3,425 research outputs found
Hybrid Optimization Schemes for Quantum Control
Optimal control theory is a powerful tool for solving control problems in
quantum mechanics, ranging from the control of chemical reactions to the
implementation of gates in a quantum computer. Gradient-based optimization
methods are able to find high fidelity controls, but require considerable
numerical effort and often yield highly complex solutions. We propose here to
employ a two-stage optimization scheme to significantly speed up convergence
and achieve simpler controls. The control is initially parametrized using only
a few free parameters, such that optimization in this pruned search space can
be performed with a simplex method. The result, considered now simply as an
arbitrary function on a time grid, is the starting point for further
optimization with a gradient-based method that can quickly converge to high
fidelities. We illustrate the success of this hybrid technique by optimizing a
holonomic phasegate for two superconducting transmon qubits coupled with a
shared transmission line resonator, showing that a combination of Nelder-Mead
simplex and Krotov's method yields considerably better results than either one
of the two methods alone.Comment: 17 pages, 5 figures, 2 table
Sampling-based Learning Control for Quantum Systems with Uncertainties
Robust control design for quantum systems has been recognized as a key task
in the development of practical quantum technology. In this paper, we present a
systematic numerical methodology of sampling-based learning control (SLC) for
control design of quantum systems with uncertainties. The SLC method includes
two steps of "training" and "testing". In the training step, an augmented
system is constructed using artificial samples generated by sampling
uncertainty parameters according to a given distribution. A gradient flow based
learning algorithm is developed to find the control for the augmented system.
In the process of testing, a number of additional samples are tested to
evaluate the control performance where these samples are obtained through
sampling the uncertainty parameters according to a possible distribution. The
SLC method is applied to three significant examples of quantum robust control
including state preparation in a three-level quantum system, robust
entanglement generation in a two-qubit superconducting circuit and quantum
entanglement control in a two-atom system interacting with a quantized field in
a cavity. Numerical results demonstrate the effectiveness of the SLC approach
even when uncertainties are quite large, and show its potential for robust
control design of quantum systems.Comment: 11 pages, 9 figures, in press, IEEE Transactions on Control Systems
Technology, 201
New class of quantum error-correcting codes for a bosonic mode
We construct a new class of quantum error-correcting codes for a bosonic mode
which are advantageous for applications in quantum memories, communication, and
scalable computation. These 'binomial quantum codes' are formed from a finite
superposition of Fock states weighted with binomial coefficients. The binomial
codes can exactly correct errors that are polynomial up to a specific degree in
bosonic creation and annihilation operators, including amplitude damping and
displacement noise as well as boson addition and dephasing errors. For
realistic continuous-time dissipative evolution, the codes can perform
approximate quantum error correction to any given order in the timestep between
error detection measurements. We present an explicit approximate quantum error
recovery operation based on projective measurements and unitary operations. The
binomial codes are tailored for detecting boson loss and gain errors by means
of measurements of the generalized number parity. We discuss optimization of
the binomial codes and demonstrate that by relaxing the parity structure, codes
with even lower unrecoverable error rates can be achieved. The binomial codes
are related to existing two-mode bosonic codes but offer the advantage of
requiring only a single bosonic mode to correct amplitude damping as well as
the ability to correct other errors. Our codes are similar in spirit to 'cat
codes' based on superpositions of the coherent states, but offer several
advantages such as smaller mean number, exact rather than approximate
orthonormality of the code words, and an explicit unitary operation for
repumping energy into the bosonic mode. The binomial quantum codes are
realizable with current superconducting circuit technology and they should
prove useful in other quantum technologies, including bosonic quantum memories,
photonic quantum communication, and optical-to-microwave up- and
down-conversion.Comment: Published versio
Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information
The remarkable discovery of Quantum Error Correction (QEC), which can
overcome the errors experienced by a bit of quantum information (qubit), was a
critical advance that gives hope for eventually realizing practical quantum
computers. In principle, a system that implements QEC can actually pass a
"break-even" point and preserve quantum information for longer than the
lifetime of its constituent parts. Reaching the break-even point, however, has
thus far remained an outstanding and challenging goal. Several previous works
have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers,
photons, and superconducting transmons. However, these works primarily
illustrate the signatures or scaling properties of QEC codes rather than test
the capacity of the system to extend the lifetime of quantum information over
time. Here we demonstrate a QEC system that reaches the break-even point by
suppressing the natural errors due to energy loss for a qubit logically encoded
in superpositions of coherent states, or cat states of a superconducting
resonator. Moreover, the experiment implements a full QEC protocol by using
real-time feedback to encode, monitor naturally occurring errors, decode, and
correct. As measured by full process tomography, the enhanced lifetime of the
encoded information is 320 microseconds without any post-selection. This is 20
times greater than that of the system's transmon, over twice as long as an
uncorrected logical encoding, and 10% longer than the highest quality element
of the system (the resonator's 0, 1 Fock states). Our results illustrate the
power of novel, hardware efficient qubit encodings over traditional QEC
schemes. Furthermore, they advance the field of experimental error correction
from confirming the basic concepts to exploring the metrics that drive system
performance and the challenges in implementing a fault-tolerant system
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