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FQXI ARTICLE

December 15, 2017

Quantum Replicants: Should future androids dream of quantum sheep?

To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

FQXi Awardees: Andrew J. P. Garner, Mile Gu

February 23, 2017

Creating a Minimal Replicant

A classical device is being simplified by use of quantum mechanics, in this artist’s

depiction.

Credit: Mile Gu via Google Tiltbrush

Humans have a longstanding fascination with the idea of replicating nature through human engineering. Accounts dating to the 4th century BC talk about mechanical birds that could purportedly fly up to 200 meters. By the 13th century, Leonardo Da Vinci had designed a robotic knight—a literally self-walking suit of armor that could sit, stand and raise its own visor all by the ingenious use of pulleys, weights and cables. Today, artificial intelligence is bringing us closer and closer to machines so sophisticated that humans may one day be unable to distinguish a machine’s answers to questions from the answers given by another human—a famous imitation game Alan Turing proposed as the holy grail for building machines that can think. A future where computers mimic the behaviour of human beings no longer seems so farfetched.

These successes towards building the ultimate mechanical replicants of nature have opened new perspectives on understanding nature itself. After all, if a computer—a device that processes information—is the key to engineering an artificial sheep, then perhaps what makes a sheep a

Harnessing Memories

This perspective offers a fascinating approach to understanding what makes a system behave the way it does, by isolating the key memories the system must store about its past, and understanding how the system harnesses these memories to make future decisions. Such memories then correspond to information that cannot be stripped away without fundamentally altering the system’s future behaviour. A minimal replicant—a system that only stores these bare bone memories—thus captures the essence of the system itself.

In addition to their philosophical importance, these questions about building the minimal replicant turn out to be of great interest to experts in complexity science (see, for example, N. Barnett, & J.P. Crutchfield, J. Stat. Phys. 161: 404 (2015) and C.R. Shalizi, & J.P. Crutchfield, J. Stat. Phys. 104: 817 (2001)). Here such constructions carry significant operational value. We are always interested in designing things more efficiently to perform the same task with less. Meanwhile the amount of memory such a minimal replicant requires captures a fundamental notion of what is complex. For instance, it takes a lot more memory to inform what a human will do next, than to imitate a goldfish’s limited repertoire of responses. Thus, humans appear more complex.

To truly isolate the

core memories that

enable a system to

behave the way it does,

quantum mechanics is

generally essential.

core memories that

enable a system to

behave the way it does,

quantum mechanics is

generally essential.

Consider a scenario where we are interrogating a system by asking one of two questions at each point in time. The first being, "do you like electric sheep?" and the second being, "are you human?". Let’s label these questions respectively by

To pass this test, the minimal replicant would need to remember two pieces of information: was our last question

Yet, by contrast, a replicant armed with only a single quantum bit, or

Heisenberg’s Mantra

It turns out that this simple replicant passes the test, thanks to the laws of quantum mechanics and Heisenberg’s uncertainty principle. The uncertainty principle states that the

Quantum replicants will

generally save memory,

for almost all tests that

one can design.

generally save memory,

for almost all tests that

one can design.

This turns out not to be an isolated case. Quantum replicants will generally save memory, for almost all tests that one can design. Formally, each such test specifies an input-output process, a mathematical specification of how the system should respond to future questions given each historic sequence of past questions and answers. The device that replicates the desired input-output behaviour for such a test, with minimal memory, is almost invariably quantum.

The reason turns out to be quantum theory’s lack of a definitive reality. A property of a quantum system is not necessarily stored within the system until the point of measurement. In the above example when we were certain about the outcome of measuring

Quantum Contextuality

The act of not existing until one looks, turns out to be exactly what allows quantum theory to mimic interactive systems with less memory than classically possible. A classical device must track enough past information to know how to respond to every potential future stimuli. A quantum device can replicate the same behaviour by identifying each different input stimuli with a different quantum measurement, thereby allowing the system not to store a realistic description of how it is going to answer all questions. Furthermore asking a quantum system one question can fundamentally alter all of its responses to the other questions—a phenomena known as quantum contextuality. (See “Quantum in Context.”) So when you ask a quantum system a question, its memory is automatically reconfigured—and this can be harnessed to ultimately reduce the memory it needs overall.

What does all this mean? It certainly doesn’t imply that life or anything else is quantum mechanical. However, if we were to build the ultimate replicants of such real life systems—replicants that held only the core memories that make them behave the way they do—then such replicants would use quantum memory. Thus, perhaps in the future, the most advanced androids will dream not only of electronic sheep, but quantum mechanical sheep as well.

This research was partly supported in part by the John Templeton Foundation and FQXi.

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