If you will cling to Nature… to the little things that hardly anyone sees, and that can so unexpectedly become big and beyond measuring; if you have this love of inconsiderable things and seek quite simply, as one who serves, to win the confidence of what seems poor: then everything will become easier, more coherent and somehow more conciliatory for you.

— Rainer Maria Rilke

A brief review of quantum physics

Quantum mechanics was developed to provide an accurate description of physics at the atomic and subatomic scale. You might know of it from counterintuitive, and often misinterpreted, statements. A quantum system can exist in a superposition of multiple physical states. When observed, this superposition collapses, and the system is found in one of these states according to some probability distribution. It is possible to know the momentum, or the position, of a quantum system — but not both at the same time. Matter exhibits both particle and wave-like characteristics.

These observations have a way of unsettling people. You might be familiar with Einstein’s statement “I, at any rate, am convinced that God does not throw dice,” offered in response to the probabilistic nature underlying the Copenhagen interpretation. It is fair to say that quantum mechanics led to a fundamental change in our understanding of nature — and as such, it helps to look at previous groundbreaking theories and the reactions to them.

Before Newton published his laws of mechanics in Principia (1687), Cartesian physics — which explained gravity through the mechanical action of invisible vortices of matter — dictated the scientific worldview. Newton challenged this view by presenting a proof that it was incompatible with Kepler’s second and third laws of planetary motion. Despite the widespread and near-immediate praise of Principia, Newton’s principles encountered resistance from peers such as Berkeley and Leibniz, as well as from several continental philosophers.

An important point of contention was action at a distance — gravitational force is exerted without contact, even through a vacuum, as with the force keeping the Earth in orbit around the Sun — which was perceived to possess an occult character. The notion that two objects could exert force on each other without contact was so counterintuitive at the time that critics argued a cause or agent is necessary for gravity, and that Newton had not identified such a cause. Philosophers would discuss and critique the implications of Principia for the centuries to come. In the decades after publication, however, Newton’s principles were used to accurately predict natural phenomena — notably, the reappearance of Halley’s comet in 1758 — and Principia garnered universal acclaim; open questions and all.

It is through a similar lens that one can view quantum mechanics. Developed over the 20th century, we are still grappling with fundamental aspects of the theory and the consequences they have for our understanding of nature. In the meanwhile, it has proved singular in its ability to model physics on the atomic scale. Precise calculations of energy levels of electrons in atoms, predictions of novel states of matter such as the Bose-Einstein condensate, and the ability to measure time to a remarkably low uncertainty of seconds — as demonstrated by modern atomic clocks — were all made possible with quantum mechanical principles.

Over the 20th century, scientists also moved beyond merely studying these systems to making them evolve and interact in a controlled manner. The quantum phenomenon of tunneling — where an object passes through an energy barrier that is classically forbidden — is exploited to store information on modern solid-state drives. Lasers, used in applications as wide-ranging as surgery, welding, and spectroscopy, exploit the phenomenon of stimulated emission. A new class of technologies, called quantum technologies, now requires control on an even finer level — including quantum sensors, quantum networks, and quantum computers.

Physical systems and computation

How does one think of quantum computers? It is instructive to start with the “computer” aspect, by drawing analogies with the computers we currently possess — termed classical computers in the quantum community. Each such computer has at its base an underlying physical system. This seemingly trivial statement has profound consequences.

The underlying system of a classical computer is that of a transistor — a semiconductor-based device operating at room temperature. Information is stored in bits, each corresponding to a base-2 number. Consider the floating-gate transistors used in portable flash drives and early SSDs: the two values of each bit are represented by two levels of electric charge stored in the gate. The amount of charge controls the conductivity of a channel — if the transistor conducts, one assigns the number ; if it does not, . Modern drives are built of trillions of transistors, allowing them to store terabytes of information.

How does one carry out calculations — that is, manipulate the stored information? This is realized by passing bits to a logic gate, a combination of transistors that performs operations on the input bits and outputs the transformed result. A NOT gate outputs if the input was , and vice versa. Using such gates as building blocks, one constructs circuits: dedicated circuits exist in our computers for basic arithmetic operations, and all applications — writing emails, playing video games — are, at the machine level, sequences of operations on circuits.

While transistors power most of our computers, alternative physical systems are also being studied. Photons propagating in optical media can carry out computation, exploiting the low latency of light and phenomena such as interference to perform highly efficient matrix multiplications. Consider also the memristor — a device with a resistance that changes continuously depending on the history of the current that has flowed through it. These systems are being investigated for enabling brain-inspired, or neuromorphic, computers: memristors can model weighted connections between neurons, or synapses, with neuroplasticity enabled by the variable resistance.

Quantum computers utilize systems that act according to the laws of quantum physics — such as atoms cooled to near-zero temperatures — for storing and manipulating information. In a quantum bit (or qubit), one maps the values and to two quantum states and of the atom. While a classical bit either has a value of or , a qubit can exist in a superposition — a linear combination of and — with its general quantum state written as

where and are complex coefficients normalized such that . The quantities and represent the probabilities that a given measurement collapses the state to either or . Two qubits can similarly exist in a superposition of , , , . The state over qubits is described by coefficients — this exponential scaling means that quantum computers excel at representing high-dimensional data.

As a concrete example: exact calculations for determining the electronic structure of propane () require roughly 19 terabytes to store the physical state over 46 spin-orbitals. A quantum computer requires only 46 qubits to store such a state. The number of qubits (bits) needed scales linearly (exponentially) with the number of orbitals. Such problems are closely related to modelling interactions between drug molecules and proteins, and quantum computers are being explored for applications in the pharmaceutical industry.

There is also an intrinsic parallelism in the way quantum computers operate: one can act on each of the coefficients simultaneously by applying a quantum gate or circuit. Classes of problems that are classically intractable can be solved efficiently on a quantum computer by exploiting this parallelism — including the simulation of complex physical systems, battery design, and the optimization of large-scale systems relevant to logistics and energy management.

Current state of quantum technologies

If by now you are sold on quantum computing, it is time for a disclaimer: quantum systems are notoriously challenging to build. To ensure that neutral atoms can be used as qubits, one must first cool them close to absolute zero and trap individual atoms in optical tweezers. To store quantum information in electronic states, one must induce transitions between those states with a laser near-resonant with the transition frequency. Quantum systems, upon interaction with the environment, can lose their quantum character — their coherence — and can subsequently be described using classical physics. Preserving coherence over the timescale required to carry out computations is, on its own, an impressive feat.

These are all achievements honored by the Nobel Prize in Physics: 1997 for cooling and trapping atoms, 2005 for quantum optics and coherence, and 2018 for optical tweezers. The long-standing skepticism at the prospect of realizing large-scale quantum computers begins to make sense when one considers that all of these capabilities, and more, must be realized in a single experimental setup. That they have been implemented in current-generation devices — admittedly at small scales and with varying amounts of error — is, to the author, rather impressive. Quantum algorithms requiring all of the aforementioned components have been demonstrated in experiment.

You might recall the classical computers of the mid-20th century, that took up half a room and were plagued by vacuum tube failures that limited both uptime and the reliability of outcomes. Several breakthrough developments were needed to go from those primitive devices to the mature consumer devices of the 1990s, and equally many to arrive at the ones we now carry in our pockets. These developments spanned many fields: theorists worked on error correction — adding redundancy to stored information to systematically reduce loss. Experimentalists studied how to scale up the devices. ASML, near Eindhoven, builds extreme ultraviolet lithography machines that print intricate patterns of transistors onto silicon wafers, enabling densities of 200 million transistors per square millimeter required for state-of-the-art chips.

I posit that quantum computers are, in their trajectory of development, at the point classical computers were in the mid-20th century. To name a few sources of error: atoms might be lost from tweezers. To realize two-qubit gates, one must excite atoms to high-lying, or Rydberg, electronic states — which have a finite lifetime and can decay, causing information loss. Lasers can be noisy; atoms might move in a trap, leading to Doppler shifts. The current generation is often termed the noisy intermediate-scale quantum (NISQ) generation — a phrase coined by John Preskill in a 2018 essay that has since become the field’s lingua franca. Significant research is focused on error correction and mitigation — ways to carry out reliable computation in the presence of such mechanisms — as well as on scaling up devices. A recent milestone: a system of 6,100 neutral atom qubits, demonstrated in 2024.

Neutral atoms are by no means the only architecture for building quantum computers. Leading alternatives include superconducting and trapped-ion platforms, and many more are under investigation. Why use atoms? One reason is that each atom of a given species is identical — in comparison to superconducting qubits, which must be manufactured. Another is scalability, owing to electrical neutrality. There are many other compelling reasons and challenges associated with neutral atoms; these are the subject of my thesis.

This article is adapted from the introduction to my doctoral thesis. For full citations and academic context, see the thesis.