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Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalised set of few-body coherent states. In particular, model Hamiltonians of the FQH effect are equivalent to the…
Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on…
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded…
Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave…
We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum…
Generally, the local interactions in a many-body quantum spin system on a lattice do not commute with each other. Consequently, the Hamiltonian of a local region will generally not commute with that of the entire system, and so the two…
We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems…
Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states…
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity measured by the quantum circuit depth…
Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the…
Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…
An important aspect of quantum simulation is the preparation of physically interesting states on a quantum computer, and this task can often be costly or challenging to implement. A digital, ``site-by-site'' scheme of state preparation was…
Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work,…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
Preparing the thermal density matrix $\rho_{\beta} \propto e^{-\beta H}$ corresponding to a given Hamiltonian $H$ is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with…