Related papers: Hamiltonian Complexity in the Thermodynamic Limit
A quantum system can be described and characterized by at least two different concepts, namely, its physical and informational properties. Here, we explicitly connect these two concepts, by equating the time-energy cost which is the product…
A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively.…
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
It has recently been argued that the rate per unit volume of baryon number violation (topological transitions) in the hot, symmetric phase of electroweak theory is of the form $\eta \alpha_w^5 T^4$ in the weak-coupling limit, where $\eta$…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
The area law for entanglement entropy fundamentally reflects the complexity of quantum many-body systems, demonstrating ground states of local Hamiltonians to be represented with low computational complexity. While this principle is…
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…
The efficient computation of observables beyond the total energy is a key challenge and opportunity for fault-tolerant quantum computing approaches in quantum chemistry. Here we consider the symmetry-adapted perturbation theory (SAPT)…
Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic…
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…
We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based quantum computation. This method was…
An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians. Recently, [Ambainis, CCC 2014] defined the complexity class P^QMA[log], and motivated its study by showing that the physical…
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM…
The processing of quantum information always has a cost in terms of physical resources such as energy or time. Determining the resource requirements is not only an indispensable step in the design of practical devices - the resources need…