Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Fermion Second-Quantization Operators and Finite Difference Method

• URL: http://arxiv.org/abs/2410.18685v1
• Date: Thu, 24 Oct 2024 12:26:50 GMT
• Title: Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Fermion Second-Quantization Operators and Finite Difference Method
• Authors: Robin Ollive, Stephane Louise,
• Abstract summary: This article proposes a simple formalism which unifies Hamiltonian simulation techniques from different fields. It leads to a gate decomposition and a scaling different from the usual strategy. It can significantly reduce the quantum circuit number of rotational gates, multi-qubit gates, and the circuit depth.
• Score: 0.0
• License:
• Abstract: This article proposes a simple formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit generation technique. It leads to a gate decomposition and a scaling different from the usual strategy based on a Linear Combination of Unitaries (LCU) reformulation of the problem. It can significantly reduce the quantum circuit number of rotational gates, multi-qubit gates, and the circuit depth. This method leads to one exact Hamiltonian simulation for each summed term and Trotter step. Each of these Hamiltonian simulation unitary matrices also allows the construction of the non-exponential terms with a maximum of six unitary matrices to be Block-encoding (BE). The formalism is easy to apply to the widely studied High-order Unconstrained Binary Optimization (HUBO), fermionic transition Hamiltonian, and basic finite difference method instances. For the HUBO, our implementation exponentially reduces the number of gates for high-order cost functions with respect to the HUBO order. The individual electronic transitions are implemented without error for the second-quantization Fermionic Hamiltonian. Finite difference proposed matrix decompositions are straightforward, very versatile, and scale as the state-of-the-art proposals.

Related papers

• Explicit gate construction of block-encoding for Hamiltonians needed for simulating partial differential equations [0.6144680854063939]
  This paper introduces an efficient quantum protocol for the explicit construction of block-encoding for an important class of Hamiltonians. The proposed algorithm exhibits scaling with respect to the spatial size, suggesting an exponential speedup over classical finite-difference methods.
  arXiv  Detail & Related papers  (2024-05-21T15:13:02Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation [0.0]
  We use fermionic and qubit algebras for the Trotterization of the electronic Hamiltonian. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. Fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step.
  arXiv  Detail & Related papers  (2022-10-18T22:22:54Z)
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices [3.1952399274829775]
  We develop a tool called quantum eigenvalue transformation of unitary matrices with reals (QET-U) This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground state energy. We demonstrate the performance of the algorithm using IBM Qiskit for the transverse field Ising model.
  arXiv  Detail & Related papers  (2022-04-12T17:11:40Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Term Grouping and Travelling Salesperson for Digital Quantum Simulation [6.945601123742983]
  Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian makes such an approach unsuitable for near-term devices. We propose a new term ordering strategy, max-commute-tsp, that simultaneously mitigates both algorithmic and physical errors.
  arXiv  Detail & Related papers  (2020-01-16T18:33:24Z)

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.