Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems (2406.01743v4)

Abstract: We introduce a comprehensive quantum solver for binary combinatorial optimization problems on gate-model quantum computers that outperforms any published alternative and consistently delivers correct solutions for problems with up to 127 qubits. We provide an overview of the internal workflow, describing the integration of a customized ansatz and variational parameter update strategy, efficient error suppression in hardware execution, and QPU-overhead-free post-processing to correct for bit-flip errors. We benchmark this solver on IBM quantum computers for several classically nontrivial unconstrained binary optimization problems -- the entire optimization is conducted on hardware with no use of classical simulation or prior knowledge of the solution. First, we demonstrate the ability to correctly solve Max-Cut instances for random regular graphs with a variety of densities using up to 120 qubits, where the graph topologies are not matched to device connectivity. Next, we apply the solver to higher-order binary optimization and successfully search for the ground state energy of a 127-qubit spin-glass model with linear, quadratic, and cubic interaction terms. Use of this new quantum solver increases the likelihood of finding the minimum energy by up to $\sim1,500\times$ relative to published results using a DWave annealer, and it can find the correct solution when the annealer fails. Furthermore, for both problem types, the Q-CTRL solver outperforms a heuristic local solver used to indicate the relative difficulty of the problems pursued. Overall, these results represent the largest quantum optimizations successfully solved on hardware to date, and demonstrate the first time a gate-model quantum computer has been able to outperform an annealer for a class of binary optimization problems.

• The paper introduces an advanced QAOA workflow on a 127-qubit IBM gate-model quantum computer that outperforms quantum annealers for binary optimization.
• It employs an enhanced variational ansatz and efficient parametric compilation to reduce circuit depth and optimize resource utilization.
• Robust error suppression and classical post-processing techniques achieve a 1500-fold improvement in accuracy over D-Wave’s performance.

Quantum Optimization on Gate-model Quantum Computers: A Comparative Performance Analysis

The paper by Sachdeva et al. investigates the capabilities of gate-model quantum computers in solving combinatorial optimization problems, specifically unconstrained binary optimization problems, leveraging a comprehensive quantum solver developed by the authors. This work is pivotal as it contrasts the performance of gate-model quantum processors, like those manufactured by IBM, against quantum annealers from D-Wave for complex, higher-order optimization problems, and delivers results that challenge the notion that quantum annealers are superior in the near term for these tasks.

Methodological Advancements

The paper presents an advanced workflow for implementing the Quantum Approximate Optimization Algorithm (QAOA) on an IBM gate-model quantum computer using up to 127 qubits. This includes several novel aspects:

• Enhanced Variational Ansatz: The authors modify the typical QAOA process by introducing a richer parameterization, incorporating initial state parameter tuning, which reduces the required QAOA depth, helping manage the limitations of current quantum hardware.
• Efficient Parametric Compilation: Their customized compiler supports enriched gate sets, allowing for an efficient circuit realization that reduces gate count and execution time, thus improving hardware resource utilization.
• Comprehensive Error Suppression: The solver integrates robust error-mitigation techniques that include layout optimization, dynamical decoupling, and AI-driven pulse replacements, achieving significant error reduction.
• Post-processing Techniques: A classical greedy optimization strategy is implemented to address output bit-flip errors efficiently, facilitating improved approximation ratios without additional quantum resources.

Results

The solver's abilities were benchmarked against several classically challenging problems:

• Max-Cut Problem: The solver effectively solved Max-Cut instances for random regular graphs with up to 120 nodes, presenting a 4-fold increase in scaling capability over previous implementations on different technologies like trapped-ion qubits. Particularly noteworthy is the solver's efficacy in non-native graph topologies concerning device connectivity.
• Higher-order Binary Optimization (HOBO) Problems: The solver's most striking results are in optimizing a 127-qubit high-order Ising spin-glass model, where it notably increased the accuracy of finding the correct solution by a factor of 1500 compared to D-Wave's quantum annealer performance.

These outcomes are critical as they represent some of the largest optimization problems tackled on quantum hardware, signifying that gate-model computers are crossing a performance threshold where they can outperform annealers in certain problem sets.

Practical and Theoretical Implications

Theoretically, this paper pushes the boundaries of what's feasible with gate-model quantum computing, providing evidence that sophisticated algorithmic and error-mitigation strategies can mitigate inherent hardware limitations effectively. Practically, these results suggest impending commercial viability, where gate-model machines could handle optimization problems that are integral to industries like logistics, finance, and more without relying heavily on classical simulation.

Future Prospects

As the field progresses, continued improvements in error correction, scalability, and robustness of quantum operations can be anticipated. Given the solver's architecture-agnostic framework, similar strategies could be employed on emerging quantum technologies (e.g., newer superconducting qubit architectures or integrated photonic processors) to further close the quantum advantage gap over classical methods.

This work sets a benchmark for subsequent research in quantum optimization and suggests that hybrid methods combining both annealers and gate-model machines could allow users to leverage each platform's strengths in tackling various facets of complex optimization problems.