相关论文: Efficient Shadow Tomography of Thermal States
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…
Verifying the proper preparation of quantum states is essential in modern quantum information science. Various protocols have been developed to estimate the fidelity of quantum states produced by different parties. Direct fidelity…
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that…
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
We show that thermal states of local Hamiltonians are separable above a constant temperature. Specifically, for a local Hamiltonian $H$ on a graph with degree $\mathfrak{d}$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
Fast-forwarding refers to the ability to simulate a system of time $t$ using significantly fewer than $t$ queries or circuit depth. While various Hamiltonian systems are known to circumvent the no fast-forwarding theorem, analogous results…
We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown $n$-qubit pure state $|\psi\rangle$, the…
We develop an efficient and robust approach to Hamiltonian identification for multipartite quantum systems based on the method of compressed sensing. This work demonstrates that with only O(s log(d)) experimental configurations, consisting…