1,768 research outputs found
Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works, this approach has been used to derive upper bounds to fault tolerance thresholds-usually by identifying a privileged resource, such as an entangling gate or a non-Clifford operation, and then deriving the noise levels required to make it 'unprivileged'. In this work, we consider extensions of this approach where noise is added to Clifford gates too and then 'commuted' around until it concentrates on attacking the non-Clifford resource. While commuting noise around is not always straightforward, we find that easy instances can be identified in popular fault tolerance proposals, thereby enabling sharper upper bounds to be derived in these cases. For instance we find that if we take Knill's (2005 Nature 434 39) fault tolerance proposal together with the ability to prepare any possible state in the XY plane of the Bloch sphere, then not more than 3.69% error-per-gate noise is sufficient to make it classical, and 13.71% of Knill's noise model is sufficient. These bounds have been derived without noise being added to the decoding parts of the circuits. Introducing such noise in a toy example suggests that the present approach can be optimized further to yield tighter bounds
Nonlocality, Asymmetry, and Distinguishing Bipartite States
Entanglement is an useful resource because some global operations cannot be
locally implemented using classical communication. We prove a number of results
about what is and is not locally possible. We focus on orthogonal states, which
can always be globally distinguished. We establish the necessary and sufficient
conditions for a general set of 2x2 quantum states to be locally
distinguishable, and for a general set of 2xn quantum states to be
distinguished given an initial measurement of the qubit. These results reveal a
fundamental asymmetry to nonlocality, which is the origin of ``nonlocality
without entanglement'', and we present a very simple proof of this phenomenon.Comment: 5 pages, 1 figure. Improved in line with referees comments,
references added, typo corrected. To appear in Phys. Rev. Let
Families of pure PEPS with efficiently simulatable local hidden variable models for most measurements
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set of measurements on their particles, and construct entangled quantum states that are essentially classical for those measurements. In particular, given any set of local measurements on a large enough Hilbert space whose dual strictly contains (i.e. contains an open neighborhood of) a pure state, we use the PEPS formalism and ideas from generalized probabilistic theories to construct pure multiparty entangled states that have (a) local hidden variable models, and (b) can be efficiently simulated classically. We believe that the examples we construct cannot be efficiently classically simulated using previous techniques. Without the restriction on the measurements, the states that we construct are non-local, and in some proof-of-principle cases are universal for measurement based quantum computation.This work was supported by EPSRC grant EP/K022512/1.This work was supported by EPSRC grant EP/K022512/1
Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
We study various distance-like entanglement measures of multipartite states
under certain symmetries. Using group averaging techniques we provide
conditions under which the relative entropy of entanglement, the geometric
measure of entanglement and the logarithmic robustness are equivalent. We
consider important classes of multiparty states, and in particular show that
these measures are equivalent for all stabilizer states, symmetric basis and
antisymmetric basis states. We rigorously prove a conjecture that the closest
product state of permutation symmetric states can always be chosen to be
permutation symmetric. This allows us to calculate the explicit values of
various entanglement measures for symmetric and antisymmetric basis states,
observing that antisymmetric states are generally more entangled. We use these
results to obtain a variety of interesting ensembles of quantum states for
which the optimal LOCC discrimination probability may be explicitly determined
and achieved. We also discuss applications to the construction of optimal
entanglement witnesses
Generalised state spaces and non-locality in fault tolerant quantum computing schemes
We develop connections between generalised notions of entanglement and
quantum computational devices where the measurements available are restricted,
either because they are noisy and/or because by design they are only along
Pauli directions. By considering restricted measurements one can (by
considering the dual positive operators) construct single particle state spaces
that are different to the usual quantum state space. This leads to a modified
notion of entanglement that can be very different to the quantum version (for
example, Bell states can become separable). We use this approach to develop
alternative methods of classical simulation that have strong connections to the
study of non-local correlations: we construct noisy quantum computers that
admit operations outside the Clifford set and can generate some forms of
multiparty quantum entanglement, but are otherwise classical in that they can
be efficiently simulated classically and cannot generate non-local statistics.
Although the approach provides new regimes of noisy quantum evolution that can
be efficiently simulated classically, it does not appear to lead to significant
reductions of existing upper bounds to fault tolerance thresholds for common
noise models.Comment: V2: 18 sides, 7 figures. Corrected two erroneous claims and one
erroneous argumen
Classical simulatability, entanglement breaking, and quantum computation thresholds
We investigate the amount of noise required to turn a universal quantum gate
set into one that can be efficiently modelled classically. This question is
useful for providing upper bounds on fault tolerant thresholds, and for
understanding the nature of the quantum/classical computational transition. We
refine some previously known upper bounds using two different strategies. The
first one involves the introduction of bi-entangling operations, a class of
classically simulatable machines that can generate at most bipartite
entanglement. Using this class we show that it is possible to sharpen
previously obtained upper bounds in certain cases. As an example, we show that
under depolarizing noise on the controlled-not gate, the previously known upper
bound of 74% can be sharpened to around 67%. Another interesting consequence is
that measurement based schemes cannot work using only 2-qubit non-degenerate
projections. In the second strand of the work we utilize the Gottesman-Knill
theorem on the classically efficient simulation of Clifford group operations.
The bounds attained for the pi/8 gate using this approach can be as low as 15%
for general single gate noise, and 30% for dephasing noise.Comment: 12 pages, 3 figures. v2: small typos changed, no change to result
Spin chains and channels with memory
In most studies of the channel capacity of quantum channels, it is assumed
that the errors in each use of the channel are independent. However, recent
work has begun to investigate the effects of memory or correlations in the
error. This work has led to speculation that interesting non-analytic behaviour
may occur in the capacity. Motivated by these observations, we connect the
study of channel capacities under correlated error to the study of critical
behaviour in many-body physics. This connection enables us the techniques of
many-body physics to either completely solve or understand qualitatively a
number of interesting models of correlated error. The models can display
analogous behaviour to associated many-body systems, including `phase
transitions'.Comment: V2: changes in presentation, some additional comments on
generalisation. V3: In accordance with published version, most (but not all)
details of proofs now included. A separate paper will shortly be submitted
separately with all details and more result
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