Google Makes Progress on Scaling Quantum Error Correction

Google has a quantum computing goal of encoding a logical qubit on 1000 physical ones with an error rate of 0.0001% and they have achieved a 3% error rate using 17 qubits. The scaling or error reduction must be 20 times better.

Using a 72-qubit chip, the Google team encoded a single logical qubit in two ways—in either a grid of 17 qubits (nine data and eight ancillary qubits) or 49 qubits (25 data and 24 ancillary qubits). Researchers put each grid through 25 cycles of measurements, looking for flipped qubits. Instead of correcting them, researchers just kept track of them, which sufficed for the experiment, says Julian Kelly, a physicist and director of quantum hardware at Google.

After the 25 cycles, they measured the data qubits directly to see whether the ancillary qubits tracked all the flips or more had sneaked in, meaning the machine lost track of the logical qubit. Over many trials, the probability per cycle of losing the logical qubit was 3.028% with the smaller grid and 2.914% with the bigger one, the team reports today in Nature. Thus, the error rate shrank as the number of physical qubits increased—although just barely.

Nature – Suppressing quantum errors by scaling a surface code logical qubit.

Other Work on Scaling Quantum Error Correction

Quantinuum has performed an experiment in which the logical qubit is more robust than the underlying physical ones, using ion qubits. Physicists at Yale University have done the same in an experiment that mixes superconducting qubits and photons. Ion systems may or may not scale as easily as superconducting qubits.

On August 3, 2022, Quantinuum researchers have hit a significant milestone by entangling logical qubits in a fault-tolerant circuit using real-time quantum error correction. The research, published in a new scientific paper that was released on August 3rd, is the first experimental comparison study of different quantum error correction codes in similar environments and presents a collection of several different experiments. These experiments include:

1. The first demonstration of entangling gates between two logical qubits done in a fully fault-tolerant manner using real-time error correction
2. The first demonstration of a logical entangling circuit that has higher fidelity than the corresponding physical circuit.

Quantinuum used a color code. The researchers combined seven logical qubits into one logical qubit in coordination with 2-3 ancillary qubits used for probing. They implemented this new color code technique on top of Quantinuum’s latest computer with 20 physical qubits to create two reliable logical qubits. These new logical qubits can be efficiently scaled in a way that increases fault tolerance that was not practical with the physical qubits or even the 5-qubit approach.

The highest fidelity operations with the color code, with the fault-tolerant SPAM operation achieving fidelities of 0.99939 and 0.99959 when preparing eigenstates of the logical X and Z operators, which is higher than the average physical qubit SPAM fidelities of 0.9968.

NOTE: practical error correct quantum computers need to look at the errors in the worst pairings of qubits in a larger number of qubits. Achieving really good results for the first two qubits does not matter if more heat and other issues cause increasing errors as the system degrades.