Cognitive decision processes are generally characterized in terms of classical Bayesian probabilities, but as the core papers in this special issue describe, cognitive decisions are far better suited to quantum mathematics. For example (Wang, Busemeyer, Atmanspacher, & Pothos, 2013): (a) Psychological conflict, ambiguity, and uncertainty can be viewed as (quantum) superposition of multiple possible judgments and beliefs; (b) measurement (e.g., answering a question, reaching a decision) reduces possibilities to definite states (“constructing reality,” “collapsing the wave function”); (c) previous questions influence subsequent answers, so sequence affects outcomes (“contextual non‐commutativity”); and (d) judgments and choices may deviate from classical logic, suggesting random, or “non‐computable,” quantum influences (Penrose, 1989, 1994).

How could quantum mathematical cognition operate in the brain? Do classical brain activities simulate quantum processes? This seems unlikely, for as Richard Feynman (1982) showed, classical simulation of quantum processes suffers exponential slowdown. Or have biomolecular quantum devices evolved? This has also seemed unlikely, because technological quantum computers are hampered by “decoherence,” disruption of quantum states by interaction with the classical environment, for example, by random thermal energy. To avoid decoherence, technological quantum computers are isolated near absolute zero temperature. Accordingly, quantum computing in warm biology has been considered impossible. However, in recent years, warm functional quantum processes have been found in plant photosynthesis (Engel et al., 2007), bird navigation (Gauger, Rieper, Morton, Benjamin, & Vedral, 2011), and olfaction (Turin, 1996). Non‐polar (but polarizable) electron resonance clouds within proteins, lipids, and nucleic acid interiors, shielded from polar interactions, appear to isolate and protect quantum states from environmental decoherence. And coherent vibrations in macromolecules may utilize heat to promote, rather than disrupt, quantum coherence (Chin et al., 2013). Functional quantum cognition in the brain is plausible.

“Quantum” refers to fundamental units of matter and energy. At the quantum level, particles: (a) exist in multiple alternative states (superposition); (b) are connected non‐locally (entanglement); and (c) condense into unitary states (coherence). Quantum computers utilize information (e.g., binary bits of 1 or 0) in superposition of multiple possible states (quantum bits, or “qubits” of both 1 and 0). Topological quantum computers utilize superposition of multiple possible pathways through a lattice as topological qubits, “braids,” or quantum walks, inherently resistant to decoherence. In both types of quantum computers, superpositioned qubits interact/compute with one another by non‐local entanglement, and eventually undergo measurement, that is, reduce (or “collapse”) to definite classical states or pathways as the solution.

In this special issue, Fuss and Navarro (2013) describe a cognitive architecture using quantum computing to make informed decisions. The architecture involves a massively parallel array of “evidence accumulators,” lattice registers which receive, accumulate, and process information, and are interconnected laterally for cooperative excitation and inhibition. In each accumulator, information inputs enter at discrete moments from external world, memory, and/or connected accumulators, and are represented as states of specific lattice subunits. The states interact (compute/integrate), evolving as a “quantum walk,” a series of quantum superpositions of different possible steps, and proceed in multiple pathways simultaneously, akin to Feynman's path integral approach applied to a lattice (e.g., the “Feynman quantum chessboard,” Fig. 1). At some point a measurement (collapse, reduction) occurs, and one pathway is selected as the output, or result of the quantum computation.

Figure 1 Open in figure viewer PowerPoint 1982 “Quantum walks” in two “Feynman chessboards” show quantum particles moving through alternate (blue, yellow) paths. Superpositions of both paths (“quantum walks”) through a lattice may occur (Feynman,). On the left is an orthogonal lattice, and on the right a skewed hexagonal lattice (e.g., microtubule “A‐lattice”).

The mechanism by which quantum superpositions reduce to classical states (“collapse of the wave function,” “measurement problem”) remains enigmatic. Possible explanations include decoherence, “multiple worlds” (each possibility branches to a new universe), and the Copenhagen interpretation (Wigner/von Neumann version) in which conscious observation causes quantum state reduction (placing consciousness outside science). Another approach is “objective reduction” (“OR”) in which some objective threshold causes reduction in superpositions to classical states. In one such proposal, Penrose (1994) suggested that (a) superpositions isolated from random environment will meet OR threshold at time t (where E G = ℏ/t, E G is gravitational self‐energy of the superposition, and ℏ is Planck's constant over 2π); (b) such OR events are moments of conscious experience; and (c) choices selected in this type of OR reflect “non‐computable” (perhaps Platonic) influences, rather than randomness. Could OR‐terminated quantum computing occur in the brain?

Most view the brain's fundamental “bit‐like” information states as neuronal firings and synaptic transmissions, but such states are too large, noisy, and environmentally interactive for quantum processes. The “one neuron/one bit” view also fails to account for memory (synaptic sensitivities are transient, yet memories last lifetimes), binding (how disparate concepts unify into conscious percepts), causal free will (measurable brain activities processing sensory inputs occur after we respond to those inputs, seemingly consciously, rendering consciousness an apparent epiphenomenal illusion; Hameroff, 2012), and the “hard problem” of phenomenal experience (Chalmers, 1996).

Indeed, the conventional view of neuronal firings as fundamental bit states is an insult to neurons! Single‐cell paramecium swim around, find food and mates, learn, and have sex with a partner: They exhibit cognition without synaptic connections. Single‐cell amoeba can escape mazes and solve equations (e.g., Adamatzky, 2012), again without synaptic connections. In performing purposeful functions, single‐cell organisms rely on cytoskeletal structures, including microtubules. Those same cytoskeletal microtubules organize activities within brain neurons and are proposed to function as quantum computers.

Microtubules (Fig. 1, right) are cylindrical polymers of peanut‐shaped “tubulin” proteins arranged in hexagonal lattices (A‐lattice and B‐lattice). Pathways along neighboring tubulins in the A‐lattice form helical pathways which repeat (3, 5, 8…) according to the Fibonacci series. Various microtubule‐associated proteins (“MAPs”) bind at specific lattice sites, for example, bridging to other microtubules to define cell architecture, regulate synapses, etc. (Fig. 1, left). Other MAPs include motor proteins which convey synaptic precursors along microtubules, guided by another MAP “tau” whose displacement results in neurofibrillary tangles and the cognitive dysfunction of Alzheimer's disease (Craddock, Tuszynski, et al., 2012; Matsuyama & Jarvik, 1989). Microtubules are particularly prevalent in neurons (109 tubulins/neuron) and are uniquely stable. Non‐neuronal cells undergo repeated cycles of cell division, for which microtubules disassemble and reassemble as mitotic spindles, then are reutilized for cell function. However, neurons do not divide and neuronal microtubules remain assembled indefinitely. Dendritic‐somatic microtubules are also capped by special MAPs, which prevent depolymerization, and are thus especially stable for information encoding and memory (Craddock, Tuszynski, & Hameroff, 2012). And unlike microtubules in axons and all other cells, dendritic‐somatic microtubules are not arrayed continuously and radially (i.e., from nucleus outward) but are interrupted in local MAP‐linked networks of mixed polarity microtubules (Fig. 2). Dendrites and soma host integration in integrate‐and‐fire neurons; their microtubules are well placed to regulate cognitive decisions to be then implemented by axonal firings (Hameroff, 2012).

Figure 2 Open in figure viewer PowerPoint Left: An “integrate‐and‐fire” brain neuron, and portions of other such neurons are shown schematically with internal microtubules (upper circle right). Dendritic‐somatic integration (with contribution from microtubules) can regulate axonal firings, decisions and behavior. Gap junctions synchronize dendritic membranes and may enable entanglement and collective integration among microtubules in adjacent neurons (lower circle right). Right: A single microtubule is a cylindrical polymer of peanut‐shaped “tubulin” proteins, shown here in two different possible tubulin states (black and white).

The Penrose–Hameroff “Orch OR” theory (Hameroff, 1998; Hameroff & Penrose, 1996, 2013; Penrose & Hameroff, 1995) suggests synaptic inputs “orchestrate” tubulin qubits in dendritic/somatic microtubules in integrate‐and‐fire neurons. Orchestrated qubits entangle, interfere, and compute according to the Schrödinger equation during integration, then spontaneously reduce, or collapse by Penrose OR (at time τ = ℏ/E G , Hameroff & Penrose, 1996; Hameroff, 2012) to classical tubulin states which regulate axonal firings, controlling behavior. The Orch OR neuron is the “Hodgkin‐Huxley” neuron with finer scale, deeper order microtubule quantum influences.

Early Orch OR papers suggested individual tubulin states as qubits, but more recently topological lattice pathway qubits have been considered. Within tubulin, electron resonance rings of aromatic amino acids form pathways enabling protein‐wide quantum dipoles which align with those in adjacent tubulins along lattice winding patterns (Craddock, St George, et al., 2012; Fig. 3). According to Orch OR, these enable helical quantum channels supporting topological quantum computing in microtubules. Multiple superpositioned braided pathways evolve and compute, then reduce, or collapse by the OR threshold to one particular pathway as functional output (Fig. 4). These selected states then regulate axonal firings, store memory, and adjust synapses.

Figure 3 Open in figure viewer PowerPoint 2012 Two topological qubits in a microtubule A‐lattice are shown. Left: pathway along “5‐start” helix in microtubule correlates, in each tubulin subunit, with aligned electron cloud (London force) dipoles through contiguously arrayed aromatic amino acid rings (Craddock, St George, et al.,). “Yellow” dipoles oriented “upward” along microtubule are energetically favorable (opposite to net dipole), designated “happy,” and proposed to correspond with the subjective feeling of happiness. “Blue” dipoles oriented “downward” are energetically unfavorable, thus “unhappy.” Right: Lattice pathway along “8‐start” helix with correlating intra‐tubulin dipoles. Middle: quantum superposition of both dipole orientations: “undecided.” Alternate pathway “bits” and superposition of both constitute topological qubits, equivalent to “quantum walks,” which can reduce from superposition to one orientation or the other.

Figure 4 Open in figure viewer PowerPoint E G (gray tubulins) until threshold is met at time τ = ℏ/E G . According to Orch OR, a conscious moment then occurs, and tubulin states are selected which regulate firing and control conscious behavior. In the example given here, energetically favorable upward “happy” dipoles/feelings result. For τ equal to 25 msec (40 Hz gamma synchrony EEG), billions of tubulins are required; a small number is used here for illustration. Topological pathways in microtubule quantum computing may be analogous to quantum walks in a “Feynman chessboard.” Quantum walk interactions are equivalent to topological quantum computing in a microtubule A‐lattice. Governed by internal dipoles (Fig. 3 ), tubulins can be in alternate black or white states, or when aligned with neighboring tubulins along extended pathways, in yellow or blue collective dipole states along winding pathways (Fig. 3 ). Tubulins and pathways may also be in quantum superposition of both dipole orientations (gray). In steps 1–3, quantum superposition/computation among winding pathway qubits evolves during integration phases with increasing quantum superposition(gray tubulins) until threshold is met at time τ =. According to Orch OR, a conscious moment then occurs, and tubulin states are selected which regulate firing and control conscious behavior. In the example given here, energetically favorable upward “happy” dipoles/feelings result. For τ equal to 25 msec (40 Hz gamma synchrony EEG), billions of tubulins are required; a small number is used here for illustration. Topological pathways in microtubule quantum computing may be analogous to quantum walks in a “Feynman chessboard.”

Topological qubits in microtubules are conceptually identical to quantum walks in Feynman accumulators (“quantum chessboards”), as described by Fuss and Navarro. Quantum brain cognition is likely to be supported by quantum brain biology.