Papers for

quantum hardware architects

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Quantum circuits achieve fastest possible depth for single qubit gates

Depth-Optimal Quantum Compilation

Abstract: We achieve the first constant-depth circuit for arbitrary single-qubit gate synthesis. Unlike prior approaches, the construction is fully unitary and requires no pre-supplied catalyst. For any constant $δ>0$, it $\varepsilon$-approximates an arbitrary single-qubit gate using $O(\log^{1+δ}(1/\varepsilon))$ clean ancillae, Hadamard and $T$ single-qubit gates, $O(\log(1/\varepsilon))$-width generalized Toffoli gates, and sublogarithmic-width Fan-Out gates. We further eliminate Fan-Out entirely, showing that Hadamard, $T$, and generalized Toffoli gates alone suffice for constant-depth synthesis. When restricted to the standard bounded-width gate model, our construction has depth $O(\log\log(1/\varepsilon))$, and we prove a matching $Ω(\log\log(1/\varepsilon))$-depth lower bound. Overall, we establish that $Θ(\log\log(1/\varepsilon))$-depth is unavoidable with only bounded-width gates, yet allowing even logarithmic-width multi-qubit gates suffices to achieve constant-depth synthesis. These results also reveal new structure in shallow quantum circuit complexity. We give a depth-preserving real simulation of bounded-error decision computation, showing that every depth-$d$ QAC circuit can be simulated in depth $O(d)$ using only Hadamard, $X$, and generalized Toffoli gates. Thus arbitrary single-qubit rotations and complex amplitudes do not increase the bounded-error decision power of QAC, even at constant depth. In particular, this reduces the long-standing conjecture Parity$\notin$QAC$^0$ to proving a Parity lower bound against circuits consisting only of Hadamard, $X$, and generalized Toffoli gates. More generally, this real normal form exposes a direct correspondence between the standard shallow-depth quantum circuit hierarchy and a hierarchy of Forrelation circuits with restricted oracle families.

Mon 28 SeptComputational Complexity
The gist
Quantum computers use circuits made of gates to perform tasks, but making these circuits as short as possible (in depth) is important for efficiency. This paper shows that synthesizing any single-qubit gate can be done with a constant-depth circuit if you allow certain multi-qubit gates, which is faster than previously thought possible. However, if you only use small-width gates, then the circuit depth must grow slowly as gate accuracy improves. The authors also connect these findings to how quantum circuits decide certain problems, simplifying the study of their complexity.
Open → 2609.34659v1