1,077 research outputs found
Quantum proof systems for iterated exponential time, and beyond
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. We show that any language solvable in nondeterministic time exp(exp(· · · exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness 1 and soundness 1 − exp(−C exp(· · · exp(n))), where the number of iterated exponentials is R(n) − 1 and C > 0 is a universal constant. The result was previously known for R = 1 and R = 2; we obtain it for any time-constructible function R. The result is based on a compression technique for interactive proof systems with entangled provers that significantly simplifies and strengthens a protocol compression result of Ji (STOC’17). As a separate consequence of this technique we obtain a different proof of Slofstra’s recent result on the uncomputability of the entangled value of multiprover games (Forum of Mathematics, Pi 2019). Finally, we show that even minor improvements to our compression result would yield remarkable consequences in computational complexity theory and the foundations of quantum mechanics: first, it would imply that the class MIP∗ contains all computable languages; second, it would provide a negative resolution to a multipartite version of Tsirelson’s problem on the relation between the commuting operator and tensor product models for quantum correlations
Efficient growth of complex graph states via imperfect path erasure
Given a suitably large and well connected (complex) graph state, any quantum
algorithm can be implemented purely through local measurements on the
individual qubits. Measurements can also be used to create the graph state:
Path erasure techniques allow one to entangle multiple qubits by determining
only global properties of the qubits. Here, this powerful approach is extended
by demonstrating that even imperfect path erasure can produce the required
graph states with high efficiency. By characterizing the degree of error in
each path erasure attempt, one can subsume the resulting imperfect entanglement
into an extended graph state formalism. The subsequent growth of the improper
graph state can be guided, through a series of strategic decisions, in such a
way as to bound the growth of the error and eventually yield a high-fidelity
graph state. As an implementation of these techniques, we develop an analytic
model for atom (or atom-like) qubits in mismatched cavities, under the
double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71,
060310 (2005)]. Compared to straightforward postselection techniques our
protocol offers a dramatic improvement in growing complex high-fidelity graph
states.Comment: 15 pages, 10 figures (which print to better quality than when viewed
as an on screen pdf
Cross-verification of independent quantum devices
Quantum computers are on the brink of surpassing the capabilities of even the
most powerful classical computers. This naturally raises the question of how
one can trust the results of a quantum computer when they cannot be compared to
classical simulation. Here we present a verification technique that exploits
the principles of measurement-based quantum computation to link quantum
circuits of different input size, depth, and structure. Our approach enables
consistency checks of quantum computations within a device, as well as between
independent devices. We showcase our protocol by applying it to five
state-of-the-art quantum processors, based on four distinct physical
architectures: nuclear magnetic resonance, superconducting circuits, trapped
ions, and photonics, with up to 6 qubits and 200 distinct circuits
Unconditionally verifiable blind computation
Blind Quantum Computing (BQC) allows a client to have a server carry out a
quantum computation for them such that the client's input, output and
computation remain private. A desirable property for any BQC protocol is
verification, whereby the client can verify with high probability whether the
server has followed the instructions of the protocol, or if there has been some
deviation resulting in a corrupted output state. A verifiable BQC protocol can
be viewed as an interactive proof system leading to consequences for complexity
theory. The authors, together with Broadbent, previously proposed a universal
and unconditionally secure BQC scheme where the client only needs to be able to
prepare single qubits in separable states randomly chosen from a finite set and
send them to the server, who has the balance of the required quantum
computational resources. In this paper we extend that protocol with new
functionality allowing blind computational basis measurements, which we use to
construct a new verifiable BQC protocol based on a new class of resource
states. We rigorously prove that the probability of failing to detect an
incorrect output is exponentially small in a security parameter, while resource
overhead remains polynomial in this parameter. The new resource state allows
entangling gates to be performed between arbitrary pairs of logical qubits with
only constant overhead. This is a significant improvement on the original
scheme, which required that all computations to be performed must first be put
into a nearest neighbour form, incurring linear overhead in the number of
qubits. Such an improvement has important consequences for efficiency and
fault-tolerance thresholds.Comment: 46 pages, 10 figures. Additional protocol added which allows
arbitrary circuits to be verified with polynomial securit
Carbon export from mountain forests enhanced by earthquake-triggered landslides over millennia
Rapid ground accelerations during earthquakes can trigger landslides that disturb mountain forests and harvest carbon from soils and vegetation. Although infrequent over human timescales, these co-seismic landslides can set the rates of geomorphic processes over centuries to millennia. However, the long-term impacts of earthquakes and landslides on carbon export from the biosphere remain poorly constrained. Here, we examine the sedimentary fill of Lake Paringa, New Zealand, which is fed by a river draining steep mountains proximal to the Alpine Fault. Carbon isotopes reveal enhanced accumulation rates of biospheric carbon after four large earthquakes over the past ~1,100 years, probably reflecting delivery of soil-derived carbon eroded by deep-seated landslides. Cumulatively these pulses of earthquake-mobilized carbon represent 23 ± 5% of the record length, but account for 43 ± 5% of the biospheric carbon in the core. Landslide simulations suggest that 14 ± 5 million tonnes of carbon (MtC) could be eroded in each earthquake. Our findings support a link between active tectonics and the surface carbon cycle and suggest that large earthquakes can significantly contribute to carbon export from mountain forests over millennia
Non-Conscious Influences on Consumer Choice
While consumer choice research has dedicated considerable research attention to aspects of choice that are deliberative and conscious, only limited attention has been paid to aspects of choice that occur outside of conscious awareness. We review relevant research that suggests that consumer choice is a mix of conscious and nonconscious influences, and argue that the degree to which nonconscious influences affect choice is much greater than many choice researchers believe. Across a series of research domains, these influences are found to include stimulus that are not consciously perceived by the consumer, nonconscious downstream effects of a consciously perceived stimuli or thought process, and decision processes that occur entirely outside of awareness
Brokered Graph State Quantum Computing
We describe a procedure for graph state quantum computing that is tailored to
fully exploit the physics of optically active multi-level systems. Leveraging
ideas from the literature on distributed computation together with the recent
work on probabilistic cluster state synthesis, our model assigns to each
physical system two logical qubits: the broker and the client. Groups of
brokers negotiate new graph state fragments via a probabilistic optical
protocol. Completed fragments are mapped from broker to clients via a simple
state transition and measurement. The clients, whose role is to store the
nascent graph state long term, remain entirely insulated from failures during
the brokerage. We describe an implementation in terms of NV-centres in diamond,
where brokers and clients are very naturally embodied as electron and nuclear
spins.Comment: 5 pages, 3 figure
Entanglement Transfer via XXZ Heisenberg chain with DM Interaction
The role of spin-orbit interaction, arises from the Dzyaloshinski-Moriya
anisotropic antisymmetric interaction, on the entanglement transfer via an
antiferromagnetic XXZ Heisenberg chain is investigated. From symmetrical point
of view, the XXZ Hamiltonian with Dzyaloshinski-Moriya interaction can be
replaced by a modified XXZ Hamiltonian which is defined by a new exchange
coupling constant and rotated Pauli operators. The modified coupling constant
and the angle of rotations are depend on the strength of Dzyaloshinski-Moriya
interaction. In this paper we study the dynamical behavior of the entanglement
propagation through a system which is consist of a pair of maximally entangled
spins coupled to one end of the chain. The calculations are performed for the
ground state and the thermal state of the chain, separately. In both cases the
presence of this anisotropic interaction make our channel more efficient, such
that the speed of transmission and the amount of the entanglement are improved
as this interaction is switched on. We show that for large values of the
strength of this interaction a large family of XXZ chains becomes efficient
quantum channels, for whole values of an isotropy parameter in the region .Comment: 21 pages, 9 figure
Design and construction of an optical test bed for LISA imaging systems and tilt-to-length coupling
The laser interferometer space antenna (LISA) is a future space-based interferometric gravitational-wave detector consisting of three spacecraft in a triangular configuration. The interferometric measurements of path length changes between satellites will be performed on optical benches in the satellites. Angular misalignments of the interfering beams couple into the length measurement and represent a significant noise source. Imaging systems will be used to reduce this tilt-to-length coupling.
We designed and constructed an optical test bed to experimentally investigate tilt-to-length coupling. It consists of two separate structures, a minimal optical bench and a telescope simulator. The minimal optical bench comprises the science interferometer where the local laser is interfered with light from a remote spacecraft. In our experiment, a simulated version of this received beam is generated on the telescope simulator. The telescope simulator provides a tilting beam, a reference interferometer and an additional static beam as a phase reference. The tilting beam can either be a flat-top beam or a Gaussian beam. We avoid tilt-to-length coupling in the reference interferometer by using a small photo diode placed at an image of the beam rotation point. We show that the test bed is operational with an initial measurement of tilt-to-length coupling without imaging systems.
Furthermore, we show the design of two different imaging systems whose performance will be investigated in future experiments
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