Related papers: Spectral Gap Amplification
We address the stochastic transmission expansion planning (STEP) problem under uncertainty in renewable generation capacity and demand. STEP's objective is to minimize total transmission investment and generation costs. To tackle the…
Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this…
Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…
A quantum algorithm is proposed to solve the Satisfiability problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit Exact Cover problem. The time cost of this…
Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that…
The quantum analogue of a constraint satisfaction problem is a sum of local Hamiltonians - each local Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state. Formalizing the intuitive…
We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…
Ground-state estimation lies at the heart of a broad range of quantum simulations. Most near-term approaches are cast as variational energy minimization and thus inherit the challenges of problem-specific energy landscapes. We develop the…
We investigate the efficiency of Quantum Adiabatic Optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at n qubit systems with symmetric cost functions f:{0, 1}^n->R where the ground…
Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…
Several challenging problem in clustering, partitioning and imaging have traditionally been solved using the "spectral technique". These problems include the normalized cut problem, the graph expander ratio problem, the Cheeger constant…
Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work has presented a nearly…
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and…
Knabe's theorem lower bounds the spectral gap of a one dimensional frustration-free local hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gap threshold for hamiltonians that are gapless…
We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the associated gap, crucial for determining the running time of the…
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as…