2,187 research outputs found
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
Preparation and manipulation of a fault-tolerant superconducting qubit
We describe a qubit encoded in continuous quantum variables of an rf
superconducting quantum interference device. Since the number of accessible
states in the system is infinite, we may protect its two-dimensional subspace
from small errors introduced by the interaction with the environment and during
manipulations. We show how to prepare the fault-tolerant state and manipulate
the system. The discussed operations suffice to perform quantum computation on
the encoded state, syndrome extraction, and quantum error correction. We also
comment on the physical sources of errors and possible imperfections while
manipulating the system.Comment: Typo corrected, title changed as suggested by the editors of Phys.
Rev. B, references adde
Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits
Resolving quantum many-body problems represents one of the greatest
challenges in physics and physical chemistry, due to the prohibitively large
computational resources that would be required by using classical computers. A
solution has been foreseen by directly simulating the time evolution through
sequences of quantum gates applied to arrays of qubits, i.e. by implementing a
digital quantum simulator. Superconducting circuits and resonators are emerging
as an extremely-promising platform for quantum computation architectures, but a
digital quantum simulator proposal that is straightforwardly scalable,
universal, and realizable with state-of-the-art technology is presently
lacking. Here we propose a viable scheme to implement a universal quantum
simulator with hybrid spin-photon qubits in an array of superconducting
resonators, which is intrinsically scalable and allows for local control. As
representative examples we consider the transverse-field Ising model, a spin-1
Hamiltonian, and the two-dimensional Hubbard model; for these, we numerically
simulate the scheme by including the main sources of decoherence. In addition,
we show how to circumvent the potentially harmful effects of inhomogeneous
broadening of the spin systems
Encoding a Qubit into a Cavity Mode in Circuit-QED using Phase Estimation
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into
an oscillator such that the qubit is protected against small shifts
(translations) in phase space. The idea underlying this encoding is that error
processes of low rate can be expanded into small shift errors. The qubit space
is defined as an eigenspace of two mutually commuting displacement operators
and which act as large shifts/translations in phase space. We
propose and analyze the approximate creation of these qubit states by coupling
the oscillator to a sequence of ancilla qubits. This preparation of the states
uses the idea of phase estimation where the phase of the displacement operator,
say , is approximately determined. We consider several possible forms of
phase estimation. We analyze the performance of repeated and adapative phase
estimation as the simplest and experimentally most viable schemes given a
realistic upper-limit on the number of photons in the oscillator. We propose a
detailed physical implementation of this protocol using the dispersive coupling
between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide
an estimate that in a current experimental set-up one can prepare a good code
state from a squeezed vacuum state using rounds of adapative phase
estimation, lasting in total about sec., with (heralded) chance
of success.Comment: 24 pages, 15 figures. Some minor improvements to text and figures.
Some of the numerical data has been replaced by more accurate simulations.
The improved simulation shows that the code performs better than originally
anticipate
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