Erasure Qubits Make Fault-Tolerant Quantum Computing Faster
New Research Shows Quantum Fault Tolerance Leap Get rid of Qubits Magic State Injection Resource Costs Drop Significantly
The highlights how erasure qubits can reduce the resource overhead of establishing magic states, a fundamental aspect of large-scale, fault-tolerant quantum computers. These qubits' error-heralding capabilities have shown that the much reduced residual Pauli error rate can virtually fully determine the logical error rate of injected magic states, resulting in significant fidelity benefits.
The reliability of non-Clifford operations like the T gate is a major impediment to fault-tolerant quantum computing. Magic states are a popular way to provide these gates in fault-tolerant architectures. Since magic states cannot be built fault-tolerantly, they must be injected and distilled to better fidelity. This distillation procedure is necessary yet resource-intensive.
The first magic state injection phase's integrity affects distillation cost. For instance, a 15-to-1 distillation process can increase distillation fidelity by three orders of magnitude if injection infidelity improves. This distinction can assist evaluate whether short-term applications require many distillation rounds.
Erase Qubits: Signalling Higher Fidelity Errors
The inaccuracy rate of the physical qubits limits injection methods' efficacy. This led to the development of erasure qubits to improve error detection.
Erasure qubits convert dominant noise mechanisms into proclaimed erasure mistakes. This means the qubit can identify a mistake by flagging it with an ancilla or by measuring it outside its computational area. This knowledge improves mistake-correction thresholds and logical error rate scaling and allows for customised strategies. Erasing qubits could be superconducting, confined ions, or neutral atoms.
After postselecting on erasure events during magic state injection, the residual Pauli error rate defines the injected state's logical error rate, which is independent of the erasure error rate. This essential decoupling occurs because the procedure discards states when an erasure error is found. Since this conversion of Pauli mistakes into heralded erasure errors only requires a few retries before a Magic State Injection is accepted, the space-time overhead is just slightly higher than non-erasure qubits with equivalent noise strength.
Injection phase error, dominated by linear contributions from low-weight mistakes, approximates the link between logical error rate, p L, and physical error rate. When erasure qubits are used, only undetectable residual Pauli mistakes p restrict injection error rate.
Hybrid Architecture: Best Value, Low Cost Some architectures make erasure qubit implementation more hard or expensive. Researchers investigated a hybrid injection strategy into the surface code that combines erasure and non-erasure qubits in a patch to address this.
The results indicated that surface code injection can keep most of the benefits of erasure qubits by strategically placing a few at important spots in the code patch. A hook injection circuit needs only three erasure qubits (D1, D3, and Z1) to cover all fault locations that contribute linearly to the logical error rate, independent of patch size.
This hybrid design has higher acceptance rates and comparable logical error rates to all-erasure. The hybrid patch error rate is mostly determined by the residual Pauli error of the carefully positioned erasing qubits (p e). This is an inexpensive way to dramatically reduce magic state overhead in systems without high-quality erasing qubits.
Growth: Embracing Erasures
Erasure qubits are better than surface code injection for the recently suggested colour code-based โMagic State Cultivationโ protocol. Along with injection and special cultivation, the culture method includes fault-tolerant measurement that detects low-order faults and increases magic state integrity.
This technique benefits from every qubit in the cultural patch being an erasing qubit, according to numerical analysis. Even though converting 6 or 9 qubits in a distance-3 colour code culture patch only modestly improves performance, converting all 15 qubits yields a 10-fold boost. If erasure rates are โผ10โ3 and residual undetected errors are โผ10โ4, magic state distillation can be avoided for early fault-tolerant horticultural applications. To attain these extremely low logical error rates and enable near-term fault-tolerant systems, injection and culture methods must be considerably improved.
In conclusion
Erasure qubits provide extra information for efficient post-selection, increasing the logical mistake rate without decreasing acceptance rate even under noisy detection. Erasure detection can reduce the overhead needed to build quantum computing.
