70 research outputs found

### Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

In quantum computation with continous-variable systems, quantum advantage can
only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian
unitary evolutions and measurements suited for computation are challenging to
realize in the lab. We propose and analyze two methods to apply a polynomial
approximation of any unitary operator diagonal in the amplitude quadrature
representation, including non-Gaussian operators, to an unknown input state.
Our protocols use as a primary non-Gaussian resource a single-photon counter.
We use the fidelity of the transformation with the target one on Fock and
coherent states to assess the quality of the approximate gate.Comment: 11 pages, 7 figure

### Effect of one-, two-, and three-body atom loss processes on superpositions of phase states in Bose-Josephson junctions

In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold
atoms, macroscopic superpositions of phase states are produced during the time
evolution after a sudden quench to zero of the coupling amplitude. Using
quantum trajectories and an exact diagonalization of the master equation, we
study the effect of one-, two-, and three-body atom losses on the
superpositions by analyzing separately the amount of quantum correlations in
each subspace with fixed atom number. The quantum correlations useful for atom
interferometry are estimated using the quantum Fisher information. We identify
the choice of parameters leading to the largest Fisher information, thereby
showing that, for all kinds of loss processes, quantum correlations can be
partially protected from decoherence when the losses are strongly asymmetric in
the two modes.Comment: 23 pages, 8 figures, to be published in Eur. Phys. J.

### Random coding for sharing bosonic quantum secrets

We consider a protocol for sharing quantum states using continuous variable
systems. Specifically we introduce an encoding procedure where bosonic modes in
arbitrary secret states are mixed with several ancillary squeezed modes through
a passive interferometer. We derive simple conditions on the interferometer for
this encoding to define a secret sharing protocol and we prove that they are
satisfied by almost any interferometer. This implies that, if the
interferometer is chosen uniformly at random, the probability that it may not
be used to implement a quantum secret sharing protocol is zero. Furthermore, we
show that the decoding operation can be obtained and implemented efficiently
with a Gaussian unitary using a number of single-mode squeezers that is at most
twice the number of modes of the secret, regardless of the number of players.
We benchmark the quality of the reconstructed state by computing the fidelity
with the secret state as a function of the input squeezing.Comment: Updated figure 1, added figure 2, closer to published versio

### Macroscopic superpositions in Bose-Josephson junctions: Controlling decoherence due to atom losses

We study how macroscopic superpositions of coherent states produced by the
nondissipative dynamics of binary mixtures of ultracold atoms are affected by
atom losses. We identify different decoherence scenarios for symmetric or
asymmetric loss rates and interaction energies in the two modes. In the
symmetric case the quantum coherence in the superposition is lost after a
single loss event. By tuning appropriately the energies we show that the
superposition can be protected, leading to quantum correlations useful for atom
interferometry even after many loss events.Comment: 6 pages, 3 figure

### Compact Gaussian quantum computation by multi-pixel homodyne detection

We study the possibility of producing and detecting continuous variable
cluster states in an optical set-up in an extremely compact fashion. This
method is based on a multi-pixel homodyne detection system recently
demonstrated experimentally, which includes classical data post-processing. It
allows to incorporate the linear optics network, usually employed in standard
experiments for the production of cluster states, in the stage of the
measurement. After giving an example of cluster state generation by this
method, we further study how this procedure can be generalized to perform
gaussian quantum computation.Comment: Eqs.(20)-(21) correcte

### Study of noise in virtual distillation circuits for quantum error mitigation

Virtual distillation has been proposed as an error mitigation protocol for
estimating the expectation values of observables in quantum algorithms. It
proceeds by creating a cyclic permutation of $M$ noisy copies of a quantum
state using a sequence of controlled-swap gates. If the noise does not shift
the dominant eigenvector of the density operator away from the ideal state,
then the error in expectation-value estimation can be exponentially reduced
with $M$. In practice, subsequent error-mitigation techniques are required to
suppress the effect of noise in the cyclic permutation circuit itself, leading
to increased experimental complexity. Here, we perform a careful analysis of
noise in the cyclic permutation circuit and find that the estimation of
expectation value of observables diagonal in the computational basis is robust
against dephasing noise. We support the analytical result with numerical
simulations and find that $67\%$ of errors are reduced for $M=2$, with physical
dephasing error probabilities as high as $10\%$. Our results imply that a broad
class of quantum algorithms can be implemented with higher accuracy in the
near-term with qubit platforms where non-dephasing errors are suppressed, such
as superconducting bosonic qubits and Rydberg atoms.Comment: 12 pages, 5 figure

### Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits

We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable

### Sufficient condition for universal quantum computation using bosonic circuits

We present a new method for quantifying the resourcefulness of
continuous-variable states in the context of promoting otherwise simulatable
circuits to universality. The simulatable, albeit non-Gaussian, circuits that
we consider are composed of Gottesman-Kitaev-Preskill states, Gaussian
operations, and homodyne measurements. We first introduce a general framework
for mapping a continuous-variable state into a qubit state. We then express
existing maps in this framework, including the modular subsystem decomposition
and stabilizer subsystem decomposition. Combining these results with existing
results in discrete-variable quantum computation provides a sufficient
condition for achieving universal quantum computation. These results also allow
us to demonstrate that for states symmetric in the position representation, the
modular subsystem decomposition can be interpreted in terms of resourceless
(simulatable) operations - i.e., included in the class of Gaussian circuits
with input stabilizer Gottesman-Kitaev-Preskill states. Therefore, the modular
subsystem decomposition is an operationally relevant mapping to analyze the
logical content of realistic Gottesman-Kitaev-Preskill states, among other
states.Comment: 30 pages, 13 figure

### Classical simulation of Gaussian quantum circuits with non-Gaussian input states

We consider Gaussian quantum circuits supplemented with non-Gaussian input
states and derive sufficient conditions for efficient classical strong
simulation of these circuits. In particular, we generalise the stellar
representation of continuous-variable quantum states to the multimode setting
and relate the stellar rank of the input non-Gaussian states, a recently
introduced measure of non-Gaussianity, to the cost of evaluating classically
the output probability densities of these circuits. Our results have
consequences for the strong simulability of a large class of near-term
continuous-variable quantum circuits.Comment: 8+6 pages, 3 figures. Comments welcome

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