Hamiltonian dynamics simulation using linear combination of unitaries on an ion trap quantum computer

• URL: http://arxiv.org/abs/2501.18515v2
• Date: Fri, 07 Feb 2025 14:39:15 GMT
• Title: Hamiltonian dynamics simulation using linear combination of unitaries on an ion trap quantum computer
• Abstract summary: The linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics.<n>Given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-intensive to implement on the current quantum computers.
• Score: 2.164508552729841
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics. However, given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-intensive to implement on the current quantum computers. In this work, we demonstrate LCU implementations on an ion trap quantum computer for calculating squared overlaps $|\langle \psi(t=0)|\psi(t>0)\rangle|^2$ of time-evolved states. This is achieved by an optimized LCU method, based on pre-selecting relevant unitaries, coupled with a compilation strategy which makes use of quantum multiplexor gates, leading to a significant reduction in the depth and number of two-qubit gates in circuits. For $L$ Pauli strings in a Taylor series expanded $n$-qubit-mapped time evolution operator, we find a two-qubit gate count of $2^{\lceil log_2(L)\rceil}(2n+1)-n-2$. We test this approach by simulating a Rabi-Hubbard Hamiltonian.

Related papers

• Optimal Lower Bounds for Hamiltonian Simulation [42.227880669333835]
  For Hamiltonian $H = sum_j h_j$, we proveally tight lower bounds on the gate and query complexities of simulating time evolution on a quantum computer.<n>Our hold for arbitrary term norms $|h_j|$, time $t$, and trace-distance error $$.
  arXiv  Detail & Related papers  (2026-07-22T07:41:32Z)
• Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth [73.08853228981701]
  Matrix chain multiplication is a problem in scientific computing, machine learning, and graph analysis.<n>We present emphTwo-Tower Matrix, a quantum subroutine that encodes the product $mathcalW$ of the $K$ matrices into a quantum state in circuit depth.
  arXiv  Detail & Related papers  (2026-07-14T18:42:40Z)
• Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation [0.0]
  We decompose an arbitrary square matrix into a linear combination of non-unitaries (LCNU) where each non-unitary term is embedded into a unitary matrix.<n>We provide an estimate of our LCNU strategy's T gate cost in conjunction with (1) encoding block oracles, and (2) the variational quantum linear solver.
  arXiv  Detail & Related papers  (2026-05-01T00:10:50Z)
• Efficient Complex-Valued State Preparation on Bucket Brigade QRAM [47.72095699729477]
  Efficient quantum state preparation is a critical component in quantum algorithms that process large classical data.<n>We present two improvements within the same architecture-aware framework.
  arXiv  Detail & Related papers  (2026-04-28T13:43:29Z)
• Practical framework for simulating permutation-equivariant quantum circuits [0.0]
  We introduce a practical algorithm for $S_n$-equivariant circuits under the assumption that the gate generators are at most $k$-local, with $kin O(1)$.<n>The resulting method runs in $O(n+1)$ time for constant depth, where $$ is the matrix multiplication exponent, significantly lowering the degree compared to existing techniques.
  arXiv  Detail & Related papers  (2026-03-13T15:18:18Z)
• Block encoding of sparse matrices with a periodic diagonal structure [67.45502291821956]
  We provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure.<n>Various applications for the presented methodology are discussed in the context of solving differential problems.
  arXiv  Detail & Related papers  (2026-02-11T07:24:33Z)
• Transmutation based Quantum Simulation for Non-unitary Dynamics [35.35971148847751]
  We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form $A=Ldagger L$.<n>Our main tool is the Kannai transform, which represents the diffusion semigroup $e-TA$ as a Gaussian-weighted superposition of unitary wave propagators.
  arXiv  Detail & Related papers  (2026-01-07T05:47:22Z)
• Quantum oracles for the finite element method [45.200826131319815]
  This study examines the quantum routines required for the implementation of oracles used in the block-encoding of the $N times N stiffness and mass matrices. We show how to construct the necessary oracles, which require the calculation of element geometry, square root and the implementation of conditional operations.
  arXiv  Detail & Related papers  (2025-04-28T14:28:31Z)
• Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC [34.32444379837011]
  We study a linear computation problem over a quantum multiple access channel (LC-QMAC)<n>We propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error-correcting codes (EAQECC)
  arXiv  Detail & Related papers  (2025-01-27T18:35:33Z)
• Quantum Algorithms for Stochastic Differential Equations: A Schrödingerisation Approach [29.662683446339194]
  We propose quantum algorithms for linear differential equations.<n>The gate complexity of our algorithms exhibits an $mathcalO(dlog(Nd))$ dependence on the dimensions.<n>The algorithms are numerically verified for the Ornstein-Uhlenbeck processes, Brownian motions, and one-dimensional L'evy flights.
  arXiv  Detail & Related papers  (2024-12-19T14:04:11Z)
• On the Constant Depth Implementation of Pauli Exponentials [49.48516314472825]
  We decompose arbitrary exponentials into circuits of constant depth using $mathcalO(n)$ ancillae and two-body XX and ZZ interactions. We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling.
  arXiv  Detail & Related papers  (2024-08-15T17:09:08Z)
• Hybrid Quantum-Classical Scheduling for Accelerating Neural Network Training with Newton's Gradient Descent [37.59299233291882]
  We propose Q-Newton, a hybrid quantum-classical scheduler for accelerating neural network training with Newton's GD. Q-Newton utilizes a streamlined scheduling module that coordinates between quantum and classical linear solvers. Our evaluation showcases the potential for Q-Newton to significantly reduce the total training time compared to commonly used quantum machines.
  arXiv  Detail & Related papers  (2024-04-30T23:55:03Z)
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method [39.671915199737846]
  We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations.<n>The presented method is validated and demonstrated for 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• Digital-Analog Quantum Computation with Arbitrary Two-Body Hamiltonians [0.0]
  Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. We design a new scheme which employs an arbitrary two-body source Hamiltonian, extending the experimental applicability of this computational paradigm to most quantum platforms.
  arXiv  Detail & Related papers  (2023-07-03T12:36:32Z)
• 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)
• Efficient parallelization of quantum basis state shift [0.0]
  We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.
  arXiv  Detail & Related papers  (2023-04-04T11:01:08Z)
• Tensor Factorized Recursive Hamiltonian Downfolding To Optimize The Scaling Complexity Of The Electronic Correlations Problem on Classical and Quantum Computers [0.15833270109954137]
  We present a new variant of post-Hartree-Fock Hamiltonian downfolding-based quantum chemistry methods with optimized scaling for high-cost simulations. We demonstrate super-quadratic speedups of expensive quantum chemistry algorithms on both classical and quantum computers.
  arXiv  Detail & Related papers  (2023-03-13T12:15:54Z)
• Unbiased random circuit compiler for time-dependent Hamiltonian simulation [8.694056486825318]
  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.
  arXiv  Detail & Related papers  (2022-12-19T13:40:05Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis [24.555887999356646]
  The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth and size complexity remain open when ancillary qubits are available. In this paper, we study efficient constructions of quantum circuits with $m$ ancillary qubits that can prepare $psi_vrangle$ in depth. Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime.
  arXiv  Detail & Related papers  (2021-08-13T09:47:11Z)
• Parallel Quantum Algorithm for Hamiltonian Simulation [9.680246554758343]
  A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians. The running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence. We show that the total gate depth of our algorithm has a $operatornamepolyloglog (1/epsilon)$ dependence in the parallel setting.
  arXiv  Detail & Related papers  (2021-05-25T12:46:33Z)
• 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)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.