Related papers: Guaranteed efficient energy estimation of quantum …
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across…
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical…
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16,…
We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3\}$ at finite temperature. These systems lie beyond the…
A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field…
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate…
We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
Shadow estimation is an efficient method for predicting many observables of a quantum state with a statistical guarantee. In the multi-shot scenario, one performs projective measurement on the sequentially prepared state for $K$ times after…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Expectation value estimation is ubiquitous in quantum algorithms. The expectation value of a Hamiltonian, which is essential in various practical applications, is often estimated by measuring a large number of Pauli strings on quantum…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to…
By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining…
How much energy does a quantum computer consume? Are they more efficient than their classical counterparts? In this work, we make a step towards answering these questions. We define the energy efficiency of a quantum computer as the ratio…