Approximation Algorithm for Noisy Quantum Circuit Simulation

• URL: http://arxiv.org/abs/2211.17028v2
• Date: Thu, 23 Nov 2023 07:28:25 GMT
• Title: Approximation Algorithm for Noisy Quantum Circuit Simulation
• Authors: Mingyu Huang, Ji Guan, Wang Fang and Mingsheng Ying
• Abstract summary: This paper introduces a novel approximation algorithm for simulating noisy quantum circuits. Our method offers a speedup over the commonly-used approximation (sampling) algorithm -- quantum trajectories method.
• Score: 3.55689240295244
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical counterpart because of the quantum state explosion problem (the dimension of state space is exponential in the number of qubits) and the complex (non-unitary) representation of noises. Consequently, only noisy circuits with up to about 50 qubits can be simulated approximately well. This paper introduces a novel approximation algorithm for simulating noisy quantum circuits when the noisy effectiveness is insignificant to improve the scalability of the circuits that can be simulated. The algorithm is based on a new tensor network diagram for the noisy simulation and uses the singular value decomposition to approximate the tensors of quantum noises in the diagram. The contraction of the tensor network diagram is implemented on Google's TensorNetwork. The effectiveness and utility of the algorithm are demonstrated by experimenting on a series of practical quantum circuits with realistic superconducting noise models. As a result, our algorithm can approximately simulate quantum circuits with up to 225 qubits and 20 noises (within about 1.8 hours). In particular, our method offers a speedup over the commonly-used approximation (sampling) algorithm -- quantum trajectories method. Furthermore, our approach can significantly reduce the number of samples in the quantum trajectories method when the noise rate is small enough.

Related papers

• Leapfrogging Sycamore: Harnessing 1432 GPUs for 7$\times$ Faster Quantum Random Circuit Sampling [40.83618005962484]
  Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms has significantly reduced the classical simulation time. Our work provides the first unambiguous experimental evidence to refute textitSycamore's claim of quantum advantage.
  arXiv  Detail & Related papers  (2024-06-27T05:01:47Z)
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics [42.29248343585333]
  We benchmark quantum hardware and error mitigation techniques on up to 133 qubits. We show reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates. Results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning.
  arXiv  Detail & Related papers  (2024-04-11T18:00:05Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• 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)
• Simulating photonic devices with noisy optical elements [0.615738282053772]
  In the near-term, the performance of any quantum algorithm should be tested and simulated in the presence of noise. We apply the recently proposed noisy gates approach to efficiently simulate noisy optical circuits. We also evaluate the performance of a photonic variational quantum algorithm to solve the MAX-2-CUT problem.
  arXiv  Detail & Related papers  (2023-11-17T16:06:20Z)
• Entanglement entropy scaling of noisy random quantum circuits in two dimensions [8.501065978448919]
  noisy quantum devices without error correction can provide quantum advantage over classical computers. In this work, the random quantum circuits are simulated with depolarizing noise on experiment relevant two-dimensional architecture.
  arXiv  Detail & Related papers  (2022-05-27T14:22:28Z)
• Limitations of variational quantum algorithms: a quantum optimal transport approach [11.202435939275675]
  We obtain extremely tight bounds for standard NISQ proposals in both the noisy and noiseless regimes. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing.
  arXiv  Detail & Related papers  (2022-04-07T13:58:44Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Logical Abstractions for Noisy Variational Quantum Algorithm Simulation [25.515765956985188]
  Existing quantum circuit simulators do not address the common traits of variational algorithms. We present a quantum circuit simulation toolchain based on logical abstractions targeted for simulating variational algorithms.
  arXiv  Detail & Related papers  (2021-03-31T17:20:13Z)
• Verifying Random Quantum Circuits with Arbitrary Geometry Using Tensor Network States Algorithm [0.0]
  Algorithm is up to $2$ orders of magnitudes faster than Sch$ddottexto$dinger-Feynman algorithm. We simulate larger random quantum circuits up to $104$ qubits, showing that this algorithm is an ideal tool to verify relatively shallow quantum circuits on near-term quantum computers.
  arXiv  Detail & Related papers  (2020-11-05T02:20:56Z)

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.