Related papers: Sparse random Hamiltonians are quantumly easy
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum…
Simulating many-body systems is one of the most promising applications of near-term quantum computers. An important open question is how to efficiently prepare the ground states of arbitrary fermionic Hamiltonians, especially those with…
Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization,…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
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…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…
Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example in ultrafast coherent…
Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian…
One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which…
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…
A new scheme is proposed which will permit electron spin resonance pulse techniques to be used to realize a quantum computer with a 100 qbits, or more. The computation is performed on effective pure states which correspond to off-diagonal…