YAQQ: Yet Another Quantum Quantizer -- Design Space Exploration of Quantum Gate Sets using Novelty Search

TL;DR

YAQQ addresses how the choice of native quantum gate sets impacts the fidelity and depth of unitary decompositions. It introduces a hardware-agnostic design-space exploration framework that uses novelty search to discover complementary gate sets conditioned on a dataset of target unitaries, optimizing a joint cost function that includes average process fidelity, circuit depth, and novelty. Key contributions include the integration of SKD, QSD, Cartan, and random decompositions within a novelty-driven search, and demonstration across random and application-specific datasets showing potential gains over standard canonical gate sets. The practical impact lies in improved quantum compilation, architecture-aware gate-set design, and informed evaluation of transversal gates and QISA concepts for NISQ and FTQC contexts.

Abstract

In the standard circuit model of quantum computation, the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits' depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques, and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases of YAQQ in comparing transversal logical gate sets in quantum error correction codes, designing optimal quantum instruction sets, and compiling to specific quantum processors.

Figures (18)

• Figure 1: 1-qubit Data Sets of size 512
• Figure 2: 2-qubit Data Sets of size 508. The axes corresponds to the $t_x, t_y, t_z$ parameters in the 2-qubit canonical gate as defined in Equation \ref{['eq:nl2']} in Section \ref{['s2p5']}.
• Figure 3: The workflow of YAQQ depicting the three usage levels, (i) gate set compiler, (ii) gate set comparator, and (iii) gate set discovery, and the nested dependencies between these levels.
• Figure 4: Module dependencies among the three usage levels. The innermost (light green) compiler modules decompose a single unitary based on a given gate set. The middle comparator level (green) iteratively uses the compiler for a specific dataset and two given gate sets, and compares the statistics of process fidelity and circuit depth. The outer discovery level (darker green) uses the comparator level iteratively to test a candidate gate set suggested by the novelty search based on the ansatz and assesses via a tunable cost function. A new optimal gate set with respect to the given gate set for the chosen data set and cost function is discovered in the process.
• Figure 5: The optimal configuration of the cost function by adjusting the weights. The experiment is conducted on a dataset containing $1$-qubit Haar random unitaries. The novel gate set contains {H1, T1} and a parameterized rotation P1$_{\vec{a}}$, optimized using the SciPy search. The performance of the optimized gate set is then compared with the primitive novel gate set {H1, T1}. Using these two gate sets, we decompose the dataset using the SKT. We investigate the variation in the difference in average process fidelity ($\Delta \langle\text{PF}\rangle$, where $\langle\text{PF}\rangle$ is the average process fidelity for a specific gate set) in decomposing $10$ data points from the dataset with respect to the variation of $w_{apf}$ while keeping the other weights fixed. The more positive the difference is, the more we improve the {H1, T1, P1$_{\vec{a}}$} gate set compared to {H1, T1}. We observe the cost function performs optimally at $w_{apf}=50$, indicating the optimal configuration of the cost function [$w_{apf}$, $w_{npf}$, $w_{acd}$, $w_{ncd}$, $w_{agf}$] = [50,1,1,1,0].