Perturbative gadgets for gate-based quantum computing: Non-recursive constructions without subspace restrictions

Abstract

Perturbative gadgets are a tool to encode part of a Hamiltonian, usually the low-energy subspace, into a different Hamiltonian with favorable properties, for instance, reduced locality. Many constructions of perturbative gadgets have been proposed over the years. Still, all of them are restricted in some ways: Either they apply to some specific classes of Hamiltonians, they involve recursion to reduce locality, or they are limited to studying time evolution under the gadget Hamiltonian, e.g., in the context of adiabatic quantum computing, and thus involve subspace restrictions. In this work, we fill the gap by introducing a versatile universal, non-recursive, non-adiabatic perturbative gadget construction without subspace restrictions, that encodes an arbitrary many-body Hamiltonian into the low-energy subspace of a three-body Hamiltonian and is therefore applicable to gate-based quantum computing. Our construction requires $rk$ additional qubits for a $k$-body Hamiltonian comprising $r$ terms. Besides a specific gadget construction, we also provide a recipe for constructing similar gadgets, which can be tailored to different properties, which we discuss.

Fixed typos

References in corpus (19)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Training variational quantum algorithms is NP-hard
• The randomized measurement toolbox
• Layerwise learning for quantum neural networks
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Large gradients via correlation in random parameterized quantum circuits
• Avoiding barren plateaus using classical shadows
• On barren plateaus and cost function locality in variational quantum algorithms
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Barren plateaus in quantum tensor network optimization
• Learning quantum data with the quantum Earth Mover's distance
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Measurement-induced entanglement phase transitions in variational quantum circuits

Cited by in corpus (2)

• Barren Plateaus in Variational Quantum Computing
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets