Application Scale Quantum Circuit Compilation with Controlled Error

TL;DR

This work develops a practical workflow for managing and optimizing quantum circuit compilation and optimization at scales of hundreds of qubits, and shows that it can simultaneously achieve substantial reductions in resource-intensive gates and control output errors.

Abstract

Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources, such as two-qubit gates or arbitrary angle single-qubit rotations, and minimizing the approximation error of the compiled circuit to the ideal target unitary describing the quantum algorithm. We develop a practical workflow for managing and optimizing this tradeoff, which enables quantum circuit compilation and optimization at scales of hundreds of qubits. Our workflow is able to tackle circuits at such large scales while providing rigorous guarantees on circuit output error by leveraging circuit partitioning and the notion of averaging over circuit ensembles. We demonstrate our workflow on several benchmark algorithmic circuits acting on up to 380 qubits, and show that it can simultaneously achieve substantial reductions in resource-intensive gates and control output errors, offering a practical and scalable strategy for both near-term and fault-tolerant quantum computing.

Figures (6)

• Figure 1: High level overview of our workflow. Each step is summarized in the text and discussed in detail in the Methods.
• Figure 2: (a) Geometric intuition for the reduced Frobenius error condition. Ensemble members (blue dots) lie within an $\epsilon$-ball (light blue) around the target $V^{(k)}$ (red star). Their convex hull (dashed orange) contains the target, ensuring the weighted ensemble (green dot) lies within an $\epsilon^2$-ball (light green).
• Figure 3: Observable errors (y-axis) for Fermi–Hubbard Model, LiH and Heisenberg benchmarks, as a function of the compilation error tolerance $\epsilon$. The left panel shows NISQ compilation results; the right panel shows FT compilation results. For each benchmark, we draw a corresponding dotted line at $K\epsilon^2$ where $K$ is the number of blocks in the benchmark. Across all benchmarks, the observable error is bounded by this line.
• Figure 4: Output state errors (y-axis) for the QAOA, Fermi Hubbard, Heisenberg, and LiH benchmarks. For each benchmark and each $\epsilon$, we generate a set of 10 random input density matrices and choose the density matrix that maximizes the output trace distance with respect to the original circuit. This metric serves as a proxy for the worst-case distance (diamond distance) which is intractable to solve. We plot this maximum trace distance (y-axis) between ensemble and ideal outputs as a function of $\epsilon$ (x-axis). The left panel shows NISQ results; the right shows FT results. For each benchmark, we draw a corresponding dotted line at $K\epsilon^2$ where $K$ is the number of blocks in the benchmark. In all cases, the trace distance is bounded by this line.
• Figure 5: Convergence of output state error, as measured by trace distance, for the 7-qubit Heisenberg benchmark as a function of the number of samples drawn from the ensemble channel. Dotted horizontal lines indicate $\epsilon^2$ for each target $\epsilon$. We run 10 different trials at each sample and plot the average (solid line) as well as the full range (area). The inset figure plots the number of samples required until the sampled empirical channel, $\hat{\mathcal{U}}[\rho]$, achieves an average output state error $\epsilon^2$ from the true channel, $\mathcal{V}[\rho]$. The number of samples required for $\epsilon \in \{ 10^{-4}, 10^{-5} \}$ are extrapolated values. The dotted blue line is equal to $\epsilon^{-2}$, and empirically upper bounds the number of samples required.