162 research outputs found
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
Zeno effect for quantum computation and control
It is well known that the quantum Zeno effect can protect specific quantum
states from decoherence by using projective measurements. Here we combine the
theory of weak measurements with stabilizer quantum error correction and
detection codes. We derive rigorous performance bounds which demonstrate that
the Zeno effect can be used to protect appropriately encoded arbitrary states
to arbitrary accuracy, while at the same time allowing for universal quantum
computation or quantum control.Comment: Significant modifications, including a new author. To appear in PR
Scaling the neutral atom Rydberg gate quantum computer by collective encoding in Holmium atoms
We discuss a method for scaling a neutral atom Rydberg gate quantum processor
to a large number of qubits. Limits are derived showing that the number of
qubits that can be directly connected by entangling gates with errors at the
level using long range Rydberg interactions between sites in an
optical lattice, without mechanical motion or swap chains, is about 500 in two
dimensions and 7500 in three dimensions. A scaling factor of 60 at a smaller
number of sites can be obtained using collective register encoding in the
hyperfine ground states of the rare earth atom Holmium. We present a detailed
analysis of operation of the 60 qubit register in Holmium. Combining a lattice
of multi-qubit ensembles with collective encoding results in a feasible design
for a 1000 qubit fully connected quantum processor.Comment: 6 figure
Loss tolerant linear optical quantum memory by measurement-based quantum computing
We give a scheme for loss tolerantly building a linear optical quantum memory which itself is tolerant to qubit loss. We use the encoding recently introduced in Varnava et al 2006 Phys. Rev. Lett. 97 120501, and give a method for efficiently achieving this. The entire approach resides within the 'one-way' model for quantum computing (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 5188–91; Raussendorf et al 2003 Phys. Rev. A 68 022312). Our results suggest that it is possible to build a loss tolerant quantum memory, such that if the requirement is to keep the data stored over arbitrarily long times then this is possible with only polynomially increasing resources and logarithmically increasing individual photon life-times
The Stability of Quantum Concatenated Code Hamiltonians
Protecting quantum information from the detrimental effects of decoherence
and lack of precise quantum control is a central challenge that must be
overcome if a large robust quantum computer is to be constructed. The
traditional approach to achieving this is via active quantum error correction
using fault-tolerant techniques. An alternative to this approach is to engineer
strongly interacting many-body quantum systems that enact the quantum error
correction via the natural dynamics of these systems. Here we present a method
for achieving this based on the concept of concatenated quantum error
correcting codes. We define a class of Hamiltonians whose ground states are
concatenated quantum codes and whose energy landscape naturally causes quantum
error correction. We analyze these Hamiltonians for robustness and suggest
methods for implementing these highly unnatural Hamiltonians.Comment: 18 pages, small corrections and clarification
Using gene expression profiles from peripheral blood to identify asymptomatic responses to acute respiratory viral infections
<p>Abstract</p> <p>Background</p> <p>A recent study reported that gene expression profiles from peripheral blood samples of healthy subjects prior to viral inoculation were indistinguishable from profiles of subjects who received viral challenge but remained asymptomatic and uninfected. If true, this implies that the host immune response does not have a molecular signature. Given the high sensitivity of microarray technology, we were intrigued by this result and hypothesize that it was an artifact of data analysis.</p> <p>Findings</p> <p>Using acute respiratory viral challenge microarray data, we developed a molecular signature that for the first time allowed for an accurate differentiation between uninfected subjects prior to viral inoculation and subjects who remained asymptomatic after the viral challenge.</p> <p>Conclusions</p> <p>Our findings suggest that molecular signatures can be used to characterize immune responses to viruses and may improve our understanding of susceptibility to viral infection with possible implications for vaccine development.</p
Analysis and Computational Dissection of Molecular Signature Multiplicity
Molecular signatures are computational or mathematical models created to diagnose disease and other phenotypes and to predict clinical outcomes and response to treatment. It is widely recognized that molecular signatures constitute one of the most important translational and basic science developments enabled by recent high-throughput molecular assays. A perplexing phenomenon that characterizes high-throughput data analysis is the ubiquitous multiplicity of molecular signatures. Multiplicity is a special form of data analysis instability in which different analysis methods used on the same data, or different samples from the same population lead to different but apparently maximally predictive signatures. This phenomenon has far-reaching implications for biological discovery and development of next generation patient diagnostics and personalized treatments. Currently the causes and interpretation of signature multiplicity are unknown, and several, often contradictory, conjectures have been made to explain it. We present a formal characterization of signature multiplicity and a new efficient algorithm that offers theoretical guarantees for extracting the set of maximally predictive and non-redundant signatures independent of distribution. The new algorithm identifies exactly the set of optimal signatures in controlled experiments and yields signatures with significantly better predictivity and reproducibility than previous algorithms in human microarray gene expression datasets. Our results shed light on the causes of signature multiplicity, provide computational tools for studying it empirically and introduce a framework for in silico bioequivalence of this important new class of diagnostic and personalized medicine modalities
Scalability of quantum computation with addressable optical lattices
We make a detailed analysis of error mechanisms, gate fidelity, and
scalability of proposals for quantum computation with neutral atoms in
addressable (large lattice constant) optical lattices. We have identified
possible limits to the size of quantum computations, arising in 3D optical
lattices from current limitations on the ability to perform single qubit gates
in parallel and in 2D lattices from constraints on laser power. Our results
suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e.,
qubits) may be achievable, provided two-qubit gates can be performed with
sufficiently high precision and degree of parallelizability. Parallelizability
of long range interaction-based two-qubit gates is qualitatively compared to
that of collisional gates. Different methods of performing single qubit gates
are compared, and a lower bound of is determined on the
error rate for the error mechanisms affecting Cs in a blue-detuned
lattice with Raman transition-based single qubit gates, given reasonable limits
on experimental parameters.Comment: 17 pages, 5 figures. Accepted for publication in Physical Review
Polynomial-time algorithm for simulation of weakly interacting quantum spin systems
We describe an algorithm that computes the ground state energy and
correlation functions for 2-local Hamiltonians in which interactions between
qubits are weak compared to single-qubit terms. The running time of the
algorithm is polynomial in the number of qubits and the required precision.
Specifically, we consider Hamiltonians of the form , where
H_0 describes non-interacting qubits, V is a perturbation that involves
arbitrary two-qubit interactions on a graph of bounded degree, and
is a small parameter. The algorithm works if is below a certain
threshold value that depends only upon the spectral gap of H_0, the maximal
degree of the graph, and the maximal norm of the two-qubit interactions. The
main technical ingredient of the algorithm is a generalized Kirkwood-Thomas
ansatz for the ground state. The parameters of the ansatz are computed using
perturbative expansions in powers of . Our algorithm is closely
related to the coupled cluster method used in quantum chemistry.Comment: 27 page
Fidelity of a Rydberg blockade quantum gate from simulated quantum process tomography
We present a detailed error analysis of a Rydberg blockade mediated
controlled-NOT quantum gate between two neutral atoms as demonstrated recently
in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010).
Numerical solutions of a master equation for the gate dynamics, including all
known sources of technical error, are shown to be in good agreement with
experiments. The primary sources of gate error are identified and suggestions
given for future improvements. We also present numerical simulations of quantum
process tomography to find the intrinsic fidelity, neglecting technical errors,
of a Rydberg blockade controlled phase gate. The gate fidelity is characterized
using trace overlap and trace distance measures. We show that the trace
distance is linearly sensitive to errors arising from the finite Rydberg
blockade shift and introduce a modified pulse sequence which corrects the
linear errors. Our analysis shows that the intrinsic gate error extracted from
simulated quantum process tomography can be under 0.002 for specific states of
Rb or Cs atoms. The relation between the process fidelity and the gate
error probability used in calculations of fault tolerance thresholds is
discussed.Comment: revised, small corrections to Table II
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