3,081 research outputs found
Quantum simulation of partially distinguishable boson sampling
Boson Sampling is the problem of sampling from the same output probability
distribution as a collection of indistinguishable single photons input into a
linear interferometer. It has been shown that, subject to certain computational
complexity conjectures, in general the problem is difficult to solve
classically, motivating optical experiments aimed at demonstrating quantum
computational "supremacy". There are a number of challenges faced by such
experiments, including the generation of indistinguishable single photons. We
provide a quantum circuit that simulates bosonic sampling with arbitrarily
distinguishable particles. This makes clear how distinguishabililty leads to
decoherence in the standard quantum circuit model, allowing insight to be
gained. At the heart of the circuit is the quantum Schur transform, which
follows from a representation theoretic approach to the physics of
distinguishable particles in first quantisation. The techniques are quite
general and have application beyond boson sampling.Comment: 25 pages, 4 figures, 2 algorithms, comments welcom
Error probability analysis in quantum tomography: a tool for evaluating experiments
We expand the scope of the statistical notion of error probability, i.e., how
often large deviations are observed in an experiment, in order to make it
directly applicable to quantum tomography. We verify that the error probability
can decrease at most exponentially in the number of trials, derive the explicit
rate that bounds this decrease, and show that a maximum likelihood estimator
achieves this bound. We also show that the statistical notion of
identifiability coincides with the tomographic notion of informational
completeness. Our result implies that two quantum tomographic apparatuses that
have the same risk function, (e.g. variance), can have different error
probability, and we give an example in one qubit state tomography. Thus by
combining these two approaches we can evaluate, in a reconstruction independent
way, the performance of such experiments more discerningly.Comment: 14pages, 2 figures (an analysis of an example is added, and the proof
of Lemma 2 is corrected
Generating entanglement with linear optics
Entanglement is the basic building block of linear optical quantum
computation, and as such understanding how to generate it in detail is of great
importance for optical architectures. We prove that Bell states cannot be
generated using only 3 photons in the dual-rail encoding, and give strong
numerical evidence for the optimality of the existing 4 photon schemes. In a
setup with a single photon in each input mode, we find a fundamental limit on
the possible entanglement between a single mode Alice and arbitrary Bob. We
investigate and compare other setups aimed at characterizing entanglement in
settings more general than dual-rail encoding. The results draw attention to
the trade-off between the entanglement a state has and the probability of
postselecting that state, which can give surprising constant bounds on
entanglement even with increasing numbers of photons.Comment: 13 pages, 10 figures, 1 table, comments welcom
Randomized benchmarking in measurement-based quantum computing
Randomized benchmarking is routinely used as an efficient method for
characterizing the performance of sets of elementary logic gates in small
quantum devices. In the measurement-based model of quantum computation, logic
gates are implemented via single-site measurements on a fixed universal
resource state. Here we adapt the randomized benchmarking protocol for a single
qubit to a linear cluster state computation, which provides partial, yet
efficient characterization of the noise associated with the target gate set.
Applying randomized benchmarking to measurement-based quantum computation
exhibits an interesting interplay between the inherent randomness associated
with logic gates in the measurement-based model and the random gate sequences
used in benchmarking. We consider two different approaches: the first makes use
of the standard single-qubit Clifford group, while the second uses recently
introduced (non-Clifford) measurement-based 2-designs, which harness inherent
randomness to implement gate sequences.Comment: 10 pages, 4 figures, comments welcome; v2 published versio
Quantum computation over the butterfly network
In order to investigate distributed quantum computation under restricted
network resources, we introduce a quantum computation task over the butterfly
network where both quantum and classical communications are limited. We
consider deterministically performing a two-qubit global unitary operation on
two unknown inputs given at different nodes, with outputs at two distinct
nodes. By using a particular resource setting introduced by M. Hayashi [Phys.
Rev. A \textbf{76}, 040301(R) (2007)], which is capable of performing a swap
operation by adding two maximally entangled qubits (ebits) between the two
input nodes, we show that unitary operations can be performed without adding
any entanglement resource, if and only if the unitary operations are locally
unitary equivalent to controlled unitary operations. Our protocol is optimal in
the sense that the unitary operations cannot be implemented if we relax the
specifications of any of the channels. We also construct protocols for
performing controlled traceless unitary operations with a 1-ebit resource and
for performing global Clifford operations with a 2-ebit resource.Comment: 12 pages, 12 figures, the second version has been significantly
expanded, and author ordering changed and the third version is a minor
revision of the previous versio
Degradation of a quantum reference frame
We investigate the degradation of reference frames, treated as dynamical
quantum systems, and quantify their longevity as a resource for performing
tasks in quantum information processing. We adopt an operational measure of a
reference frame's longevity, namely, the number of measurements that can be
made against it with a certain error tolerance. We investigate two distinct
types of reference frame: a reference direction, realized by a spin-j system,
and a phase reference, realized by an oscillator mode with bounded energy. For
both cases, we show that our measure of longevity increases quadratically with
the size of the reference system and is therefore non-additive. For instance,
the number of measurements that a directional reference frame consisting of N
parallel spins can be put to use scales as N^2. Our results quantify the extent
to which microscopic or mesoscopic reference frames may be used for repeated,
high-precision measurements, without needing to be reset - a question that is
important for some implementations of quantum computing. We illustrate our
results using the proposed single-spin measurement scheme of magnetic resonance
force microscopy.Comment: 9 pages plus appendices, 4 figures, published versio
Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis
Motivated by studies of typical properties of quantum states in statistical
mechanics, we introduce phase-random states, an ensemble of pure states with
fixed amplitudes and uniformly distributed phases in a fixed basis. We first
show that canonical states typically appear in subsystems of phase-random
states. We then investigate the simulatability of phase-random states, which is
directly related to that of time evolution in closed systems, by studying their
entanglement properties. We find that starting from a separable state, time
evolutions under Hamiltonians composed of only separable eigenstates generate
extremely high entanglement and are difficult to simulate with matrix product
states. We also show that random quantum circuits consisting of only two-qubit
diagonal unitaries can generate an ensemble with the same average entanglement
as phase-random states.Comment: Revised, 12 pages, 4 figur
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