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This research confirms linear-depth circuits as optimal for constructing approximate designs within specific quantum groups like Clifford and matchgate sets, effectively closing a theoretical loophole regarding sublinear depth expansions. By leveraging invariant states to probe circuit complexity, the study establishes fundamental bottlenecks that will influence benchmarking protocols and scalability assessments for near-term quantum hardware.
Shallow Circuits Fail to Realise Approximate Designs for Quantum Groups
Linear-depth quantum circuit constructions are now confirmed as optimal for key groups of unitaries, defying previous attempts to circumvent this limitation. Earlier work explored whether expanding to ‘ambient’ unitaries could enable shallower circuits, but this research demonstrates such approaches remain ineffective. The finding solidifies a fundamental bottleneck in quantum computation and benchmarking protocols for matchgate, orthogonal, symplectic, and Clifford groups.
Maxwell West of Los Alamos National Laboratory and colleagues have shown that constructing approximate designs, key for quantum computation and benchmarking, is fundamentally limited for specific quantum groups. A loophole allowing faster, sublinear circuit depths using additional unitaries beyond these groups does not exist. The team has confirmed a fundamental limit to the efficiency of constructing specific quantum computations. Building circuits utilising operations…
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