Hardware · Quantum Computing
Sandia runs fault-tolerant additions below threshold on Quantinuum’s Helios-1
With two small error detection codes, additions of one to three bits fail less often on Helios-1 than unencoded ones. With four and five bits, they do not.
Key points
- On Helios-1, encoded additions of one to three bits fail less often than physical ones; with four and five bits they do not.
- The best figure, more than 50 times fewer failures in the one-bit addition, rests on a single observed failure and has an error bar almost equal to the value.
- The codes detect and discard: valid attempts fall from over 60 % with one bit to about 1 % with five.
A team from Sandia National Laboratories and the University of New Mexico has run fault-tolerant additions on Helios-1, Quantinuum’s 98-qubit trapped-ion quantum computer, with fewer failures than the same addition run directly on the physical qubits. Jacob S. Nelson, Andrew J. Landahl and Andrew D. Baczewski report it in a preprint posted on arXiv on 9 October, which has not yet been peer reviewed.
Addition is a basic building block of many quantum algorithms, including factoring algorithms. The authors compiled a classical ripple-carry adder, the one by Cuccaro and colleagues, for numbers of one to five bits, on an architecture of their own that encodes the information in two small codes, of 8 and 4 physical qubits. These are error detection codes, not correction codes: when they detect an error, the attempt is discarded.
What they measured
- A free check. The adder returns an auxiliary qubit to zero when it finishes. Checking that it does catches errors the codes alone would miss: according to the authors, at many points in the circuit four errors, not two, are needed for one to go undetected.
- One to three bits, better than unencoded. In the one-bit addition, after removing the batches with error bursts, they observed a single logical failure: an estimated rate of (6.0 ± 5.9) × 10−5, against (3.5 ± 1.3) × 10−3 unencoded, more than 50 times lower. With two and three bits the encoded version also fails less often.
- Four and five bits, just above. With four bits, the encoded version fails slightly more often than the physical one. With five, the results break from the trend of the others; they were repeated on several days and the authors do not yet have a full explanation.
- Many discards. The share of attempts that pass every check falls from just over 60 % with one bit to about 1 % with five. In the unencoded circuit it stays above 95 %.
Note · what this work does not show
The one-bit figure rests on a single failure, and its error bar is almost as large as the value. It comes from removing the batches in which, according to the authors, the machine was not performing as usual, something they identified after collecting the data. The inputs were classical numbers, not superpositions, and detecting and discarding does not scale: the share of valid attempts falls exponentially with circuit size.
What changes for decision-makers
It does not bring the factoring of keys any closer: five bits are many orders of magnitude short of what would be needed. What it shows is the real state of early fault-tolerant computing: small codes pay off in short circuits and the advantage is lost as soon as the circuit grows, mainly because qubits waiting unchecked build up errors and, according to the authors, Helios-1 does not allow several encoded blocks to be checked in parallel. Their conclusion, to design the algorithm and the architecture together to make use of checks like the adder’s, is a useful pointer for reading announcements of logical milestones: it is worth looking at how many attempts are discarded and at what circuit size the measurement is made.