A milestone in semiconductor quantum computing first error correction

Future large-scale quantum computers will rely on quantum error correction (QEC) to protect the fragile quantum information during computation. Serial advances in silicon-based quantum bits have enabled high-quality single-quantum-bit, two-quantum-bit systems; however, challenges remain with three or more coupled quantum bits, three-quantum-bit gates, or measurement-based feedback QEC demonstrations.

Researchers at the RIKEN Institute (Japan) have demonstrated error correction in a silicon spin (semiconductor quantum dot) three-quantum-bit computing system, an important step toward the realization of a large-scale, practical quantum computer. on August 24, the related research was published in Nature under the title "Quantum error correction using silicon spin quantum bits" [1].

01Silicon Quantum Bits: Nanotechnology Compatible, Error Correction in Need of Development

Quantum computers are a hot area of research today, and they promise to solve important problems that are difficult to solve using traditional computers. Compared to classical computers, they have a completely different architecture: using superposition states from quantum physics; however, because they are designed in a completely different way, they are very sensitive to other problems such as environmental noise and decoherence, and require error correction to perform accurate calculations.

An important challenge today is to choose which systems are best able to act as "quantum bits" - the basic units used for quantum computing. Different candidate systems have their own strengths and weaknesses. Popular systems include superconducting circuits and trapped ions, which have the advantage of having demonstrated some error correction and can be put to practical use on a small scale. Silicon-based quantum technology, which has only begun to be developed in the last decade, has the advantage of utilizing semiconductor nanostructures similar to the integration of billions of transistors in a small chip, and can therefore take advantage of current production techniques: the compatibility of silicon-based spin quantum bits with established nanofabrication techniques offers the promise of scaling device sizes from today's prototypes to large-scale computers.

However, a major problem with silicon-based technology is the lack of error correction (error correction) techniques. Researchers have previously demonstrated control of two quantum bits, but this is not sufficient for error correction: a three-qubit system is needed.

02First silicon quantum bit error correction: complete control of a three-qubit system

In this study, conducted by researchers at the RIKEN Center for Emerging Matter Science and the RIKEN Center for Quantum Computing, together they have achieved this feat: demonstrating full control of a three-quantum-bit system (one of the largest quantum-bit systems in silicon), thus providing the first prototype of silicon quantum-bit error correction. They achieved this by implementing a three-quantum-bit Tooffoli-type quantum gate.

Three-quantum-bit QEC and silicon-based three-quantum-bit devices. a) Outline of a three-quantum-bit phase-flip quantum error correction code. It includes the data quantum bit Q 2 and two auxiliary quantum bits Q 1 and Q 3. The two-qubit CNOT gate entangles the three quantum bits, and then the Hadamard (H) gate rotates the quantum bits to generate the phase-flip error. Decoding is the inverse process of encoding. Finally, the correction is performed by a three-qubit Tooffoli gate. b) Scanning electron microscope image of the device. c) Schematic cross section of the device.

The sample specimen used in the experiment is a three-quantum bit defined by a gate in an isotopically natural silicon/silicon-germanium (Si/SiGe) heterostructure, resulting in a silicon spin quantum bit with a mean relaxation time T1 of 22 ms, an inhomogeneous decay time picture of 1.8 μs, and a Hahn echo decay time picture of 43 μs.

To correct the decoded states, the team implemented a Toffoli three-qubit quantum gate and performed tomography of the GHZ state (Greenberger-Horne-Zeilinger state, a three-qubit quantum entanglement state). Subsequently, the experimental team combined with microwave pulses and turned to the implementation of the phase-flip correction code. The results show that the state of the auxiliary quantum bit reflects the error in the encoded quantum bit state: the error detection on the encoded three-qubit state is correctly performed.

Three quantum bit GHZ states and resonance driven iToffoli gate encoding. a) Quantum circuit for generating three quantum bit GHZ states, the two CNOT gates acting on adjacent quantum bits are implemented by a combination of single and double quantum bit gates; b&c) Measured density matrix of three quantum bit GHZ states; d) GHZ state generation results for various input states; e) Three spin state energy schematic; f) Q2 resonance peaks for four different control quantum bit states; g) Schematic of iToffoli gate truth table measurements; h) Measurement results of iToffoli gate truth table.

Single quantum bit phase error correction. a) Schematic diagram of the quantum circuit. The operations used for encoding and decoding are decomposed into single-quantum bit gates and two-quantum bit gates. b) Results of single-quantum bit phase error correction. The fidelity of the uncorrected error fluctuates between 0 and 1, and the fidelity of the corrected error is always equal to 1. c) Results of auxiliary quantum bit measurements. The auxiliary quantum bit states are flipped en masse compared to the case of using standard Toffoli gates.

However, errors in a real quantum computer may occur on all quantum bits at the same time instead of only on one quantum bit. To further demonstrate the successful implementation of a three-qubit phase correction code in silicon, the team verified the performance of the error correction code with all errors having the same effective error rate p. Ultimately, the generation of various three-qubit entangled states, an effective single-step resonantly driven iToffoli gate, and the fundamental properties of three-qubit QEC in silicon were successfully demonstrated.

Three-qubit phase error correction. a) Schematic diagram of a quantum circuit for three-qubit phase error correction. c) Schematic diagram of a quantum circuit for three-qubit degenerate phase error correction. d) Comparison of state fidelity of error-corrected and uncorrected quantum bits.

03Scaling up experiments and collaborating with semiconductor companies

In response to this breakthrough experimental progress, Kenta Takeda, the first author of the paper, stated [2], "The idea of implementing quantum error correction codes in quantum dots was proposed about a decade ago, so this is not a completely new concept, but rather a series of improvements to the material; device fabrication and measurement techniques have enabled us to succeed in this work. We are very pleased to have been able to achieve this."

Research team leader Seigo Tarucha further stated that the next step will be to scale up the system. "We see scaling up as the next step. For this, it would be desirable to collaborate with semiconductor industry groups that can manufacture silicon-based quantum devices on a large scale."

Reference links：

[1]https://www.nature.com/articles/s41586-022-04986-6

[2]https://phys.org/news/2022-08-error-silicon-qubit.html