Efficient quantum algorithm to simulate open systems through a single environmental qubit

• URL: http://arxiv.org/abs/2311.10009v2
• Date: Mon, 14 Oct 2024 10:06:48 GMT
• Title: Efficient quantum algorithm to simulate open systems through a single environmental qubit
• Authors: Giovanni Di Bartolomeo, Michele Vischi, Tommaso Feri, Angelo Bassi, Sandro Donadi,
• Abstract summary: We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers. Under fixed accuracy conditions, our algorithm enables a reduction in the number of trotter steps compared to other approaches.
• Score: 0.0
• License:
• Abstract: We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves two significant advancements. First, we employ a repetition of unitary gates on a set of $n$ system qubits and, remarkably, only a single ancillary bath qubit representing the environment. It follows that, for the typical case of $m$-locality of the Lindblad operators, we reach an exponential improvement of the number of ancilla in terms of $m$ and up to a polynomial improvement in ancilla overhead for large $n$ with respect to other approaches. Although stochasticity is introduced, requiring multiple circuit realizations, the sampling overhead is independent of the system size. Secondly, we show that, under fixed accuracy conditions, our algorithm enables a reduction in the number of trotter steps compared to other approaches, substantially decreasing circuit depth. These advancements hold particular significance for near-term quantum computers, where minimizing both width and depth is critical due to inherent noise in their dynamics.

Related papers

• Practical, optimal preparation of general quantum state with exponentially improved robustness [5.149586838873632]
  In this work, we overcome existing methods with a bucket-brigade approach. Our approach is the first to simultaneously achieve linear Clifford$+T$ circuit depth, gate count number, and space-time allocation. These advancements offer the opportunity for processing big data in both near-term and fault-tolerant quantum devices.
  arXiv  Detail & Related papers  (2024-11-05T03:48:00Z)
• Error filtration from optimized quantum circuit interference [0.0]
  We develop an optimized hardware strategy to mitigate errors in a noisy qubit. Our scheme builds on the physical principle of error filtration and exploits auxiliary qubits.
  arXiv  Detail & Related papers  (2024-09-02T17:58:44Z)
• Quantum-Trajectory-Inspired Lindbladian Simulation [15.006625290843187]
  We propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $epsilon$ and introduces only an additional $tildeO(m)$ factor.
  arXiv  Detail & Related papers  (2024-08-20T03:08:27Z)
• High-Entanglement Capabilities for Variational Quantum Algorithms: The Poisson Equation Case [0.07366405857677226]
  This research attempts to resolve problems by utilizing the IonQ Aria quantum computer capabilities. We propose a decomposition of the discretized equation matrix (DPEM) based on 2- or 3-qubit entanglement gates and is shown to have $O(1)$ terms with respect to system size. We also introduce the Globally-Entangling Ansatz which reduces the parameter space of the quantum ansatz while maintaining enough expressibility to find the solution.
  arXiv  Detail & Related papers  (2024-06-14T16:16:50Z)
• Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach [1.806183113759115]
  Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve quantum advantages. We present a novel $gammaPPP method based on the integral path of observables back-propagation on paths. We conduct classical simulations of IBM's zeronoised experimental results on the 127-qubit Eagle processor.
  arXiv  Detail & Related papers  (2023-06-09T10:42:07Z)
• A single $T$-gate makes distribution learning hard [56.045224655472865]
  This work provides an extensive characterization of the learnability of the output distributions of local quantum circuits. We show that for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth $d=omega(log(n))$ Clifford circuits is hard.
  arXiv  Detail & Related papers  (2022-07-07T08:04:15Z)
• 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)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• 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.