Bigger Quantum Computers Could Freeze Up Instead of Speeding Up

Chill a quantum chip to within a hair of absolute zero, minus 273.15 degrees Celsius, wrap the whole assembly in shielding against stray electromagnetic radiation, and you would think you had given the thing every possible chance. A group of theorists in Dresden has just worked out that it might seize up anyway. Not because of a manufacturing flaw or a burst of heat, but because the outside world cannot stop peeking.

The machines in question are adiabatic quantum computers, and they work elegantly. Rather than firing off a long sequence of logic gates, you park the qubits in their ground state, the lowest energy configuration available, and slowly reshape the energy landscape they sit in. Slowly enough, and they follow along, staying in the ground state throughout. When the reshaping finishes, the answer is sitting right there in the state the machine has settled into.

Part of the appeal is that this trick doesn’t much care what your qubits are made of. “Adiabatic algorithms are considered robust and can be executed by quantum computers largely independently of the hardware that is used,” says Ralf Schützhold, who directs the Institute of Theoretical Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). Superconducting circuits etched into solid state, or single ions suspended in electromagnetic traps: both are already running adiabatic algorithms in the lab, and both are meant to be shielded from the sort of low-energy noise that wrecks gate-based machines.

Which is why the finding from Schützhold’s group is a bit of an awkward one. “The quantum Zeno effect is a previously overlooked obstacle to a certain class of quantum computers,” says Gernot Schaller, who heads quantum technologies at the institute.

The Oven Door

Zeno of Elea gave us the tortoise. Achilles must first reach the spot where the tortoise started, by which time the tortoise has shuffled onward, and so on down an infinite regress in which the hero never quite catches up. Calculus dissolves the paradox. Quantum mechanics hands it back with teeth. Measure a quantum system often enough and you really can stop it moving, because each measurement projects it onto a definite state and leaves you adding small probabilities instead of small amplitudes. Watch the pot hard enough and it never boils.

The team’s own comparison is a cake. Leave it alone in the oven and it rises; keep opening the door to check, and it stays flat or sinks. What Schaller, Schützhold and their colleagues Naser Ahmadiniaz and Dennis Kraft have shown, in a paper in the New Journal of Physics, is that an adiabatic quantum computer’s environment plays the part of the person who cannot stop opening the door. “However, a quantum computer can only function properly if its qubits are not disturbed too much,” says Schützhold. Shielding helps. Cooling helps. Neither is ever complete. “But despite all these measures, environmental impacts on the qubits can never be fully eliminated,” he says.

Crucially, nobody has to be doing the measuring. A stray photon, phonon or magnon whose interaction with a single qubit depends on the state of that qubit is already, in effect, taking a weak measurement. The environment is monitoring the machine whether anyone intends it to or not. “This is where the quantum Zeno effect kicks in,” says Schaller. “Each disturbance acts like an unwanted measurement, slowing down the system’s evolution.”

Why Bigger Gets Worse

The whole game of adiabatic computing hangs on the energy gap between the ground state and the first excited state, and somewhere in the middle of the run that gap gets very narrow indeed. For the adiabatic version of Grover’s database search, the version studied in the paper, the smallest gap shrinks roughly as two to the power of minus N over two, where N is the number of qubits. Add qubits and the gap collapses exponentially, so the run time has to stretch exponentially to compensate.

The environment, meanwhile, does no such thing. Its temperature, its coupling strength, its correlation time: none of them shrink exponentially just because you have soldered on more qubits. The team’s estimate has the effective measurement rate actually creeping upward with system size. So you have a transition rate falling off a cliff and a monitoring rate holding steady or rising, and at some point they cross. Past that crossing you are in the Zeno regime, and the quadratic speed-up that made the algorithm worth building in the first place is gone. Push the run time out far enough to get an answer anyway and you are back to the linear scaling of a brute-force classical search. “In the worst case, a calculation could even freeze completely,” says Schaller.

There’s a sting in the tail, and it has to do with method rather than machinery. The equations physicists normally reach for when modeling a noisy quantum system carry a built-in shortcut, one that assumes the states in play are drifting out of step quickly enough that the messy interference between them washes out. Fair enough, most of the time. It stops being fair at exactly the point where the energy gap goes narrow, which is the point that decides everything here. So the Dresden group dropped the shortcut and worked the problem through two other ways. Both gave the same answer: the environment wrecks the delicate relationship between the two competing states. Which means earlier studies pronouncing adiabatic algorithms robust may have been leaning on a tool that stops working right where the interesting physics lives.

Locking the Oven

None of this is a death sentence, and the paper doesn’t claim one. It is theory. The model assumes the environment only nudges the qubits gently, and it stops well short of proving that every adiabatic algorithm will suffer. What the team does argue is that the trouble should turn up in any machine whose answer depends on one big leap: a moment when the qubits have to switch, more or less all at once, from one arrangement to a very different one. That covers a lot of what the industry calls quantum annealing. The label is a loose one, the authors point out, stretched to cover everything from genuinely quantum hardware to classical algorithms in fancy dress.

The escape routes are real enough. Shield harder. Or intervene: “Using the spin-echo method, we can apply coherent pulses to reduce the coupling of qubits to their environment,” says Schützhold. Flip the system’s phase quickly enough and the interaction with the environment averages out to nothing, though you have to be careful the flipping doesn’t itself break adiabaticity.

Alternatively, hide the two competing states inside a decoherence-free subspace, where the environment simply can’t tell them apart, and the Lindblad operators go trivial. Most intriguingly, you could redesign the algorithm so that the ground state morphs gradually rather than tunneling between two distant minima, something closer to a second-order phase transition than a first-order one. That might widen the minimum gap and shorten the run time as well as blunting the Zeno mechanism. Two problems, one fix.

“Our study shows that we can only develop powerful quantum computers when we factor in environmental impacts from the very beginning,” says Schützhold.

We’re used to thinking of decoherence as a thief, scrambling delicate states, knocking answers off course. This is something else: an environment so attentive that it pins the machine in place, holding it still out of sheer relentless observation.

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