Related papers: Hamiltonian Simulation with Optimal Sample Complex…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
A central challenge in quantum simulation is to prepare low-energy states of strongly interacting many-body systems. In this work, we study the problem of preparing a quantum state that optimizes a random all-to-all, sparse or dense, spin…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
We study the problem of learning a Hamiltonian $H$ to precision $\varepsilon$, supposing we are given copies of its Gibbs state $\rho=\exp(-\beta H)/\operatorname{Tr}(\exp(-\beta H))$ at a known inverse temperature $\beta$. Anshu,…
Density matrix exponentiation (DME) is a general procedure that converts an unknown quantum state into the Hamiltonian evolution. This enables state-dependent operations and can reveal nontrivial properties of the state, among other…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…
Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…