Heuristic Quantum Advantage with Peaked Circuits

• URL: http://arxiv.org/abs/2510.25838v1
• Date: Wed, 29 Oct 2025 18:00:03 GMT
• Title: Heuristic Quantum Advantage with Peaked Circuits
• Authors: Hrant Gharibyan, Mohammed Zuhair Mullath, Nicholas E. Sherman, Vincent P. Su, Hayk Tepanyan, Yuxuan Zhang,
• Abstract summary: We design and demonstrate quantum advantage with peaked circuits (HQAP circuits) on Quantinuum's System Model H2 quantum processor.<n>Our largest instance involves all-to-all connectivity with 2000 two-qubit gates, which H2 can produce the target peaked bitstring directly in under 2 hours.<n>This work marks an important milestone toward verifiable quantum advantage, as well as providing a useful benchmarking protocol for current utility-scale quantum hardware.
• Score: 4.0791360680079185
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We design and demonstrate heuristic quantum advantage with peaked circuits (HQAP circuits) on Quantinuum's System Model H2 quantum processor. Through extensive experimentation with state-of-the-art classical simulation strategies, we identify a clear gap between classical and quantum runtimes. Our largest instance involves all-to-all connectivity with 2000 two-qubit gates, which H2 can produce the target peaked bitstring directly in under 2 hours. Our extrapolations from leading classical simulation techniques such as tensor networks with belief propagation and Pauli path simulators indicate the same instance would take years on exascale systems (Frontier, Summit), suggesting a potentially exponential separation. This work marks an important milestone toward verifiable quantum advantage, as well as providing a useful benchmarking protocol for current utility-scale quantum hardware. We sketch our protocol for designing these circuits and provide extensive numerical results leading to our extrapolation estimates. Separate from our constructed HQAP circuits, we prove hardness on a decision problem involving generic peaked circuits. When both the input and output bitstrings of a peaked circuit are unknown, determining whether the circuit is peaked constitutes a QCMA-complete problem, meaning the problem remains hard even for a quantum polynomial-time machine under commonly accepted complexity assumptions. Inspired by this observation, we propose an application of the peaked circuits as a potentially quantum-safe encryption scheme~\cite{chen2016report,kumar2020post,joseph2022transitioning,dam2023survey}. We make our peaked circuits publicly available and invite the community to try additional methods to solve these circuits to see if this gap persists even with novel classical techniques.

Related papers

• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage [17.38734393793605]
  We propose an approximate method for compiling target quantum circuits into brick-wall layouts.<n>This new circuit design consists of two-qubit CNOT gates that can be directly implemented on real quantum computers.
  arXiv  Detail & Related papers  (2025-01-13T15:04:39Z)
• On verifiable quantum advantage with peaked circuit sampling [9.551919087634522]
  We show that getting $1/textpoly(n)$ peakedness from such circuits requires $tau_p = Omega(tau_r/n)0.19)$ with overwhelming probability. We also give numerical evidence that nontrivial peakedness is possible in this model.
  arXiv  Detail & Related papers  (2024-04-22T18:00:06Z)
• Polynomial-Time Classical Simulation of Noisy IQP Circuits with Constant Depth [0.5188841610098435]
  We show that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, the output distribution can be efficiently sampled by a classical computer. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit.
  arXiv  Detail & Related papers  (2024-03-21T17:55:26Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits [63.83649593474856]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years.<n>However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number.<n>This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Circuit connectivity boosts by quantum-classical-quantum interfaces [0.4194295877935867]
  High-connectivity circuits are a major roadblock for current quantum hardware. We propose a hybrid classical-quantum algorithm to simulate such circuits without swap-gate ladders. We numerically show the efficacy of our method for a Bell-state circuit for two increasingly distant qubits.
  arXiv  Detail & Related papers  (2022-03-09T19:00:02Z)
• An Optimized Quantum Implementation of ISD on Scalable Quantum Resources [2.274915755738124]
  We show that Prange's ISD algorithm can be implemented rather efficiently on a quantum computer. We leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs.
  arXiv  Detail & Related papers  (2021-12-12T06:01:10Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Machine Learning Optimization of Quantum Circuit Layouts [63.55764634492974]
  We introduce a quantum circuit mapping, QXX, and its machine learning version, QXX-MLP. The latter infers automatically the optimal QXX parameter values such that the layed out circuit has a reduced depth. We present empiric evidence for the feasibility of learning the layout method using approximation.
  arXiv  Detail & Related papers  (2020-07-29T05:26:19Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.