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We consider whether or not Hamiltonians which are sums of commuting projectors have "trivial" ground states which can be constructed by a local quantum circuit of bounded depth and range acting on a product state. While the toric code only…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. We study the natural special case of the Local Hamiltonian problem where the same 2-local interaction, with differing weights,…
We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state $\rho = e^{-\beta H}/\textrm{tr}(e^{-\beta H})$ at a known inverse temperature $\beta>0$. Anshu, Arunachalam, Kuwahara, and Soleimanifar…
While the impact of locality restrictions on quantum dynamics and algorithmic complexity has been well studied in the general case of time-dependent Hamiltonians, the capabilities of time-independent protocols are less well understood.…
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions.…
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…
Commuting local Hamiltonians provide a testing ground for studying many of the most interesting open questions in quantum information theory, including the quantum PCP conjecture and the existence of area laws. Although they are a…
We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter is described by a map between modules…
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
Solvability of the rational quantum integrable systems related to exceptional root spaces $G_2, F_4$ is re-examined and for $E_{6,7,8}$ is established in the framework of a unified approach. It is shown the Hamiltonians take algebraic form…
Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences. To learn the Gibbs state of local Hamiltonians at any inverse temperature…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. Not all Hamiltonians can be uniquely recovered from a steady state. HL success depends on the Hamiltonian model and steady state. Here, we analyze…
We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and PCPs of proximity. Namely, we show that the structure of every algorithm that makes $q$ adaptive queries and…
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…