22 research outputs found
Trellises for stabilizer codes: definition and uses
Trellises play an important theoretical and practical role for classical
codes. Their main utility is to devise complexity-efficient error estimation
algorithms. Here, we describe trellis representations for quantum stabilizer
codes. We show that they share the same properties as their classical analogs.
In particular, for any stabilizer code it is possible to find a minimal trellis
representation. Our construction is illustrated by two fundamental error
estimation algorithms.Comment: 5 pages, 2 figure
Quantum serial turbo-codes
We present a theory of quantum serial turbo-codes, describe their iterative
decoding algorithm, and study their performances numerically on a
depolarization channel. Our construction offers several advantages over quantum
LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that
deteriorate the performances of iterative decoding. Secondly, the iterative
decoder makes explicit use of the code's degeneracy. Finally, there is complete
freedom in the code design in terms of length, rate, memory size, and
interleaver choice.
We define a quantum analogue of a state diagram that provides an efficient
way to verify the properties of a quantum convolutional code, and in particular
its recursiveness and the presence of catastrophic error propagation. We prove
that all recursive quantum convolutional encoder have catastrophic error
propagation. In our constructions, the convolutional codes have thus been
chosen to be non-catastrophic and non-recursive. While the resulting families
of turbo-codes have bounded minimum distance, from a pragmatic point of view
the effective minimum distances of the codes that we have simulated are large
enough not to degrade the iterative decoding performance up to reasonable word
error rates and block sizes. With well chosen constituent convolutional codes,
we observe an important reduction of the word error rate as the code length
increases.Comment: 24 pages, 15 figures, Published versio
Securing Quantum Computations in the NISQ Era
Recent experimental achievements motivate an ever-growing interest from
companies starting to feel the limitations of classical computing. Yet, in
light of ongoing privacy scandals, the future availability of quantum computing
through remotely accessible servers pose peculiar challenges: Clients with
quantum-limited capabilities want their data and algorithms to remain hidden,
while being able to verify that their computations are performed correctly.
Research in blind and verifiable delegation of quantum computing attempts to
address this question. However, available techniques suffer not only from high
overheads but also from over-sensitivity: When running on noisy devices,
imperfections trigger the same detection mechanisms as malicious attacks,
resulting in perpetually aborted computations. Hence, while malicious quantum
computers are rendered harmless by blind and verifiable protocols, inherent
noise severely limits their usability.
We address this problem with an efficient, robust, blind, verifiable scheme
to delegate deterministic quantum computations with classical inputs and
outputs. We show that: 1) a malicious Server can cheat at most with an
exponentially small success probability; 2) in case of sufficiently small
noise, the protocol succeeds with a probability exponentially close to 1; 3)
the overhead is barely a polynomial number of repetitions of the initial
computation interleaved with test runs requiring the same physical resources in
terms of memory and gates; 4) the amount of tolerable noise, measured by the
probability of failing a test run, can be as high as 25% for some computations
and will be generally bounded by 12.5% when using a planar graph resource
state. The key points are that security can be provided without universal
computation graphs and that, in our setting, full fault-tolerance is not needed
to amplify the confidence level exponentially close to 1.Comment: 18 pages, 3 figures. Results from this article have been extended to
allow verification of BQP computations in arXiv:2109.0404
Unifying Quantum Verification and Error-Detection: Theory and Tools for Optimisations
With the recent availability of cloud quantum computing services, the
question of verifying quantum computations delegated by a client to a quantum
server is becoming of practical interest. While Verifiable Blind Quantum
Computing (VBQC) has emerged as one of the key approaches to address this
challenge, current protocols still need to be optimised before they are truly
practical.
To this end, we establish a fundamental correspondence between
error-detection and verification and provide sufficient conditions to both
achieve security in the Abstract Cryptography framework and optimise resource
overheads of all known VBQC-based protocols. As a direct application, we
demonstrate how to systematise the search for new efficient and robust
verification protocols for computations. While we have chosen
Measurement-Based Quantum Computing (MBQC) as the working model for the
presentation of our results, one could expand the domain of applicability of
our framework via direct known translation between the circuit model and MBQC.Comment: 45 pages, 9 figure
Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe
We study the role of the information deposited in the environment of an open
quantum system in course of the decoherence process. Redundant spreading of
information -- the fact that some observables of the system can be
independently ``read-off'' from many distinct fragments of the environment --
is investigated as the key to effective objectivity, the essential ingredient
of ``classical reality''. This focus on the environment as a communication
channel through which observers learn about physical systems underscores
importance of quantum Darwinism -- selective proliferation of information about
``the fittest states'' chosen by the dynamics of decoherence at the expense of
their superpositions -- as redundancy imposes the existence of preferred
observables. We demonstrate that the only observables that can leave multiple
imprints in the environment are the familiar pointer observables singled out by
environment-induced superselection (einselection) for their predictability.
Many independent observers monitoring the environment will therefore agree on
properties of the system as they can only learn about preferred observables. In
this operational sense, the selective spreading of information leads to
appearance of an objective ``classical reality'' from within quantum substrate.Comment: New figures, to appear in PR
Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
We present an efficient quantum algorithm to measure the average fidelity
decay of a quantum map under perturbation using a single bit of quantum
information. Our algorithm scales only as the complexity of the map under
investigation, so for those maps admitting an efficient gate decomposition, it
provides an exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where it is
conjectured to be a signature of quantum chaos. Our result also illustrates the
role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure
Description of a quantum convolutional code
We describe a quantum error correction scheme aimed at protecting a flow of
quantum information over long distance communication. It is largely inspired by
the theory of classical convolutional codes which are used in similar
circumstances in classical communication. The particular example shown here
uses the stabilizer formalism, which provides an explicit encoding circuit. An
associated error estimation algorithm is given explicitly and shown to provide
the most likely error over any memoryless quantum channel, while its complexity
grows only linearly with the number of encoded qubits.Comment: 4 pages, uses revtex4. Minor correction in the encoding and decoding
circuit
Asymmetric Quantum Secure Multi-Party Computation With Weak Clients Against Dishonest Majority
Secure multi-party computation (SMPC) protocols allow several parties that distrust each other to collectively compute a function on their inputs. In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party. Unlike previous quantum SMPC protocols, our proposal only requires very limited quantum resources from all but one party; it suffices that the weak parties, i.e. the clients, are able to prepare single-qubit states in the X-Y plane.
The novel quantum SMPC protocol is constructed in a naturally modular way, and relies on a new technique for quantum verification that is of independent interest. This verification technique requires the remote preparation of states only in a single plane of the Bloch sphere. In the course of proving the security of the new verification protocol, we also uncover a fundamental invariance that is inherent to measurement-based quantum computing
Objective properties from subjective quantum states: Environment as a witness
We study the emergence of objective properties in open quantum systems. In
our analysis, the environment is promoted from a passive role of reservoir
selectively destroying quantum coherence, to an active role of amplifier
selectively proliferating information about the system. We show that only
preferred pointer states of the system can leave a redundant and therefore
easily detectable imprint on the environment. Observers who--as it is almost
always the case--discover the state of the system indirectly (by probing a
fraction of its environment) will find out only about the corresponding pointer
observable. Many observers can act in this fashion independently and without
perturbing the system: they will agree about the state of the system. In this
operational sense, preferred pointer states exist objectively.Comment: 5 pages, 1 figure, extensive changes, presentation improve
A direct approach to fault-tolerance in measurement-based quantum computation via teleportation
International audienceWe discuss a simple variant of the one-way quantum computing model [R. Raussendorf and H.-J. Briegel, PRL 86, 5188, 2001], called the Pauli measurement model, where measurements are restricted to be along the eigenbases of the Pauli X and Y operators, while auxiliary qubits can be prepared both in the state, and the usual state. We prove the universality of this quantum computation model, and establish a standardization procedure which permits all entanglement and state preparation to be performed at the beginning of computation. This leads us to develop a direct approach to fault-tolerance by simple transformations of the entanglement graph and preparation operations, while error correction is performed naturally via syndrome-extracting teleportations