141 research outputs found
Noise in One-Dimensional Measurement-Based Quantum Computing
Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum
circuit model, whereby the computation proceeds via measurements on an
entangled resource state. Noise processes are a major experimental challenge to
the construction of a quantum computer. Here, we investigate how noise
processes affecting physical states affect the performed computation by
considering MBQC on a one-dimensional cluster state. This allows us to break
down the computation in a sequence of building blocks and map physical errors
to logical errors. Next, we extend the Matrix Product State construction to
mixed states (which is known as Matrix Product Operators) and once again map
the effect of physical noise to logical noise acting within the correlation
space. This approach allows us to consider more general errors than the
conventional Pauli errors, and could be used in order to simulate noisy quantum
computation.Comment: 16 page
Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
One of the leading quantum computing architectures is based on the
two-dimensional (2D) surface code. This code has many advantageous properties
such as a high error threshold and a planar layout of physical qubits where
each physical qubit need only interact with its nearest neighbours. However,
the transversal logical gates available in 2D surface codes are limited. This
means that an additional (resource intensive) procedure known as magic state
distillation is required to do universal quantum computing with 2D surface
codes. Here, we examine three-dimensional (3D) surface codes in the context of
quantum computation. We introduce a picture for visualizing 3D surface codes
which is useful for analysing stacks of three 3D surface codes. We use this
picture to prove that the and gates are transversal in 3D surface
codes. We also generalize the techniques of 2D surface code lattice surgery to
3D surface codes. We combine these results and propose two quantum computing
architectures based on 3D surface codes. Magic state distillation is not
required in either of our architectures. Finally, we show that a stack of three
3D surface codes can be transformed into a single 3D color code (another type
of quantum error-correcting code) using code concatenation.Comment: 23 pages, 24 figures, v2: published versio
Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation
Magic state distillation is an important primitive in fault-tolerant quantum
computation. The magic states are pure non-stabilizer states which can be
distilled from certain mixed non-stabilizer states via Clifford group
operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli
eigenstates are not expected to be magic state distillable, but it has been an
open question whether all mixed states outside this set may be distilled. In
this Letter we show that, when resources are finitely limited, non-distillable
states exist outside the stabilizer octahedron. In analogy with the bound
entangled states, which arise in entanglement theory, we call such states bound
states for magic state distillation.Comment: Published version. This paper builds on a theorem proven in "On the
Structure of Protocols for Magic State Distillation", arXiv:0908.0838. These
two papers jointly form the content of a talk entitled "Neither Magical nor
Classical?", which was presented at TQC 2009, Waterlo
Stronger Quantum Correlations with Loophole-free Post-selection
One of the most striking non-classical features of quantum mechanics is in
the correlations it predicts between spatially separated measurements. In local
hidden variable theories, correlations are constrained by Bell inequalities,
but quantum correlations violate these. However, experimental imperfections
lead to "loopholes" whereby LHV correlations are no longer constrained by Bell
inequalities, and violations can be described by LHV theories. For example,
loopholes can emerge through selective detection of events. In this letter, we
introduce a clean, operational picture of multi-party Bell tests, and show that
there exists a non-trivial form of loophole-free post-selection. Surprisingly,
the same post-selection can enhance quantum correlations, and unlock a
connection between non-classical correlations and non-classical computation.Comment: 4 pages, 2 figures, substantially revised in response to referee
suggestion
Fault-tolerant error correction with the gauge color code
The constituent parts of a quantum computer are inherently vulnerable to
errors. To this end we have developed quantum error-correcting codes to protect
quantum information from noise. However, discovering codes that are capable of
a universal set of computational operations with the minimal cost in quantum
resources remains an important and ongoing challenge. One proposal of
significant recent interest is the gauge color code. Notably, this code may
offer a reduced resource cost over other well-studied fault-tolerant
architectures using a new method, known as gauge fixing, for performing the
non-Clifford logical operations that are essential for universal quantum
computation. Here we examine the gauge color code when it is subject to noise.
Specifically we make use of single-shot error correction to develop a simple
decoding algorithm for the gauge color code, and we numerically analyse its
performance. Remarkably, we find threshold error rates comparable to those of
other leading proposals. Our results thus provide encouraging preliminary data
of a comparative study between the gauge color code and other promising
computational architectures.Comment: v1 - 5+4 pages, 11 figures, comments welcome; v2 - minor revisions,
new supplemental including a discussion on correlated errors and details on
threshold calculations; v3 - Author accepted manuscript. Accepted on
21/06/16. Deposited on 29/07/16. 9+5 pages, 17 figures, new version includes
resource scaling analysis in below threshold regime, see eqn. (4) and methods
sectio
Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
Two-level quantum systems, qubits, are not the only basis for quantum
computation. Advantages exist in using qudits, d-level quantum systems, as the
basic carrier of quantum information. We show that color codes, a class of
topological quantum codes with remarkable transversality properties, can be
generalized to the qudit paradigm. In recent developments it was found that in
three spatial dimensions a qubit color code can support a transversal
non-Clifford gate, and that in higher spatial dimensions additional
non-Clifford gates can be found, saturating Bravyi and K\"onig's bound [Phys.
Rev. Lett. 110, 170503 (2013)]. Furthermore, by using gauge fixing techniques,
an effective set of Clifford gates can be achieved, removing the need for state
distillation. We show that the qudit color code can support the qudit analogues
of these gates, and show that in higher spatial dimensions a color code can
support a phase gate from higher levels of the Clifford hierarchy which can be
proven to saturate Bravyi and K\"onig's bound in all but a finite number of
special cases. The methodology used is a generalisation of Bravyi and Haah's
method of triorthogonal matrices [Phys. Rev. A 86 052329 (2012)], which may be
of independent interest. For completeness, we show explicitly that the qudit
color codes generalize to gauge color codes, and share the many of the
favorable properties of their qubit counterparts.Comment: Authors' final cop
Improved maximum-likelihood quantum amplitude estimation
Quantum amplitude estimation is a key subroutine in a number of powerful
quantum algorithms, including quantum-enhanced Monte Carlo simulation and
quantum machine learning. Maximum-likelihood quantum amplitude estimation
(MLQAE) is one of a number of recent approaches that employ much simpler
quantum circuits than the original algorithm based on quantum phase estimation.
In this article, we deepen the analysis of MLQAE to put the algorithm in a more
prescriptive form, including scenarios where quantum circuit depth is limited.
In the process, we observe and explain particular ranges of `exceptional'
values of the target amplitude for which the algorithm fails to achieve the
desired precision. We then propose and numerically validate a heuristic
modification to the algorithm to overcome this problem, bringing the algorithm
even closer to being useful as a practical subroutine on near- and mid-term
quantum hardware.Comment: 22+2 pages, 10 figure
Tsirelson's bound and Landauer's principle in a single-system game
We introduce a simple single-system game inspired by the
Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary
gates and projective measurements, we prove that any strategy in our game can
be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound
also holds in our setting. More generally, we show that the optimal success
probability depends on the reversible or irreversible character of the gates,
the quantum or classical nature of the system and the system dimension. We
analyse the bounds obtained in light of Landauer's principle, showing the
entropic costs of the erasure associated with the game. This shows a connection
between the reversibility in fundamental operations embodied by Landauer's
principle and Tsirelson's bound, that arises from the restricted physics of a
unitarily-evolving single-qubit system.Comment: 7 pages, 5 figures, typos correcte
Computational power of correlations
We study the intrinsic computational power of correlations exploited in
measurement-based quantum computation. By defining a general framework the
meaning of the computational power of correlations is made precise. This leads
to a notion of resource states for measurement-based \textit{classical}
computation. Surprisingly, the Greenberger-Horne-Zeilinger and
Clauser-Horne-Shimony-Holt problems emerge as optimal examples. Our work
exposes an intriguing relationship between the violation of local realistic
models and the computational power of entangled resource states.Comment: 4 pages, 2 figures, 2 tables, v2: introduction revised and title
changed to highlight generality of established framework and results, v3:
published version with additional table I
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