64 research outputs found
On fault-tolerance with noisy and slow measurements
It is not so well-known that measurement-free quantum error correction
protocols can be designed to achieve fault-tolerant quantum computing. Despite
the potential advantages of using such protocols in terms of the relaxation of
accuracy, speed and addressing requirements on the measurement process, they
have usually been overlooked because they are expected to yield a very bad
threshold as compared to error correction protocols which use measurements.
Here we show that this is not the case. We design fault-tolerant circuits for
the 9 qubit Bacon-Shor code and find a threshold for gates and preparation of
(30% of the best known result for the
same code using measurement based error correction) while admitting up to 1/3
error rates for measurements and allocating no constraints on measurement
speed. We further show that demanding gate error rates sufficiently below the
threshold one can improve the preparation threshold to .
We also show how these techniques can be adapted to other
Calderbank-Shor-Steane codes.Comment: 11 pages, 7 figures. v3 has an extended exposition and several
simplifications that provide for an improved threshold value and resource
overhea
Multi-qubit compensation sequences
The Hamiltonian control of n qubits requires precision control of both the
strength and timing of interactions. Compensation pulses relax the precision
requirements by reducing unknown but systematic errors. Using composite pulse
techniques designed for single qubits, we show that systematic errors for n
qubit systems can be corrected to arbitrary accuracy given either two
non-commuting control Hamiltonians with identical systematic errors or one
error-free control Hamiltonian. We also examine composite pulses in the context
of quantum computers controlled by two-qubit interactions. For quantum
computers based on the XY interaction, single-qubit composite pulse sequences
naturally correct systematic errors. For quantum computers based on the
Heisenberg or exchange interaction, the composite pulse sequences reduce the
logical single-qubit gate errors but increase the errors for logical two-qubit
gates.Comment: 9 pages, 5 figures; corrected reference formattin
Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
I describe a procedure for calculating thresholds for quantum computation as
a function of error model given the availability of ancillae prepared in
logical states with independent, identically distributed errors. The thresholds
are determined via a simple counting argument performed on a single qubit of an
infinitely large CSS code. I give concrete examples of thresholds thus
achievable for both Steane and Knill style fault-tolerant implementations and
investigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised,
submitted to PR
High-fidelity quantum operations on superconducting qubits in the presence of noise
We present a scheme for implementing quantum operations with superconducting
qubits. Our approach uses a "coupler" qubit to mediate a controllable, secular
interaction between "data" qubits, pulse sequences which strongly mitigate the
effects of 1/f flux noise, and a high-Q resonator-based local memory. We
develop a Monte-Carlo simulation technique capable of describing arbitrary
noise-induced dephasing and decay, and demonstrate in this system a set of
universal gate operations with O(10^-5) error probabilities in the presence of
experimentally measured levels of 1/f noise. We then add relaxation and
quantify the decay times required to maintain this error level
Fault-tolerant quantum computation versus Gaussian noise
We study the robustness of a fault-tolerant quantum computer subject to
Gaussian non-Markovian quantum noise, and we show that scalable quantum
computation is possible if the noise power spectrum satisfies an appropriate
"threshold condition." Our condition is less sensitive to very-high-frequency
noise than previously derived threshold conditions for non-Markovian noise.Comment: 30 pages, 6 figure
Asymmetric quantum error correction via code conversion
In many physical systems it is expected that environmental decoherence will
exhibit an asymmetry between dephasing and relaxation that may result in qubits
experiencing discrete phase errors more frequently than discrete bit errors. In
the presence of such an error asymmetry, an appropriately asymmetric quantum
code - that is, a code that can correct more phase errors than bit errors -
will be more efficient than a traditional, symmetric quantum code. Here we
construct fault tolerant circuits to convert between an asymmetric subsystem
code and a symmetric subsystem code. We show that, for a moderate error
asymmetry, the failure rate of a logical circuit can be reduced by using a
combined symmetric asymmetric system and that doing so does not preclude
universality.Comment: 5 pages, 8 figures, presentation revised, figures and references
adde
Accuracy threshold for concatenated error detection in one dimension
Estimates of the quantum accuracy threshold often tacitly assume that it is
possible to interact arbitrary pairs of qubits in a quantum computer with a
failure rate that is independent of the distance between them. None of the many
physical systems that are candidates for quantum computing possess this
property. Here we study the performance of a concatenated error-detection code
in a system that permits only nearest-neighbor interactions in one dimension.
We make use of a new message-passing scheme that maximizes the number of errors
that can be reliably corrected by the code. Our numerical results indicate that
arbitrarily accurate universal quantum computation is possible if the
probability of failure of each elementary physical operation is below
approximately 10^{-5}. This threshold is three orders of magnitude lower than
the highest known.Comment: 7 pages, 4 figures, now with error bar
Long-range coupling and scalable architecture for superconducting flux qubits
Constructing a fault-tolerant quantum computer is a daunting task. Given any
design, it is possible to determine the maximum error rate of each type of
component that can be tolerated while still permitting arbitrarily large-scale
quantum computation. It is an underappreciated fact that including an
appropriately designed mechanism enabling long-range qubit coupling or
transport substantially increases the maximum tolerable error rates of all
components. With this thought in mind, we take the superconducting flux qubit
coupling mechanism described in PRB 70, 140501 (2004) and extend it to allow
approximately 500 MHz coupling of square flux qubits, 50 um a side, at a
distance of up to several mm. This mechanism is then used as the basis of two
scalable architectures for flux qubits taking into account crosstalk and
fault-tolerant considerations such as permitting a universal set of logical
gates, parallelism, measurement and initialization, and data mobility.Comment: 8 pages, 11 figure
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
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