Quantum Replicants: Should future androids dream of quantum sheep?

The movie Blade Runner describes a future where society can engineer machines that almost perfectly imitate the behaviour of various living things, from sheep to human beings. These machines—referred to as "replicants"—interact with both the environment and other humans so convincingly that it is almost impossible to differentiate between what is natural and what is artificial. This raised a provocative question: what is actually happening beneath the surface of such machines, or as the book by Philip K. Dick that inspired the movie aptly asked, "Do androids dream of electric sheep?"

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 sheep can be understood through how it processes information. Indeed, this was a central theme in Blade Runner. There, the key to a replicant’s success in mimicking a human was memory—information it gathered over the process of a lifetime. This information went on to define how the replicant viewed and acted upon the world.

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.

Yet, information is not always classical. At the fundamental level, it can feature remarkable quantum mechanical properties. To truly isolate the memory needed to inform the system’s future behaviour, would such quantum effects need to be considered? We might immediately be inclined to answer "no," especially if the system in question interacts in the macroscopic world. Yet, our current research, along with quantum physicists Andrew Garner and Vlatko Vedral at the Centre for Quantum Technologies, in Singapore, appearing this month in Nature Quantum Information, demonstrates otherwise (npj Quantum Information 3, Article number: 6 (2017)). To truly isolate the 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 A and B. Suppose our test is particularly rudimentary. To pass, all the system generally needs to do is answer "Yes" or "No" at random. The only requirement is that if we ask the same question twice in a row, it should be consistent and answer the same way both times.

To pass this test, the minimal replicant would need to remember two pieces of information: was our last question A or B, and did it answer "Yes" or "No." Thus if we fire questions off at random, the replicant needs to store two bits of classical information: one encoding the last question asked, and the other encoding its answer. This turns out to be the provably optimal construction—assuming that the replicant is capable of only classical thought.

Yet, by contrast, a replicant armed with only a single quantum bit, or qubit, of information can pass this test with flying colours. Suppose its memory consists of a single electron inside a box. Now whenever it receives question A, the replicant measures the electron’s spin in one direction, the x-direction. (Spin is an internal quantum property of a particle that can take one of two values when measured along a certain direction.) The outcome of this measurement can take two values, "up" or "down," which it interprets as "Yes" or "No." When it receives question B, it repeats this process, but measures the spin along a perpendicular direction instead, in the z-direction.

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 x and z components of the electron’s spin can never simultaneously take definitive values. When the replicant measures the spin along x to give a definitive answer to question A, its subsequent answer to question B by measuring along z must be completely random. (This aligns with Heisenberg’s well known mantra, that the better we know x, the more uncertain we become about z.) Meanwhile, if the replicant is asked the same question twice in a row, it would make two consecutive measurements of the spin in the same direction. According to the rules of quantum mechanics, the first measurement would collapse the spin into a definitive state, either up or down in the measurement direction (due to the collapse of the wave function). This means that its second spin measurement outcome along the same axis must always agree with the first, exactly as required.

This quantum device thus runs on a single qubit— half the memory of its 2-bit classical counterpart.

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 x, the outcome of measuring z simply did not exist prior to the act of measurement. Instead, this outcome was created by the act of measurement itself. This view that nature has no definitive reality was one of the most contentious features of quantum theory when it was first discovered. So contentious in fact, that Einstein once asked Bohr: "Do you really believe the moon is not there when you are not looking at it?"

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.

Jayne Thompson is a quantum physicist at the Centre for Quantum Technologies, National University of Singapore; Mile Gu is a quantum physicist at the Complexity Institute and the School of Physical and Mathematical Sciences at Nanyang Technological University.

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