The MegaQuOp (shorthand for one million reliable quantum operations) is the threshold where quantum computers will start to outperform classical supercomputers. However, the number of logical qubits will initially remain limited, posing challenges and leading many quantum experts to ask: What could we do with a MegaQuOp anyway?
In answer to this question, a team of UCL and Riverlane researchers introduces "Mitigated Magic Dilution" (MMD), a method that leverages quantum error mitigation techniques to synthesize small-angle rotations. This allows us to sample logical Clifford circuits using noisy encoded magic states.
Fault-tolerant quantum computers will initially have a limited number of qubits. Magic state distillation, a resource-intensive process for implementing non-Clifford gates, is challenging with few qubits. MMD offers a more efficient way to perform small-angle rotations without distillation or gate synthesis overheads, maximising the computational capabilities of early fault-tolerant devices.
In quantum computing, small-angle rotations are an efficient method for implementing non-Clifford operations. They are crucial for implementing various quantum algorithms and can be used to approximate any single-qubit operation with a sufficiently high accuracy.
The "smallness" of the angle is relative; it means the angle is significantly smaller than π or π/2, for example. The smaller the angle, the more challenging it is to implement with conventional gate synthesis approaches, but also the less "powerful" or resource-intensive they are supposed to be, in theory.
In the paper, the researchers use quantum error mitigation techniques to reduce noise-induced bias when sampling logical Clifford circuits given noisy magic states. The process of small-angle single-qubit rotations is then optimised through mitigated magic dilution to achieve better sample complexity.
As a result, the team demonstrated that MMD outperforms the traditional Ross-Selinger gate synthesis method in shorter time evolution regimes when simulating the 2D Fermi-Hubbard model, reducing the amount of noisy encoded magic states required.
The results demonstrate that MMD can provide a practical advantage, showing better-than-quadratic improvement in resource requirements for small-angle rotations over classical simulators.
As experimental quantum error correction and logical computation advance, the need for practical applications for the anticipated "MegaQuOp" era becomes imperative. Our approach addresses the limitations of current techniques in the face of limited qubit availability, making it particularly relevant now.
The prospect of unlocking early fault-tolerant quantum computers with mitigated magic dilution is exciting. I'm particularly interested in exploring how MMD can be further optimised and adapted to other quantum algorithms, including non-Clifford operations. You can read the full paper here.