191 research outputs found
Accelerated randomized benchmarking
© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine whether we have implemented a desired gate, and refine accordingly. Randomized benchmarking reduces the difficulty of this task by exploiting symmetries in quantum operations. Here, we bound the resources required for benchmarking and show that, with prior information, we can achieve several orders of magnitude better accuracy than in traditional approaches to benchmarking. Moreover, by building on state-of-the-art classical algorithms, we reach these accuracies with near-optimal resources. Our approach requires an order of magnitude less data to achieve the same accuracies and to provide online estimates of the errors in the reported fidelities. We also show that our approach is useful for physical devices by comparing to simulations
Complete quantum teleportation using nuclear magnetic resonance
Quantum mechanics provides spectacular new information processing abilities
(Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called
quantum teleportation (Bennett et al 1993) that allows the quantum state of a
system to be transported from one location to another, without moving through
the intervening space. Partial implementations of teleportation (Bouwmeester et
al 1997, Boschi et al 1998) over macroscopic distances have been achieved using
optical systems, but omit the final stage of the teleportation procedure. Here
we report an experimental implementation of the full quantum teleportation
operation over inter-atomic distances using liquid state nuclear magnetic
resonance (NMR). The inclusion of the final stage enables for the first time a
teleportation implementation which may be used as a subroutine in larger
quantum computations, or for quantum communication. Our experiment also
demonstrates the use of quantum process tomography, a procedure to completely
characterize the dynamics of a quantum system. Finally, we demonstrate a
controlled exploitation of decoherence as a tool to assist in the performance
of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published
versio
Geometric quantum computation with NMR
The experimental realisation of the basic constituents of quantum information
processing devices, namely fault-tolerant quantum logic gates, requires
conditional quantum dynamics, in which one subsystem undergoes a coherent
evolution that depends on the quantum state of another subsystem. In
particular, the subsystem may acquire a conditional phase shift. Here we
consider a novel scenario in which this phase is of geometric rather than
dynamical origin. As the conditional geometric (Berry) phase depends only on
the geometry of the path executed it is resilient to certain types of errors,
and offers the potential of an intrinsically fault-tolerant way of performing
quantum gates. Nuclear Magnetic Resonance (NMR) has already been used to
demonstrate both simple quantum information processing and Berry's phase. Here
we report an NMR experiment which implements a conditional Berry phase, and
thus a controlled phase shift gate. This constitutes the first elementary
geometric quantum computation.Comment: Minor additions at request of referees. 4 pages revtex including 2
figures (1 eps). Nature in pres
Implementation of a Quantum Search Algorithm on a Nuclear Magnetic Resonance Quantum Computer
We demonstrate an implementation of a quantum search algorithm on a two qubit
NMR quantum computer based on cytosine.Comment: Six pages, three figure
A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field
Using the Weyl commutation relations over a finite field we introduce a
family of error-correcting quantum stabilizer codes based on a class of
symmetric matrices over the finite field satisfying certain natural conditions.
When the field is GF(2) the existence of a rich class of such symmetric
matrices is demonstrated by a simple probabilistic argument depending on the
Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these
symmetric matrices are assumed to be circulant it is possible to obtain
concrete examples by a computer program. The quantum codes thus obtained admit
elegant encoding circuits.Comment: 16 pages, 2 figure
Implementation of a Toffoli Gate with Superconducting Circuits
The quantum Toffoli gate allows universal reversible classical computation.
It is also an important primitive in many quantum circuits and quantum error
correction schemes. Here we demonstrate the realization of a Toffoli gate with
three superconducting transmon qubits coupled to a microwave resonator. By
exploiting the third energy level of the transmon qubit, the number of
elementary gates needed for the implementation of the Toffoli gate, as well as
the total gate time can be reduced significantly in comparison to theoretical
proposals using two-level systems only. We characterize the performance of the
gate by full process tomography and Monte Carlo process certification. The gate
fidelity is found to be %.Comment: 4 pages, 5figure
Quantum optical coherence can survive photon losses: a continuous-variable quantum erasure correcting code
A fundamental requirement for enabling fault-tolerant quantum information
processing is an efficient quantum error-correcting code (QECC) that robustly
protects the involved fragile quantum states from their environment. Just as
classical error-correcting codes are indispensible in today's information
technologies, it is believed that QECC will play a similarly crucial role in
tomorrow's quantum information systems. Here, we report on the first
experimental demonstration of a quantum erasure-correcting code that overcomes
the devastating effect of photon losses. Whereas {\it errors} translate, in an
information theoretic language, the noise affecting a transmission line, {\it
erasures} correspond to the in-line probabilistic loss of photons. Our quantum
code protects a four-mode entangled mesoscopic state of light against erasures,
and its associated encoding and decoding operations only require linear optics
and Gaussian resources. Since in-line attenuation is generally the strongest
limitation to quantum communication, much more than noise, such an
erasure-correcting code provides a new tool for establishing quantum optical
coherence over longer distances. We investigate two approaches for
circumventing in-line losses using this code, and demonstrate that both
approaches exhibit transmission fidelities beyond what is possible by classical
means.Comment: 5 pages, 4 figure
Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
Entanglement is one of the key resources required for quantum computation, so
experimentally creating and measuring entangled states is of crucial importance
in the various physical implementations of a quantum computer. In
superconducting qubits, two-qubit entangled states have been demonstrated and
used to show violations of Bell's Inequality and to implement simple quantum
algorithms. Unlike the two-qubit case, however, where all maximally-entangled
two-qubit states are equivalent up to local changes of basis, three qubits can
be entangled in two fundamentally different ways, typified by the states
and . Here we demonstrate the operation of three coupled
superconducting phase qubits and use them to create and measure
and states. The states are fully characterized
using quantum state tomography and are shown to satisfy entanglement witnesses,
confirming that they are indeed examples of three-qubit entanglement and are
not separable into mixtures of two-qubit entanglement.Comment: 9 pages, 5 figures. Version 2: added supplementary information and
fixed image distortion in Figure 2
Random walk with barriers: Diffusion restricted by permeable membranes
Restrictions to molecular motion by barriers (membranes) are ubiquitous in
biological tissues, porous media and composite materials. A major challenge is
to characterize the microstructure of a material or an organism
nondestructively using a bulk transport measurement. Here we demonstrate how
the long-range structural correlations introduced by permeable membranes give
rise to distinct features of transport. We consider Brownian motion restricted
by randomly placed and oriented permeable membranes and focus on the
disorder-averaged diffusion propagator using a scattering approach. The
renormalization group solution reveals a scaling behavior of the diffusion
coefficient for large times, with a characteristically slow inverse square root
time dependence. The predicted time dependence of the diffusion coefficient
agrees well with Monte Carlo simulations in two dimensions. Our results can be
used to identify permeable membranes as restrictions to transport in disordered
materials and in biological tissues, and to quantify their permeability and
surface area.Comment: 8 pages, 3 figures; origin of dispersion clarified, refs adde
Quantum Correlations in NMR systems
In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin
ensembles are much lower than their thermal energies, and accordingly exhibit
tiny polarizations. Generally such low-purity quantum states are devoid of
quantum entanglement. However, there exist certain nonclassical correlations
which can be observed even in such systems. In this chapter, we discuss three
such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal
correlations, and quantum discord. In each case, we provide a brief theoretical
background and then describe some results from NMR experiments.Comment: 21 pages, 7 figure
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