Improved Quantum Computing with the Higher-order Trotter Decomposition

• URL: http://arxiv.org/abs/2205.02520v2
• Date: Mon, 24 Oct 2022 03:52:57 GMT
• Title: Improved Quantum Computing with the Higher-order Trotter Decomposition
• Authors: Xiaodong Yang, Xinfang Nie, Yunlan Ji, Tao Xin, Dawei Lu, and Jun Li
• Abstract summary: We use Trotter decompositions to reduce the propagator into a combination of single-qubit operations and fixed-time system evolutions. We show that the higher-order Trotter decompositions can provide efficient Ans"atze for the variational quantum algorithm.
• Score: 9.713857446596721
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ans\"atze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.

Related papers

• Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems [0.22120851074630177]
  We show how to use the spin-state path path to shape the geometry of quantum adiabatic evolution. Our method works for large systems and may thus be used to improve the performance of state-of-the-art quantum devices.
  arXiv  Detail & Related papers  (2024-11-12T08:54:13Z)
• 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)
• Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond [0.0]
  Simulation of continuous time evolution requires time discretization on both classical and quantum computers. We introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. Our algorithm can be potentially useful on a more general level whenever time discretization is involved concerning, for instance, also numerical approaches based on time-evolving block decimation methods.
  arXiv  Detail & Related papers  (2022-09-26T12:54:32Z)
• Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction [77.97248520278123]
  We propose Shuffle-QUDIO to involve shuffle operations into local Hamiltonians during the quantum distributed optimization. Compared with QUDIO, Shuffle-QUDIO significantly reduces the communication frequency among quantum processors and simultaneously achieves better trainability.
  arXiv  Detail & Related papers  (2022-09-26T06:51:20Z)
• 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)
• Ultrafast Holonomic Quantum Gates [4.354697470999286]
  We propose a nonadiabatic holonomic quantum scheme with detuned interactions on $Delta$-type three-level system. Our numerical simulations show that the gate robustness is also stronger than previous schemes. We present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding.
  arXiv  Detail & Related papers  (2021-08-03T14:31:38Z)
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing [0.0]
  We introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits. Our strategy can improve upon the Trotter- Suzuki accuracy by several orders of magnitude. We can extrapolate our method to beyond classically simulatable system sizes.
  arXiv  Detail & Related papers  (2021-06-07T14:59:50Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• 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)
• Optimizing adiabatic quantum pathways via a learning algorithm [10.664271328456728]
  We propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.
  arXiv  Detail & Related papers  (2020-06-27T06:57:59Z)

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.