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Hybrid Method of Efficient Simulation of Physics Applications for a Quantum Computer

Carla Rieger, Albert T. Schmitz, Gehad Salem, Massimiliano Incudini, Sofia Vallecorsa, Anne Y. Matsuura, Michele Grossi, Gian Giacomo Guerreschi

TL;DR

The paper tackles the computational bottleneck of simulating trotterized quantum chemistry Hamiltonians on classical hardware. It introduces a Clifford-fullstate hybrid simulator (CFHS) that uses a Pauli frame to efficiently handle Clifford operations while delegating non-Clifford multi-qubit rotations to a full-state backend, yielding substantial speedups. Empirical benchmarks on random and chemistry Hamiltonians (up to 24 qubits) show locality-independent runtime and speedups up to roughly 18–22×, with MPI further enhancing gains and without shifting compilation costs. This approach advances quantum-software benchmarking and algorithm development by enabling larger, more realistic classical simulations that inform quantum hardware requirements and algorithm design.

Abstract

Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum circuits are essential for determining the problem size at which quantum solutions outperform classical methods. In this work, we present a novel hybrid simulation approach, forming a hybrid of a fullstate and a Clifford simulator, specifically designed to address the computational challenges associated with the time evolution of quantum chemistry Hamiltonians. Our method focuses on the efficient emulation of multi-qubit rotations, a critical component of Trotterized Hamiltonian evolution. By optimizing the representation and execution of multi-qubit operations leveraging the Pauli frame, our approach significantly reduces the computational cost of simulating quantum circuits, enabling more efficient simulations. Beyond its impact on chemistry applications, our emulation strategy has broad implications for any computational workload that relies heavily on multi-qubit rotations. By increasing the efficiency of quantum simulations, our method facilitates more accurate and cost-effective studies of complex quantum systems. We quantify the performance improvements and computational savings for this emulation strategy, and we obtain a speedup of a factor $\approx 18$ ($\approx 22$ with MPI) for our evaluated chemistry Hamiltonians with 24 qubits. Thus, we evaluate our integration of this emulation strategy into the Intel Quantum SDK, further bridging the gap between theoretical algorithm development and practical quantum software implementations.

Hybrid Method of Efficient Simulation of Physics Applications for a Quantum Computer

TL;DR

The paper tackles the computational bottleneck of simulating trotterized quantum chemistry Hamiltonians on classical hardware. It introduces a Clifford-fullstate hybrid simulator (CFHS) that uses a Pauli frame to efficiently handle Clifford operations while delegating non-Clifford multi-qubit rotations to a full-state backend, yielding substantial speedups. Empirical benchmarks on random and chemistry Hamiltonians (up to 24 qubits) show locality-independent runtime and speedups up to roughly 18–22×, with MPI further enhancing gains and without shifting compilation costs. This approach advances quantum-software benchmarking and algorithm development by enabling larger, more realistic classical simulations that inform quantum hardware requirements and algorithm design.

Abstract

Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum circuits are essential for determining the problem size at which quantum solutions outperform classical methods. In this work, we present a novel hybrid simulation approach, forming a hybrid of a fullstate and a Clifford simulator, specifically designed to address the computational challenges associated with the time evolution of quantum chemistry Hamiltonians. Our method focuses on the efficient emulation of multi-qubit rotations, a critical component of Trotterized Hamiltonian evolution. By optimizing the representation and execution of multi-qubit operations leveraging the Pauli frame, our approach significantly reduces the computational cost of simulating quantum circuits, enabling more efficient simulations. Beyond its impact on chemistry applications, our emulation strategy has broad implications for any computational workload that relies heavily on multi-qubit rotations. By increasing the efficiency of quantum simulations, our method facilitates more accurate and cost-effective studies of complex quantum systems. We quantify the performance improvements and computational savings for this emulation strategy, and we obtain a speedup of a factor ( with MPI) for our evaluated chemistry Hamiltonians with 24 qubits. Thus, we evaluate our integration of this emulation strategy into the Intel Quantum SDK, further bridging the gap between theoretical algorithm development and practical quantum software implementations.
Paper Structure (27 sections, 1 theorem, 38 equations, 14 figures, 2 tables)

This paper contains 27 sections, 1 theorem, 38 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Elements of Clifford simulation and notation
  3. Pauli and Clifford Group
  4. Pauli Masks
  5. Details on Clifford Simulation
  6. Multi-qubit rotations in a fullstate simulator
  7. Clifford-Fullstate Hybrid Simulator
  8. Pauli Frame as a Lookup Table for Multi-qubit Rotations and Measurements
  9. Description of the Clifford-fullstate hybrid simulation
  10. Alternative Interpretation of the Clifford-Fullstate Hybrid Simulation
  11. Extraction of Expectation Values
  12. Applications and Benchmarking
  13. Preliminaries of Hamiltonian Simulation
  14. Evaluation on Random Hamiltonians
  15. Evaluation on Chemistry Hamiltonians
  16. ...and 12 more sections

Key Result

Theorem 1

A Clifford unitary $U \in \mathcal{C}_n$ can be implemented using at most $\mathcal{O}(n)$ multi-qubit rotations of the form $R(\theta) = e^{-i\theta/2 P}$ with Paulis $P \in \mathcal{P}_n$.

Figures (14)

  • Figure 1: Workings of the hybrid approach combining Clifford and fullstate simulation. This includes, on the one hand, the efficient simulation of Pauli gates using Pauli frame tracking and the emulation of non-Clifford gates by utilizing the Pauli frame as a lookup table, which allows for representing multi-qubit Pauli rotations as single-qubit Pauli rotations with a modified rotation axis. The updated element is highlighted in green, respectively.
  • Figure 2: Demonstration of the sequential updates applied to the respective Pauli frame as defined in Eq. \ref{['eq:framemat']} under the gate-by-gate action of the Cliffords. Thus, by tracking updates to the Pauli frame, we can efficiently simulate this Clifford circuit.
  • Figure 3: Illustrating the commutation behavior as described in Eq. \ref{['eq:single_to_multirot']}, we can commute the Clifford unitary $U$ (here given by a single CNOT gate as an example) past the rotation, translating the single qubit rotation to a multi-qubit one.
  • Figure 4: The unitary $e^{-i \frac{\theta}{2} P}$ generated by the Pauli $P=\sigma_x \otimes \sigma_y \otimes \sigma_z \otimes \sigma_x$ acting on 4 qubits can be decomposed in the presented CNOT staircase trotter1959productwhitfield2011simulation for implementation with one and two qubit gates.
  • Figure 5: Comparison of the simulation time (runtime [s]) for random Hamiltonians with varying locality $L$, 100 terms and 24 qubits, comparing results based on CFHS and IQS with and without MPI in this exemplary case. We observe a significant reduction in simulation time with our new CFHS method in both cases, with and without MPI. The linear increase of IQS simulation time in terms of the locality $L$, in contrast to the constant scaling of CFHS in locality $L$, is nicely visible for results obtained with and without MPI.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Definition 1: kitaev2002classicalbluhm2024hamiltonian
  • Theorem 1
  • proof
  • Definition 2: Clifford Pauli rotation