337 research outputs found
Constructions and Noise Threshold of Hyperbolic Surface Codes
We show how to obtain concrete constructions of homological quantum codes
based on tilings of 2D surfaces with constant negative curvature (hyperbolic
surfaces). This construction results in two-dimensional quantum codes whose
tradeoff of encoding rate versus protection is more favorable than for the
surface code. These surface codes would require variable length connections
between qubits, as determined by the hyperbolic geometry. We provide numerical
estimates of the value of the noise threshold and logical error probability of
these codes against independent X or Z noise, assuming noise-free error
correction
Space-Time Circuit-to-Hamiltonian Construction and Its Applications
The circuit-to-Hamiltonian construction translates dynamics (a quantum
circuit and its output) into statics (the groundstate of a circuit Hamiltonian)
by explicitly defining a quantum register for a clock. The standard
Feynman-Kitaev construction uses one global clock for all qubits while we
consider a different construction in which a clock is assigned to each
interacting qubit. This makes it possible to capture the spatio-temporal
structure of the original quantum circuit into features of the circuit
Hamiltonian. The construction is inspired by the original two-dimensional
interacting fermionic model (see
http://link.aps.org/doi/10.1103/PhysRevA.63.040302) We prove that for
one-dimensional quantum circuits the gap of the circuit Hamiltonian is
appropriately lower-bounded, partially using results on mixing times of Markov
chains, so that the applications of this construction for QMA (and partially
for quantum adiabatic computation) go through. For one-dimensional quantum
circuits, the dynamics generated by the circuit Hamiltonian corresponds to
diffusion of a string around the torus.Comment: 27 pages, 5 figure
Quantum Data Hiding
We expand on our work on Quantum Data Hiding -- hiding classical data among
parties who are restricted to performing only local quantum operations and
classical communication (LOCC). We review our scheme that hides one bit between
two parties using Bell states, and we derive upper and lower bounds on the
secrecy of the hiding scheme. We provide an explicit bound showing that
multiple bits can be hidden bitwise with our scheme. We give a preparation of
the hiding states as an efficient quantum computation that uses at most one
ebit of entanglement. A candidate data hiding scheme that does not use
entanglement is presented. We show how our scheme for quantum data hiding can
be used in a conditionally secure quantum bit commitment scheme.Comment: 19 pages, IEEE style, 8 figures, submitted to IEEE Transactions on
Information Theor
Dispersive Qubit Measurement by Interferometry with Parametric Amplifiers
We perform a detailed analysis of how an amplified interferometer can be used
to enhance the quality of a dispersive qubit measurement, such as one performed
on a superconducting transmon qubit, using homodyne detection on an amplified
microwave signal. Our modeling makes a realistic assessment of what is possible
in current circuit-QED experiments; in particular, we take into account the
frequency-dependence of the qubit-induced phase shift for short microwaves
pulses. We compare the possible signal-to-noise ratios obtainable with
(single-mode) SU(1,1) interferometers with the current coherent measurement and
find a considerable reduction in measurement error probability in an
experimentally-accessible range of parameters
Optimal Decompositions of Barely Separable States
Two families of bipartite mixed quantum states are studied for which it is
proved that the number of members in the optimal-decomposition ensemble --- the
ensemble realizing the entanglement of formation --- is greater than the rank
of the mixed state. We find examples for which the number of states in this
optimal ensemble can be larger than the rank by an arbitrarily large factor. In
one case the proof relies on the fact that the partial transpose of the mixed
state has zero eigenvalues; in the other case the result arises from the
properties of product bases that are completable only by embedding in a larger
Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of
the J. Mod. Opt. V2: Change in terminology from "ensemble length" to
"ensemble cardinality
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