Related papers: The Detectability Lemma and Quantum Gap Amplificat…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
A large number of problems in science can be solved by preparing a specific eigenstate of some Hamiltonian H. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of H for that eigenstate and…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
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…
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…
The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian $H_0(t)$, satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form $\epsilon H_1(t)$. Here…
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here…
Entanglement is the cornerstone of quantum communication, yet conventional detection relies solely on local measurements. In this work, we present a unified theoretical and experimental framework demonstrating that one-way local operations…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently…
Quantum Information and the new informational paradigm are entering the domain of quantum field theory and gravity, suggesting the quantum automata framework. The quantum automaton is the minimal-assumption extension to the Planck and…
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…