How a quantum computer works
A classical computer stores information in bits. Each bit is a 0 or a 1, and the machine computes by flipping them. A quantum computer uses qubits instead. A qubit can hold a 0, a 1, or a blend of both, plus a phase that relates the two. Put many qubits together and those blends span a huge space of possibilities at once. A quantum algorithm steers that space so the wrong answers cancel and the right one stands out.
Running a program takes three steps. First, initialize every qubit to a known state. Next, apply gates: pulses that rotate single qubits and entangle pairs. Finally, measure, which collapses each qubit back to a plain 0 or 1. Measurement is probabilistic, so the circuit is run many times to build up the answer.
One constraint sits above all of this: coherence. A qubit slowly leaks its quantum state into its surroundings, and once that information escapes, the computation is lost with it.
What a qubit is
Physically a qubit is some controllable two-level system: the spin of an electron, the internal state of a trapped ion, or, most commonly today, the two lowest energy levels of a small superconducting circuit. The catch is that these systems usually have more than two levels. A usable qubit needs its zero-to-one transition cleanly separated in frequency from every other transition, so that a control pulse moves only the two states you mean. That separation is called anharmonicity.
A processor is many such qubits, and the hardware has to control each one, couple them together for two-qubit gates, and read each out without disturbing its neighbors. Every one of those is a tension in the layout: strong coupling where a gate happens and almost none everywhere else, a clear path for control and readout signals and no path at all for noise and loss. Resolving those tensions is a matter of geometry, which is why the design problem is electromagnetic before it is quantum.
A qubit is designed at its boundaries
The state of a qubit is quantum, but the thing a hardware team actually draws is not. It is a layout: patterned metal, gaps, dielectric, and a few special elements. The design problem is to choose that geometry so the device has the right energy levels, couples to the things it should, and stays isolated from the things it should not.
That problem runs down a short ladder. Geometry sets the electromagnetic fields. The fields set the Hamiltonian parameters that physicists actually care about. Those parameters set the error budget. When a device behaves wrong, the team walks back up the same ladder to find which edge of the geometry caused it.
The chip is a collection of microwave objects
Take the most common platform, superconducting qubits. Up close the chip is a microwave circuit at millikelvin temperatures [Krantz 2019]. There is a ground plane, a feedline that carries control and readout signals, a resonator for reading the qubit out, and the qubit itself: two capacitor pads bridged by a Josephson junction, the one genuinely nonlinear element on the chip.
Every part except the junction is passive metal. A resonator is a shaped piece of transmission line. A coupler is two structures placed close enough to share fields. Before any quantum mechanics enters, these are antennas, capacitors, and cavities, and they behave exactly the way electromagnetic structures behave.
First, the capacitances
The starting point for a transmon is electrostatics. The two pads form a capacitor, and that capacitance fixes the charging energy, which together with the junction sets the qubit frequency and its anharmonicity, the small detuning between levels that lets you address two of them as a qubit [Koch 2007].
So the first electromagnetic question is a capacitance extraction: put charge on each conductor, solve for the field through the dielectric, and read off the capacitance matrix between every pair of metal pieces. The diagonal sets each qubit's energy. The off-diagonal terms are stray coupling you usually did not ask for. Move a pad by a few micrometers and these numbers move, which is why the layout and the physics are the same conversation.
Modes become Hamiltonians
Capacitance alone does not capture a resonator or the way a qubit and a cavity share energy. For that the tool is an eigenmode solve: with no source applied, find the resonant field patterns of the structure and their frequencies. Each mode is a standing electromagnetic field with a frequency and a loss rate.
The useful step is turning those classical modes into the quantized Hamiltonian. Energy participation ratio analysis does this by asking, for each mode, what fraction of its energy sits in the nonlinear junction [Minev 2021]. From one eigenmode solve you recover the quantities a quantum engineer designs against: mode frequencies, anharmonicity, qubit to resonator coupling, the dispersive shift used for readout, and the loss rate. The field solve and the Hamiltonian are two views of the same object.
Not every question is an eigenmode
Eigenmodes describe the chip sitting still. Many of the questions that decide whether a device works are about the chip being driven. Readout sends a microwave tone down the feedline and measures the transmitted and reflected signal; the qubit state pulls the resonance, and the shift is what you detect. Crosstalk is a driven question too: drive one qubit and ask how much field shows up at its neighbor.
These are scattering problems, not eigenvalue problems. A source is applied at a port, and the solver returns transmission, reflection, and where the rest of the energy went, often as scattering parameters. The same geometry supports both kinds of solve, and a real design uses both: eigenmodes for the spectrum, driven solves for control and isolation.
The error budget lives at the edges
Here is where the geometry stops being a convenience and becomes the whole game. The dominant loss mechanisms in superconducting qubits are not in the bulk metal. They live at surfaces and interfaces: a few-nanometer oxide on the metal, the metal to substrate interface, and the sharp edges of the patterned film.
This is a boundary effect in the literal electromagnetic sense. At a sharp re-entrant metal corner the field does not stay finite; it concentrates and formally diverges, a classic field singularity at an edge [Van Bladel 1991]. Loss accumulates wherever the field is intense, so it accumulates exactly at those edges and thin lossy layers. Coherence is decided in regions micrometers and nanometers across, which means a simulator has to resolve the corner, not average over it. Getting the boundary right is the difference between a predicted lifetime and a measured one.
The same pattern across platforms
Superconducting qubits make the pattern visible, but it is not specific to them.
| Platform | What you draw | The boundary-value problem |
|---|---|---|
| Superconducting | Pads, junction, resonators | Eigenmode and energy participation |
| Spin qubits | Gate electrodes over a heterostructure | Electrostatics, then confined electron states |
| Trapped ions | RF and DC electrodes | Fields that shape the trapping potential |
| Photonic | Waveguides and resonators | Optical modes and scattering |
In each case the substance inside the box is different, but the design move is the same: solve a field problem on a piece of geometry, then read physical parameters off the solution. The quantum behavior is downstream of an electromagnetic boundary-value problem.
Why this matters as quantum scales
It is tempting to treat the layout as packaging around the real physics. It is closer to the truth to say the layout is the physics, expressed as boundaries. The energy levels come from a capacitance, the couplings come from shared modes, and the coherence comes from what happens at a handful of edges and surfaces.
The practical consequence is that design is iteration. You change the geometry, recompute the fields, modes, and couplings, extract the quantum parameters, check the error budget, and redesign. Every turn of that loop is an electromagnetic solve, so how fast and how accurately you can solve sets how fast you can design. The need is not a prettier field plot; it is fast multiscale electromagnetics, because the layout directly sets the Hamiltonian, the couplings, the loss, the crosstalk, and the package modes.
What makes it hard is that one device spans many length scales at once. In a superconducting qubit the same problem reaches from the nanometer oxide layers at the interfaces, through the micron gaps and junction leads, the hundred-micron qubit pads, and the millimeter chip, out to the centimeter package. Resolving all of that is what produces the numbers a quantum engineer designs against: qubit and resonator frequencies, coupling rates, cross-Kerr and ZZ interactions, surface participation, external Q and Purcell decay, package modes, and crosstalk.
As quantum processors scale, the bottleneck is not only fabrication or control. It is predicting how geometry creates fields, and how those fields become quantum behavior. Fast multiscale electromagnetic simulation is what turns quantum hardware design from hand-tuned physics into engineering.
Planck Labs is building an integrated design platform for high-frequency 3D devices, with electromagnetic simulation at its core. Quantum hardware is a clean example of why that matters: the device is quantum, but the design knobs are geometry and fields, and the error budget is set at the boundaries.
References
- Koch, J., Yu, T. M., Gambetta, J., et al. (2007). Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A 76, 042319.
- Krantz, P., Kjaergaard, M., Yan, F., et al. (2019). A quantum engineer's guide to superconducting qubits. Applied Physics Reviews 6, 021318.
- Minev, Z. K., Leghtas, Z., Mundhada, S. O., et al. (2021). Energy-participation quantization of Josephson circuits. npj Quantum Information 7, 131.
- Van Bladel, J. (1991). Singular Electromagnetic Fields and Sources. Oxford University Press.