Genesis: A Compiler Framework for Hamiltonian Simulation on Hybrid CV-DV Quantum Computers

TL;DR

This paper introduces Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems, and introduces an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set.

Abstract

This paper introduces Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems. Genesis is a two-level compilation system. At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer. At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level. Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set. Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, $\mathbb{Z}_2-$Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry. Our implementation is available at Genesis-CVDV-Compiler(https://github.com/ruadapt/Genesis-CVDV-Compiler).

Figures (7)

• Figure 1: A typical hybrid CV-DV architecture using the superconducting technology. The qumodes are connected in a sparse manner. Each qubit connects to a qumode, and there is no direct connection between qubits liu2024hybridoscillatorqubitquantumprocessors.
• Figure 2: Compilation workflow of Genesis. It first decomposes the Hamiltonian into CV-DV basis gate sets, as well as the Pauli gate we defined in this paper, in the CVDV-QASM language format. Finally, it considers connectivity constraints, performs the hardware mapping and routing stage, and outputs physical circuits.
• Figure 3: Decomposing $(a^{\dagger})^2 a^2$ into three child states, i.e., splitting it into subterms $M$ and $N$ using three methods.
• Figure 4: Recursive decomposition and gate synthesis of $(a^{\dagger})^2 a^2$ into a sequence of basic gates. The red circle indicates the template matching rules from the Decomposition Rules Set (Table \ref{['tab:operatorDecompositionRules']}), and the blue square represents the template matching rules from the hybrid CV-DV gate set (Table \ref{['tab:gateSetGrouped']}).
• Figure 5: An ancilla qumode interacts with every qubit on the path from A to N via Control Parity (CP) gates, performs an unconditional Displacement gate, and then travels back to A's location while performing CP gates. This implements a CD gate in Equation \ref{['eq:multiqubitCD']}. Note that the ancilla qumode can be any qumode, and the CP gates can run in any order. We just pick the qumode below qubit A to illustrate this idea.