# Shapes of Possibility

### Felicitas Rohden

Logic is a subject concerned with the most general laws of truth. Formal logic is connected with mathematical reasoning. Wandering around a library last year, my eye fell on a book called, *The Game of Logic* by Lewis Carroll. He is known as the author of *Alice’s Adventures in Wonderland*. What most people don’t know is that he was a gifted mathematician as well. With humor and mathematical correctness, he showed how the “rules of the game” can be interpreted in mathematics, physics, and language. Carroll suggested a logic to understand our Western use of language in a different and more non-linear way. Reading this book and learning about the grammar of his game made me think about quantum mechanics.

As an artist, I often draw my inspiration from science and collaborate with scientists. Last year, I met scientist Shaun Datta at the Massachusetts Institute of Technology (MIT) in Boston to learn more about his research on quantum mechanics and the future of quantum computers. I wanted to see the logic behind the character of a quantum, an indivisible physical entity that can’t be broken down, and understand the complexity of the scientific illustrations I found. Shaun participated in my work, *Shapes of Possibility*, a set of five book sculptures. Each book deals with logic, rules, orientation, and direction. The drawings we made last September resulted in the book, *Qubits,* and the topics we discussed led to the following interview. Our conversation takes you on a journey to the tiniest particles and their possible appearances.

**Felicitas Rohden: **Last year, I invited you to take part in my work, *Shapes of Possibility*, to learn more about the characteristics of quantum mechanics and participate in realizing the book object, *Qubits*. When I met you in Cambridge, we sat down to discuss, sketch, and try to visualize the future of quantum computing and its endless computing possibilities. We discussed the character of a quantum state, which is a combination and co-existence of mutually exclusive possibilities. There are too many possibilities to measure each quantum state separately, thus, you measure an ensemble of systems and predict their general character on the long term. How do you deal with this in a mathematical way and do we need another way of thinking to understand its predictability?

**Shaun Datta:** When you make a single measurement on a superposition state, e.g. a hybrid of heads and tails, you can only reveal one of the constituents of the superposition, in this case either heads or tails. Furthermore, the measurement is disruptive, by which I mean that the original superposition state cannot be recovered after making the measurement. Thus, in order to determine the original superposition state, I need many of the same exact quantum state, a so-called ensemble. “Ensemble” is the word physicists use to describe this collection of many identically prepared systems. If we consider the quantum superposition of heads and tails as a single system, then the ensemble in question would be a vast collection of these quantum coins. I can make a single, disruptive measurement of each member of the ensemble and based on the results of this experiment, I can infer the underlying superposition.

Notice that the kind of unpredictability we have here is different than what we’re used to. Imagine that we have a jar of marbles, half of which are red and half of which are blue. There is uncertainty as to which color we will find when we choose a marble from the jar but each marble is either red or blue. For a single marble, there is no uncertainty as to which color characterizes the marble. Quantum mechanics introduces an additional kind of unpredictability: If we imagine a jar of “quantum marbles,” each of which is a superposition of red and blue, we do not know beforehand whether we will find red or blue when we measure a particular marble. Suppose we measure red for a particular marble. Do we know now that the marble is red? No! Likewise if we were to measure blue. That was a valid conclusion for the original marble scenario since there was no uncertainty as to which color characterized the marble. A quantum marble is neither red or blue; it is both! That is what we mean by “superposition.” So when I say that quantum mechanics introduces a new kind of unpredictability, I mean that there is uncertainty as to which color one will measure *even when the state of the marble,* in this case a superposition of red and blue,* is known.*

**SD:** In the exhibit I saw some gloves similar to those drawn in the booklet. What exactly do they convey about the physical phenomenon of entanglement?

**FR: **During our conversation, you told me that pairs or groups of particles interact even when being separated by a large distance. This physical phenomenon is called “quantum entanglement.” The gloves and the drawing of gloves in our book-object relate to entanglement. I am interested in how to bounce abstract theory back to a tactile understanding. How do these particles work together and where does the communication take place? What’s the function of that void in between? Imagine your hands to be a pair of particles, two single entities who perform together. Understand that one hand movement will automatically affect the movement of the other. The double-sided silk glove is a simple metaphor for this action to unravel the inseparable character of elementary particles by one’s own body movement.

You are fascinated by the future of the quantum computer—a device that performs quantum computing. This new computer is based on a logical system using the alogical character of quantum bits (qubits). These devices are much different from the classic transistor-based computers. Quantum computers are still in their infancy but may one day be able to efficiently solve problems not feasible on classic computers. In a classic system, such as our current technology, bits((A BIT or binary digit can have only one of two values. These state values are most commonly represented as either a 0 or 1. A QUBIT is a unit of quantum information and can be in a superposition of both states 0 and 1 at the same time.)) have to be in one state or the other (0 or 1). Quantum mechanics allow the qubit to be in a superposition of both states (0 and 1) at the same time. Is this feature of reversibility unique to quantum mechanics? And does this allow us a more convoluted way of calculating?

**SD: **For context, a logic gate is an object that transforms and manipulates information stored in bits or qubits. Some examples of logic gates are depicted in the *Qubits *book. Consider the NOT gate, which negates a bit, switching 0 to 1 and 1 to 0. This is a classic, reversible gate: classic because the gate acts on bits, and reversible because you can determine what the input was based on the output. So, reversibility is not unique to quantum logic gates. There is also a quantum NOT gate, which acts similarly and is also reversible. Reversibility does not mean that information flows in the reverse direction, but rather that you can trace how the bits or qubits transform as they pass through the logic gates. In short, there are reversible logic gates in both classical and quantum computation. In quantum computation, however, reversibility is a requirement. Why? A tenet of quantum computation is that information, as conveyed by qubits, is never lost. This means that I must be able to trace the transformation of information as it passes through logic gates, backwards or forwards. This mandates reversibility.

I am curious about the process of turning the abstract rules of quantum information into tangible, visual artwork. How did you conceive of the pillow-shaped qubits?

**FR: **The pillow-shaped books as well as the series of pillow-shaped poly dice and qubits run as a common denominatorthrough *Shapes of Possibility*. You refer to the abstract rules of quantum information and the fact that quantum mechanics introduces a new kind of unpredictability. To determine the original state, you need to measure many of

the same exact quantum states. In the process of comprehending these abstract facts, I started playing around with dice and executing them in different materials by drawing shapes and numbers on flexible paper and constructing new objects. Going back and forth between different dimensions made me wonder about the distortions that occured throughout the process as well as the functionality of the dice. These sphere shaped dice have the illusion of their edges but would never fall on just one number and never show just one direction. There would always be many possibilities.

The unruly character of qubits is fascinating but their true existence still seems to be very fragile. You told me that some current designs for qubits need extreme cold to survive, and thus a quantum computer would look like a gigantic freezer. Why is that?

**SD:** Quantum information systems can be finicky because they are very sensitive to random fluctuations, like external vibrations. If a quantum system interacts too much with the external environment, the state decoheres, which is to say that the state loses its useful quantum properties. Scientists and engineers go to great lengths to mitigate these sources

of instability. Extremely low temperatures and vibration damping address some of these problems.

In the book *Qubits,* I saw a drawing of a cat reminiscent of the Cheshire Cat. There is a famous cat in quantum mechanics folklore—Schrödinger’s cat. Can you tell me more about the interplay between the Cheshire Cat and Schrödinger’s cat?

**FR: **I brought *The Game of Logic* by Lewis Carroll and your insights about quantum mechanics together. Carroll transferred complex mathematical and physical facts into children’s books. In chapter six of *Alice’s Adventures in Wonderland*, Alice meets the Cheshire Cat. It constantly grins, can disappear, and can reappear whenever it likes. Sometimes it disappears and leaves its grin behind. The Cheshire Cat’s attitude, reminded me of Schrödinger’s cat,((Schrödinger’s cat is a thought experiment about the nature of quantum mechanics. There is cat in a box who could be dead or alive at the same time depending on its surrounding conditions. It demonstrates the foolishness of thinking about quantum states for

large objects.)) a thought experiment by Austrian physicist Erwin Schrödinger. The Schrödinger’s cat paradox illustrates the problem of quantum mechanics when applied to everyday objects. The scenario implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other. For me, there are many similarities between the Cheshire Cat and Schrödinger’s cat. They both share a similar context of perception and reality. A reality where two different states of existence can exist similarly. Maybe Schrödinger drew the inspiration for his paradox in 1935 from Carroll’s Cheshire Cat, maybe not.

The size of a quantum is almost unimaginable when we relate it to our human size and the world that surrounds us. How we relate to scale depends on our perspective, and that makes it difficult to think about measurement in an abstract way. You told me about h-bar, a perfect mathematical entity.

**SD:** Just to clarify, despite having a name, h-bar is a number (and what number it is depends on which units you use!). We call h-bar fundamental because it appears in lots of equations that describe ubiquitous laws of nature. h-bar provides a natural sense of scale for a quantum system. Just as a meter stick provides a useful unit of length on human scales, so too does h-bar provide a useful sense of scale for a kind of momentum on quantum scales.

What previous collaborations and artwork motivated the medium for *Shapes of Possibility*, like the qubit that opened into a book?

**FR:** I’m really interested to see what happens to mathematical and digital visual surfaces and spaces when they are converted back to physical space. I shift and connect these spaces, digitally and manually, to follow an abstract way of thinking. It results in sculptures and installations. These works are characterized by a blurring between geometrical and organic forms. During conversations with scientists, I invite them to draw with me. The unusual form of the book and its unanticipated position can break through the viewing habits of the spectators and scientists, and can lead to new insights.