presented, based on, (1) long-term potentiation (LTP), (2) recursive neural pulses, and (3) a combination of these two.

The recursive neuron is easily changed into a *simulated qubit* that can hold true and false simultaneously, corresponding to a higher and a lower frequency of a circulating pulse. Frequency and phase for a single simulated qubit may be represented by a point on a sphere of probability, the location of which determines the resulting probability of a true. Output is established with a sampling circuit that results in true or false logic value with specific complementary probabilities. Simulated qubit circuits as developed in this book may stand in for physical (real) qubits within neurons, and are important.

Simulated qubits have advantages over straightforward neurons. For example, during cue editing, it is desirable to treat conflicting cues probabilistically. Also, simulated qubits easily convert into controlled toggles that are useful for massively parallel calculations.

Indeed, arrays of controlled toggle devices are central to recall editing to determine highest priority, a topic of a later chapter. Two circuits for controlled toggling are given, one using a combination of excitory and inhibitory synapses, and one using AND, XOR dendritic logic. These circuits are verified by simulation experiments for toggles in an appendix to this book.

Two independent simulated qubits, each prepared to 50 % chance for true or false, will provide four possible combinations of true and false, each with 25 % probability; thus *n* qubits provide exponentially increased possibilities. This opens up possibilities for data storage in probability space, as well as for binary function identification and binary function satisfiability as presented in a later chapter.

Formulas are given for the approximate probabilities of a true or a false from a simulated qubit. The phases of recursive waveforms are controllable, but phase generally does not affect the probability. In order for phase to have an effect, suitable transforms need to be implemented on the probability sphere, a topic of a later chapter.

Simulated qubits using recursive neurons are compared below to the physical qubits of quantum theory. Entanglement is discussed, with its weird possibility of teleportation, or communication without known physical connections. Simulated qubits cannot become entangled like particles in a quantum system, although it may be possible to imitate certain kinds of entanglement using interneurons.

## Keywords

Duty Cycle Single Pulse Probability Fraction Memory Element Sampling Pulse## References

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