Programming a Quantum Computer

They are more upfront with caveats now. A quantum computer could break modern encryption methods — but only if it had millions of qubits. (The current record: 72 qubits, which Google announced during the meeting.) The hardware wranglers have steadily increased the number of qubits in a machine over the last two years — but quality matters more than quantity, and nobody has demonstrated how to correct qubit errors in an economically viable way. Even with these errors, they anticipate that these relatively few qubits will soon be able to execute an algorithm that a classical computer can’t — a turning point called "quantum supremacy" — but the result will probably just be the solution to a useless, abstract math problem.

But nevertheless researchers are developing useful algorithms. At this year’s March Meeting, several presenters described algorithms motivated by physics problems that could run on existing prototype computers at Google, Intel, and IBM. Many of these algorithms are simulations of well-studied quantum systems, but researchers could eventually extend computing techniques to study less-understood phenomena.

Sonika Johri of Intel is working on an algorithm for the company’s 17-qubit quantum computer that simulates the so-called fractional quantum Hall effect. This effect occurs in two-dimensional electron gases under a strong magnetic field. The electrons in the gas behave collectively such that the ensemble appears to be composed of individual fractional charges, rather than whole electrons.

She aims to simulate a system where the ensemble appears to be composed of thirds of an electron, a phenomenon that has been indirectly observed in experiments. This state should be relatively insensitive to external noise, so it’s a good candidate for quantum information storage. If Johri can make Intel’s superconducting qubits mimic this state, it could potentially be used as quantum computer memory.

Jarrod McClean of Google is developing algorithms to run molecular simulations on a quantum computer. The computer would solve Schrödinger’s equation for a molecule to calculate its allowed energy states. Or, simply put, "given where the nuclei are, how do I figure out where the electrons are going to be?" says McClean.

Quantum computers potentially offer the capability to simulate complicated molecules that classical computers can’t. However, so far researchers have managed to tackle only small molecules with two to three atoms, which classical computers can still manage. The largest molecule modeled to date with a quantum computer is beryllium hydride (BeH₂), simulated on IBM’s 7-qubit machine last September.

These simulations are reasonable near-term goals because the systems map naturally onto the quantum computing architecture. In McClean’s simulations, for example, each qubit could represent a possible electron site in a lattice. If an electron occupies the site, for example, the qubit would read 1; if the site is vacant, 0; if the electron is partly there, partly not — then the qubit would be in a superposition of 1 and 0. The quantum computer would then apply a series of microwave pulses to the qubits to mimic the interactions between the molecule’s constituent particles.

Algorithm developers like Johri and McClean don’t usually interact directly with hardware. Instead, they work on theoretical proofs and protocols at different levels of abstraction. This might include estimating how long the computer will take to solve a problem, writing "pseudocode" (a sort of high-level model of a programming language that is not hardware-specific) or writing an actual sequence of operations performed by logic "gates" on the qubits.

For example, when developing a chemistry simulation, McClean has to translate Schrödinger’s equation into a representation that maps onto the qubits. He also streamlines the gate sequences. "If you imagine physically laying out the qubits, one in the top right corner might not easily talk to the bottom left, depending on how they’re set up," says McClean. "I try to compact these gate sequences so they’re as short and efficient as possible."

Stephen Jordan of Microsoft presented work on algorithms for simulating quantum field theory on quantum computers. He and his collaborators designed pseudocode to simulate two simple quantum field theories: one that described purely bosons, and another that described purely fermions, and estimated how long different versions of the algorithm would take to run. One motivation for this work, Jordan says, is to simulate the entire Standard Model on a quantum computer, or to simulate a scattering experiment or collisions in a particle collider.

Although quantum computing companies are competing with each other, algorithm development culture is relatively open. McClean says that his group at Google behaves in a more "academic" fashion: for example, collaborating with researchers from both academia and other companies, McClean’s group has recently released an open source library called OpenFermion for simulating quantum chemistry problems. Before Jordan joined Microsoft, for example, he made sure the company would let him still publish his research.

But the potential of these near-term algorithms is still unclear. A big challenge facing the field is error correction. State-of-the-art qubits are prone to errors less than 1% of the time, but the errors multiply quickly. While algorithm developers have come up with methods to correct qubit errors, they haven’t yet demonstrated these techniques in full on actual hardware.

To compensate for these errors, McClean’s group will likely use a quantum-classical hybrid algorithm called the variational quantum eigensolver. This algorithm involves an iterative process where different steps of the simulation are fed back and forth between a quantum computer and a classical one. Hybrid approaches can also speed up total computation time.

"The big question is, can we do practical problems without error correction?" says McClean. Small-scale algorithm demonstrations suggest yes. The near-term strategy, he says, is to try the same approaches on progressively larger quantum computers — until they fail. Then, they will develop new methods — and repeat the process.

The author is a freelance writer based in Tucson, Arizona.