Unbiased random circuit compiler for time-dependent Hamiltonian simulation

• URL: http://arxiv.org/abs/2212.09445v1
• Date: Mon, 19 Dec 2022 13:40:05 GMT
• Title: Unbiased random circuit compiler for time-dependent Hamiltonian simulation
• Authors: Xiao-Ming Zhang, Zixuan Huo, Kecheng Liu, Ying Li and Xiao Yuan
• Abstract summary: Time-dependent Hamiltonian simulation is a critical task in quantum computing. We develop an unbiased random compiler for TDHS. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems.
• Score: 8.694056486825318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(\Lambda^2)$ with a constant sampling overhead, where $\Lambda$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.

Related papers

• Fast-forwarding quantum algorithms for linear dissipative differential equations [2.5677613431426978]
  We show that a quantum algorithm based on truncated Dyson series can prepare history states of dissipative ODEs up to time $T$ with cost $widetildemathcalO(log(T) (log (1/epsilon))2 )$. As applications, we show that quantum algorithms can simulate dissipative non-Hermitian quantum dynamics and heat process with fast-forwarded complexity sub-linear in time.
  arXiv  Detail & Related papers  (2024-10-17T03:33:47Z)
• A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation [24.332332092371303]
  We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians. We derive a new quantum Gibbs sampler algorithm that utilizes jump operators sampled from a Clifford-random circuit.
  arXiv  Detail & Related papers  (2024-07-09T06:55:19Z)
• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian [0.5097809301149342]
  We show that a na"ive partitioning and low-order splitting formula can yield, through our divide and conquer formalism, superior scaling to qubitization for large $Lambda$. We also give new algorithmic and circuit level techniques for gate optimization including a new way of implementing a group of multi-controlled-X gates.
  arXiv  Detail & Related papers  (2023-06-19T23:20:30Z)
• On the average-case complexity of learning output distributions of quantum circuits [55.37943886895049]
  We show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model. This learning model is widely used as an abstract computational model for most generic learning algorithms.
  arXiv  Detail & Related papers  (2023-05-09T20:53:27Z)
• On the complexity of implementing Trotter steps [2.1369834525800138]
  We develop methods to perform faster Trotter steps with complexity sublinear in number of terms. We also realize faster Trotter steps when certain blocks of Hamiltonian coefficients have low rank. Our result suggests the use of Hamiltonian structural properties as both necessary and sufficient to implement Trotter synthesis steps with lower gate complexity.
  arXiv  Detail & Related papers  (2022-11-16T19:00:01Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Tightening the Dependence on Horizon in the Sample Complexity of Q-Learning [59.71676469100807]
  This work sharpens the sample complexity of synchronous Q-learning to an order of $frac|mathcalS|| (1-gamma)4varepsilon2$ for any $0varepsilon 1$. Our finding unveils the effectiveness of vanilla Q-learning, which matches that of speedy Q-learning without requiring extra computation and storage.
  arXiv  Detail & Related papers  (2021-02-12T14:22:05Z)
• Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation [0.8057006406834467]
  We present a quantum algorithm to solve systems of linear equations of the form $Amathbfx=mathbfb$. The algorithm achieves an exponential improvement with respect to $N$ over classical methods.
  arXiv  Detail & Related papers  (2020-09-09T18:00:09Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

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.