Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Chemistry and Finite Difference Method

Abstract

This article proposes a 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 Highorder 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.

References in corpus (20)

• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Quantum algorithm for solving linear systems of equations
• Ising formulations of many NP problems
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Efficient quantum algorithms for simulating sparse Hamiltonians
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• A Theory of Trotter Error
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• A random compiler for fast Hamiltonian simulation
• Low Depth Quantum Simulation of Electronic Structure
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Grover Adaptive Search for Constrained Polynomial Binary Optimization
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Quantum simulation of partial differential equations via Schrodingerisation
• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits
• Synthesizing efficient circuits for Hamiltonian simulation
• Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation
• Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations