900 research outputs found
Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
We consider topological quantum computation (TQC) with a particular class of
anyons that are believed to exist in the Fractional Quantum Hall Effect state
at Landau level filling fraction nu=5/2. Since the braid group representation
describing statistics of these anyons is not computationally universal, one
cannot directly apply the standard TQC technique. We propose to use very noisy
non-topological operations such as direct short-range interaction between
anyons to simulate a universal set of gates. Assuming that all TQC operations
are implemented perfectly, we prove that the threshold error rate for
non-topological operations is above 14%. The total number of non-topological
computational elements that one needs to simulate a quantum circuit with
gates scales as .Comment: 17 pages, 12 eps figure
Proposed experiments to probe the non-abelian \nu=5/2 quantum Hall state
We propose several experiments to test the non-abelian nature of
quasi-particles in the fractional quantum Hall state of \nu=5/2. One set of
experiments studies interference contribution to back-scattering of current,
and is a simplified version of an experiment suggested recently. Another set
looks at thermodynamic properties of a closed system. Both experiments are only
weakly sensitive to disorder-induced distribution of localized quasi-particles.Comment: Additional references and an improved figure, 5 page
Experimental Quantum Process Discrimination
Discrimination between unknown processes chosen from a finite set is
experimentally shown to be possible even in the case of non-orthogonal
processes. We demonstrate unambiguous deterministic quantum process
discrimination (QPD) of non-orthogonal processes using properties of
entanglement, additional known unitaries, or higher dimensional systems. Single
qubit measurement and unitary processes and multipartite unitaries (where the
unitary acts non-separably across two distant locations) acting on photons are
discriminated with a confidence of in all cases.Comment: 4 pages, 3 figures, comments welcome. Revised version includes
multi-partite QP
Computational Difficulty of Computing the Density of States
We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.Comment: v2: Accepted version. 9 pages, 1 figur
The computational difficulty of finding MPS ground states
We determine the computational difficulty of finding ground states of
one-dimensional (1D) Hamiltonians which are known to be Matrix Product States
(MPS). To this end, we construct a class of 1D frustration free Hamiltonians
with unique MPS ground states and a polynomial gap above, for which finding the
ground state is at least as hard as factoring. By lifting the requirement of a
unique ground state, we obtain a class for which finding the ground state
solves an NP-complete problem. Therefore, for these Hamiltonians it is not even
possible to certify that the ground state has been found. Our results thus
imply that in order to prove convergence of variational methods over MPS, as
the Density Matrix Renormalization Group, one has to put more requirements than
just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde
Minimum construction of two-qubit quantum operations
Optimal construction of quantum operations is a fundamental problem in the
realization of quantum computation. We here introduce a newly discovered
quantum gate, B, that can implement any arbitrary two-qubit quantum operation
with minimal number of both two- and single-qubit gates. We show this by giving
an analytic circuit that implements a generic nonlocal two-qubit operation from
just two applications of the B gate. We also demonstrate that for the highly
scalable Josephson junction charge qubits, the B gate is also more easily and
quickly generated than the CNOT gate for physically feasible parameters.Comment: 4 page
The Topological Relation Between Bulk Gap Nodes and Surface Bound States : Application to Iron-based Superconductors
In the past few years materials with protected gapless surface (edge) states
have risen to the central stage of condensed matter physics. Almost all
discussions centered around topological insulators and superconductors, which
possess full quasiparticle gaps in the bulk. In this paper we argue systems
with topological stable bulk nodes offer another class of materials with robust
gapless surface states. Moreover the location of the bulk nodes determines the
Miller index of the surfaces that show (or not show) such states. Measuring the
spectroscopic signature of these zero modes allows a phase-sensitive
determination of the nodal structures of unconventional superconductors when
other phase-sensitive techniques are not applicable. We apply this idea to
gapless iron based superconductors and show how to distinguish accidental from
symmetry dictated nodes. We shall argue the same idea leads to a method for
detecting a class of the elusive spin liquids.Comment: updated references, 6 pages, 4 figures, RevTex
Universal 2-local Hamiltonian Quantum Computing
We present a Hamiltonian quantum computation scheme universal for quantum
computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the
number of gates L in the quantum circuit) of time-independent, constant-norm,
2-local qubit-qubit interaction terms. Furthermore, each qubit in the system
interacts only with a constant number of other qubits. The computer runs in
three steps - starts in a simple initial product-state, evolves it for time of
order L^2 (up to logarithmic factors) and wraps up with a two-qubit
measurement. Our model differs from the previous universal 2-local Hamiltonian
constructions in that it does not use perturbation gadgets, does not need large
energy penalties in the Hamiltonian and does not need to run slowly to ensure
adiabatic evolution.Comment: recomputed the necessary number of interactions, new geometric
layout, added reference
Fast Decoders for Topological Quantum Codes
We present a family of algorithms, combining real-space renormalization
methods and belief propagation, to estimate the free energy of a topologically
ordered system in the presence of defects. Such an algorithm is needed to
preserve the quantum information stored in the ground space of a topologically
ordered system and to decode topological error-correcting codes. For a system
of linear size L, our algorithm runs in time log L compared to L^6 needed for
the minimum-weight perfect matching algorithm previously used in this context
and achieves a higher depolarizing error threshold.Comment: 4 pages, 4 figure
Preparing ground states of quantum many-body systems on a quantum computer
Preparing the ground state of a system of interacting classical particles is
an NP-hard problem. Thus, there is in general no better algorithm to solve this
problem than exhaustively going through all N configurations of the system to
determine the one with lowest energy, requiring a running time proportional to
N. A quantum computer, if it could be built, could solve this problem in time
sqrt(N). Here, we present a powerful extension of this result to the case of
interacting quantum particles, demonstrating that a quantum computer can
prepare the ground state of a quantum system as efficiently as it does for
classical systems.Comment: 7 pages, 1 figur
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