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We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N…
Variational quantum algorithms (VQA) based on Hamiltonian simulation represent a specialized class of quantum programs well-suited for near-term quantum computing applications due to its modest resource requirements in terms of qubits and…
Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in…
In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum…
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
BellQMA protocols are a subclass of multi-prover quantum Merlin-Arthur protocols in which the verifier is restricted to perform nonadaptive,unentangled measurements on the quantum states received from each Merlin. In this paper, we prove…
Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding…
We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial…
Ground state counting plays an important role in several applications in science and engineering, from estimating residual entropy in physical systems, to bounding engineering reliability and solving combinatorial counting problems. While…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
What could happen if we pinned a single qubit of a system and fixed it in a particular state? First, we show that this can greatly increase the complexity of static questions -- ground state properties of local Hamiltonian problems with…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
We study a parameterized version of the local Hamiltonian problem, called the weighted local Hamiltonian problem, where the relevant quantum states are superpositions of computational basis states of Hamming weight $k$. The Hamming weight…
We study the limitations of black-box amplification in the quantum complexity class QMA. Amplification is known to boost any inverse-polynomial gap between completeness and soundness to exponentially small error, and a recent result…