In the 1990s__ cognitive researchers asked one group of test subjects a single question__: Do you think Bill Clinton is honest and trustworthy? Respondents were evenly split on the question: 50% yes, 50% no. Next, independently of the first group, researchers asked a second group: Do you find Al Gore honest and trustworthy? 68% percent of respondents answered yes. Finally, they then asked a third group of respondents these two questions in succession–first asking them to rate Al Gore’s honesty and trustworthiness, and then Bill Clinton’s. The result–58% of respondents stating they found Clinton honest and trustworthy–is a strong example of the problems that exist at the intersection of probability and human cognition.

How to explain such a huge deviation? Researchers believe that when humans have a proposition in mind, and associate that proposition with other propositions, our cognition allows the former to influence the latter. In other words, Bill Clinton’s association with Al Gore caused people to rate his trustworthiness higher than if they evaluated him in isolation.

## The difference between classical and quantum probability

According to classical probability, this doesn’t make any sense.

Classical probability compares volumes where data sets have a relative size or relative proportion that is overlapping. It assumes that out of the total population, some subset thinks Bill Clinton is honest, and some subset thinks Al Gore is honest. So when you ask these questions you're just asking a question about a binary state and classifying individuals in one or the other. It doesn't matter which questions you ask, or which order–if you ask the same combination of questions, you will always get the same answer. The actual human behavior researchers observed does not fit this theory at all.

The observed behavior can, however, be modeled using quantum probability theory.

*Quantum probability theory as envisioned by Midjourney AI*

Unlike classical probability’s reliance on ‘0’ and ‘1’, the qubits used in quantum calculations can be ‘0’, ‘1’, or a mixture of these (and because quantum mechanics uses complex numbers, there is some variety between these mixtures). But at the same time, if you measure a qubit as spin up, and then you measure it again, you will get the same result unless something changes between the measurements. This is analogous to asking people their opinions about something, (i.e.: Who are you going to vote for?). But critically, if there is an intervening factor, the nature of the calculation changes, pushing you towards a probability that includes that intervening event.

You can use these interactions as stepping stones to get to a certain desired mathematical response, in exactly the same way that you can increase the probability someone will say they find Bill Clinton trustworthy by first asking them the intervening question of if they find Al Gore trustworthy.

What we’ve done at IonQ is–in __work published jointly__ with other top researchers–run cognitive models for these intervening questions and order effects on quantum computers, with the help of collaborators from psychology.

## Moving toward a new model of human cognition

There are too many examples of instances where people systematically jump to conclusions and don't reason all the way through things for psychologists to believe that classical logic can accurately model human behavior. While it’s not fair to call human behavior ‘irrational’ it is definitely fair to classify it as non-classical from a probabilistic standpoint.

For __example__, people are willing to pay an average of $26 for a $50 gift certificate, but only $16 for a lottery that pays either a $50 or $100 gift certificate, with equal probability.

Psychologically, this can be explained via the mere presence of uncertainty, even if that uncertainty isn’t logically applicable to the decision being made. It’s these types of probabilities that can be explained in terms of quantum mechanics' interference principle. If we have more than two states, and they start to interfere with each other, they can ‘cancel’ each other out–exactly like the uncertainty around two possible outcomes of an election interfering with one another and preventing an investor from wanting to make a decision to commit to the market.

Another less abstract way to demonstrate the plausibility of quantum models of cognition is to think about more common instances where we answer questions via pre-existing conclusions. Colors are one example. Once we’ve been told that purple-colored wine is actually called ‘red’ wine, or that brown-colored leaves are called ‘red’ leaves, we don’t question it–we’ve learned that the word ‘red’ can be used to describe these not-quite-red things. Because the label ‘red’ is close enough (at least in contrast to other most common color words), we then have no trouble associating those non-red things with the color red in the future. Our previous experience has materially impacted the probability that we will describe brown-shaded leaves as ‘red’ in the future.

## Have we invented a true digitized consciousness?

These examples demonstrate how asking questions in different orders gives rise to cognitive behaviors that are not described by classical set theory in classical probability, and we believe can be modeled more accurately via quantum probability. But does this mean that we are succeeding in creating a more realistic computational consciousness via quantum mechanics?

Today, the science is far from making this claim.