Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

• URL: http://arxiv.org/abs/2210.04378v4
• Date: Tue, 01 Oct 2024 15:51:57 GMT
• Title: Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms
• Authors: Teague Tomesh, Nicholas Allen, Daniel Dilley, Zain Saleem,
• Abstract summary: computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case.
• Score: 0.4677099525783277
• License:
• Abstract: The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case -- applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost.

Related papers

• YAQQ: Yet Another Quantum Quantizer -- Design Space Exploration of Quantum Gate Sets using Novelty Search [0.9932551365711049]
  We present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates.
  arXiv  Detail & Related papers  (2024-06-25T14:55:35Z)
• A Fast and Adaptable Algorithm for Optimal Multi-Qubit Pathfinding in Quantum Circuit Compilation [0.0]
  This work focuses on multi-qubit pathfinding as a critical subroutine within the quantum circuit compilation mapping problem. We introduce an algorithm, modelled using binary integer linear programming, that navigates qubits on quantum hardware optimally with respect to circuit SWAP-gate depth. We have benchmarked the algorithm across a variety of quantum hardware layouts, assessing properties such as computational runtimes, solution SWAP depths, and accumulated SWAP-gate error rates.
  arXiv  Detail & Related papers  (2024-05-29T05:59:15Z)
• Scaling Up the Quantum Divide and Conquer Algorithm for Combinatorial Optimization [0.8121127831316319]
  We propose a method for constructing quantum circuits which greatly reduces inter-device communication costs. We show that we can construct tractable circuits nearly three times the size of previous QDCA methods while retaining a similar or greater level of quality.
  arXiv  Detail & Related papers  (2024-05-01T20:49:50Z)
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice [44.99833362998488]
  Topological quantum error correction is a milestone in the scaling roadmap of quantum computers. The square-lattice surface code has become the workhorse to address this challenge. In some platforms, however, the connectivities are kept even lower in order to minimise gate errors.
  arXiv  Detail & Related papers  (2024-02-03T15:28:27Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Optimizing quantum gates towards the scale of logical qubits [78.55133994211627]
  A foundational assumption of quantum gates theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Here we report on a strategy that can overcome such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunablebits to execute single qubit while superconducting errors.
  arXiv  Detail & Related papers  (2023-08-04T13:39:46Z)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm [0.0]
  This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
  arXiv  Detail & Related papers  (2021-11-10T11:25:32Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)

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.