Search Results

This note indicates an error in the proof of Theorem 3.1 in [T. Vidick, SIAM J. Comput., 45 (2016), pp. 1007--1063]. Due to an induction step in the soundness analysis not being carried out correctly, the analysis fails to prove the claimed result. The ...

Harrow, Hassidim, and Lloyd [Phys. Rev. Lett., 103 (2009), 150502] showed that for a suitably specified $N \times N$ matrix $A$ and an $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the ...

The calculation of ground-state energies of physical systems can be formalized as the $k$-local Hamiltonian problem, which is a natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more physically meaningful ...

Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum k-local Hamiltonian up to an absolute error ε. Typically, gadget constructions involve terms with large interaction strengths of ...

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the second level of ...

In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that ...

This paper gives a QMA (Quantum Merlin-Arthur) protocol for 3-SAT with two logarithmic-size quantum proofs (that are not entangled with each other) such that the gap between the completeness and the soundness is Ω(1/npolylog(n)). This improves the best ...

The main purpose of this paper is to prove that (promise) problem Quantum State Identicalness (abbreviated QSI) is <em>essentially</em> complete for perfect zero-knowledge quantum interactive proof (QPZK). Loosely speaking, problem QSI is to decide ...

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term individually is in ...

Quantum computing is widely regarded as being able to offer computational complexity benefits beyond the possibilities of classical computing. Yet the relationship of quantum to classical computational complexity is little understood. A fundamental ...

Universal circuits can be viewed as general-purpose simulators for central classes ofcircuits and can be used to capture the computational power of the circuit class beingsimulated. We define and construct quantum universal circuits which are efficient ...

We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE.This relationship is obtained by means of an efficient parallel algorithm, based on the matrix multiplicative weights update method, ...

The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot success with probability greater than than 1-ln2 (approximately 0.31), no matter how many players are ...

We consider the resource bounded quantum circuit model with circuits restricted by thenumber of qubits they act upon and by their depth. Focusing on natural universal setsof gates which are familiar from classical circuit theory, several new lower ...

We study the complexity of a problem "Common Eigenspace" -- verifying consistency of eigenvalue equations for composite quantum systems. The input of the problem is a family of pairwise commuting Hermitian operators H₁,..., H_r on a Hilbert space (C^d)^⊗n ...

QMA and QCMA are possible quantum analogues of the complexity class NP. In QMA the proof is a quantum state and the verification is a quantum circuit. In contrast, in QCMA the proof is restricted to be a classical state. It is not known whether QMA ...

We consider a quantum computer consisting of n spins with an arbitrary but fixed pair-interaction Hamiltonian and describe how to simulate other pair-interactions by interspersing the natural time evolution with fast local transformations. Calculating ...

Studies the quantum complexity of the static set membership problem: given a subset S (|S|/spl les/n) of a universe of size m(/spl Gt/n), store it as a table, T:(0,1)/sup r//spl rarr/(0,1), of bits so that queries of the form 'is x in S__ __' can be ...