Quantum Error Correction Paves Way for Reliable Quantum Computing, Study From Microsoft and Quantinuum

Quantum computers can potentially solve complex problems beyond the capabilities of classical computing. However, their error rates need to be significantly improved. Quantum error correction and fault-tolerant quantum computing are key to this improvement. Experiments have shown physical error rates approaching the required threshold, but none have demonstrated logical error rates better than physical ones. The transition from noisy intermediate-scale quantum computing to reliable quantum computing can be achieved through hardware and software co-optimization.

Experiments on Quantinuum’s H2 trapped-ion processor have shown that logical error rates can be suppressed below physical ones, marking a significant step towards large-scale fault-tolerant quantum computing.

What is the Promise of Quantum Computers?

Quantum computers hold the potential to solve complex problems that are currently beyond the reach of classical computing. However, to realize this potential, the error rates of quantum computers need to be significantly improved beyond those of the underlying physical hardware. This is where the concept of quantum error correction and fault-tolerant quantum computing comes into play. These theoretical breakthroughs have paved the way for the development of reliable quantum computers.

Without quantum fault tolerance, there is little to no indication that quantum computers can solve important practical problems outside the reach of modern-day supercomputers and machine learning. The experimental challenges remain significant as fault tolerance requires that physical error rates be sufficiently low before the overhead of error correction leads to an improvement over physical non-fault-tolerant operations.

Several experiments have shown indications of physical error rates approaching this critical so-called threshold, while others have demonstrated operations on multiple logical qubits. However, to our knowledge, none of these experiments have shown logical error rates better than the physical error rates, a notable exception being a demonstration of Bell correlations stronger than physical correlations.

How Can We Transition from Noisy Intermediate Scale Quantum Computing to Reliable Quantum Computing?

The transition from noisy intermediate scale quantum computing to reliable quantum computing can be achieved through the co-optimization of hardware and software with a present-day commercial quantum processor. The aim is to show convincingly a large separation between logical and physical error rates in a setting where all single circuit faults are corrected while using logical circuits representative of what would be used for computation.

A commercial trapped-ion quantum charge-coupled device (QCCD) processor has demonstrated several fault-tolerant protocols. The observed logical error rates are conclusively lower than the error rates for their unencoded physical counterparts. This signifies an important transition from noisy intermediate scale quantum computing to reliable quantum computing and demonstrates advanced capabilities toward large-scale fault-tolerant quantum computing.

What is the Methodology Behind Quantum Error Correction?

The approach to quantum error correction largely builds on Gottesman’s proposal. The proposal benchmarks complete quantum circuits and contrasts the error rates of the classical outputs of these circuits. This is a comparison between the outputs of the unencoded physical circuit to that of the corresponding fault-tolerantly encoded circuit on the same hardware.

The metric considered in Gottesman’s proposal is the total variation distance between the output distribution of the ideal circuit and the experimental circuits, encoded or otherwise. For this proposal, the statistical distance between outputs is also considered, but with the addition of classical processing of the measurement outputs so that it is possible to determine success or failure for each individual run of the experiment.

What is the Hardware Platform Used for Quantum Error Correction?

All reported demonstrations of quantum error correction were performed on Quantinuum’s H2 trapped-ion processor. The device was recently reported on in detail and provides a brief overview here. H2 is a shuttle-based quantum charge-coupled device (QCCD) processor that uses 171Yb+ ions as qubits. The ions are confined in a linear Paul trap and manipulated using lasers.

The device has a total of 32 zones, which are used for loading, initialization, readout, and quantum operations. The ions are shuttled between these zones to perform quantum operations. The device is capable of performing single-qubit rotations and two-qubit entangling operations, which are the basic building blocks of any quantum computation.

What are the Results and Implications of Quantum Error Correction?

The results of the experiments on the trapped-ion QCCD processor show that through the use of fault-tolerant encoding and error correction, logical error rates can be suppressed to levels below the physical error rates. In particular, logical qubits encoded in the 7-13 code had error rates 9.8 to 500 times lower than at the physical level, and logical qubits encoded in a 12-24 code had error rates 4.7 to 800 times lower than at the physical level.

These results signify an important transition from noisy intermediate scale quantum computing to reliable quantum computing. They demonstrate advanced capabilities toward large-scale fault-tolerant quantum computing. This is a significant step towards the ambitious goal of scaling quantum computers to large system sizes, for example, to run quantum computations consisting of more than 100 million operations fault-tolerantly.