Related papers: A Full Characterization of Quantum Advice
We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…
We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$ by a single quantum state $|\Psi>$ of size O(n) qubits, such that: for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$, the values of the bits $a_{i_1},...,a_{i_k}$ can…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in…
This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomial-size quantum state, in such a way…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)\rho]$, where $f$ is an unknown function,…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |\psi\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a…
Yes, we show that they are. We initiate the study of languages that necessarily need uncloneable quantum proofs and advice. We define strictly uncloneable versions of the classes QMA, BQP/qpoly and FEQP/qpoly (which is the class of…
The physics of a quantum system with many degrees of freedom is often approximated by downfolding: most of the degrees of freedom are "folded into" a much smaller number of degrees of freedom, resulting in an effective Hamiltonian that…
For two unknown mixed quantum states $\rho$ and $\sigma$ in an $N$-dimensional Hilbert space, computing their fidelity $F(\rho,\sigma)$ is a basic problem with many important applications in quantum computing and quantum information, for…
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…
$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…
We show that combining two different hypothetical enhancements to quantum computation---namely, quantum advice and non-collapsing measurements---would let a quantum computer solve any decision problem whatsoever in polynomial time, even…
We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
We consider the problems of testing and learning an unknown $n$-qubit Hamiltonian $H$ from queries to its evolution operator $e^{-iHt}$ under the normalized Frobenius norm. We prove: 1. Local Hamiltonians: We give a tolerant testing…
We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn. However, the same…
We prove several new results concerning the pure quantum polynomial hierarchy (pureQPH). First, we show that QMA(2) is contained in pureQSigma2, that is, two unentangled existential provers can be simulated by competing existential and…