157 research outputs found
Flag fault-tolerant error correction with arbitrary distance codes
In this paper we introduce a general fault-tolerant quantum error correction
protocol using flag circuits for measuring stabilizers of arbitrary distance
codes. In addition to extending flag error correction beyond distance-three
codes for the first time, our protocol also applies to a broader class of
distance-three codes than was previously known. Flag circuits use extra ancilla
qubits to signal when errors resulting from faults in the circuit have
weight greater than . The flag error correction protocol is applicable to
stabilizer codes of arbitrary distance which satisfy a set of conditions and
uses fewer qubits than other schemes such as Shor, Steane and Knill error
correction. We give examples of infinite code families which satisfy these
conditions and analyze the behaviour of distance-three and -five examples
numerically. Requiring fewer resources than Shor error correction, flag error
correction could potentially be used in low-overhead fault-tolerant error
correction protocols using low density parity check quantum codes of large code
length.Comment: 29 pages (18 pages main text), 22 figures, 7 tables. Comments
welcome! V3 represents the version accepted to quantu
Lower bounds on the non-Clifford resources for quantum computations
We establish lower-bounds on the number of resource states, also known as
magic states, needed to perform various quantum computing tasks, treating
stabilizer operations as free. Our bounds apply to adaptive computations using
measurements and an arbitrary number of stabilizer ancillas. We consider (1)
resource state conversion, (2) single-qubit unitary synthesis, and (3)
computational tasks.
To prove our resource conversion bounds we introduce two new monotones, the
stabilizer nullity and the dyadic monotone, and make use of the already-known
stabilizer extent. We consider conversions that borrow resource states, known
as catalyst states, and return them at the end of the algorithm. We show that
catalysis is necessary for many conversions and introduce new catalytic
conversions, some of which are close to optimal.
By finding a canonical form for post-selected stabilizer computations, we
show that approximating a single-qubit unitary to within diamond-norm precision
requires at least
-states on average. This is the first lower bound that applies to synthesis
protocols using fall-back, mixing techniques, and where the number of ancillas
used can depend on .
Up to multiplicative factors, we optimally lower bound the number of or
states needed to implement the ubiquitous modular adder and
multiply-controlled- operations. When the probability of Pauli measurement
outcomes is 1/2, some of our bounds become tight to within a small additive
constant.Comment: 62 page
Universal transversal gates with color codes - a simplified approach
We provide a simplified, yet rigorous presentation of the ideas from
Bomb\'{i}n's paper "Gauge Color Codes" [arXiv:1311.0879v3]. Our presentation is
self-contained, and assumes only basic concepts from quantum error correction.
We provide an explicit construction of a family of color codes in arbitrary
dimensions and describe some of their crucial properties. Within this
framework, we explicitly show how to transversally implement the generalized
phase gate , which deviates from the method
in "Gauge Color Codes", allowing an arguably simpler proof. We describe how to
implement the Hadamard gate fault-tolerantly using code switching. In three
dimensions, this yields, together with the transversal , a fault-tolerant
universal gate set without state-distillation.Comment: 13 pages, 6 figure
Contemporary marketing practice: a research agenda and preliminary findings
International audienc
Three-dimensional color code thresholds via statistical-mechanical mapping
Three-dimensional (3D) color codes have advantages for fault-tolerant quantum
computing, such as protected quantum gates with relatively low overhead and
robustness against imperfect measurement of error syndromes. Here we
investigate the storage threshold error rates for bit-flip and phase-flip noise
in the 3D color code on the body-centererd cubic lattice, assuming perfect
syndrome measurements. In particular, by exploiting a connection between error
correction and statistical mechanics, we estimate the threshold for 1D
string-like and 2D sheet-like logical operators to be and . We obtain these
results by using parallel tempering Monte Carlo simulations to study the
disorder-temperature phase diagrams of two new 3D statistical-mechanical
models: the 4- and 6-body random coupling Ising models.Comment: 4+7 pages, 6 figures, 1 tabl
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As the record spins: materialising connections
Purpose – The purpose of this paper is to examine how the material nature of legacy technology makes its users passionately prefer it over its digital alternatives.
Design/methodology/approach – This ethnographic study uses data from 26 in-depth interviews with vinyl collectors, augmented with longitudinal participant–observation of vinyl collecting and music store events.
Findings – The findings reveal how the physicality of vinyl facilitates the passionate relationships (with music, the vinyl as performative object and other people) that make vinyl so significant in vinyl users’ lives. Research limitations/implications – As this study examines a single research context (vinyl) from the perspective of participants from three developed, Anglophone nations, its key theoretical contributions should be examined in other technological contexts and other cultures.
Practical implications – The findings imply that miniturisation and automation have lower limits for some products, material attributes should be added to digitised products and that legacy technology products could be usually be reframed as tools of authentic self-expression.
Originality/value – This study explains what can happen beyond the top of the “S” curve in the Technology Acceptance Model, furthering our understanding of consumers’ reactions to the proliferation of digital technology in their lives
Surface code compilation via edge-disjoint paths
We provide an efficient algorithm to compile quantum circuits for
fault-tolerant execution. We target surface codes, which form a 2D grid of
logical qubits with nearest-neighbor logical operations. Embedding an input
circuit's qubits in surface codes can result in long-range two-qubit operations
across the grid. We show how to prepare many long-range Bell pairs on qubits
connected by edge-disjoint paths of ancillas in constant depth that can be used
to perform these long-range operations. This forms one core part of our
Edge-Disjoint Paths Compilation (EDPC) algorithm, by easily performing many
parallel long-range Clifford operations in constant depth. It also allows us to
establish a connection between surface code compilation and several
well-studied edge-disjoint paths problems. Similar techniques allow us to
perform non-Clifford single-qubit rotations far from magic state distillation
factories. In this case, we can easily find the maximum set of paths by a
max-flow reduction, which forms the other major part of EDPC. EDPC has the best
asymptotic worst-case performance guarantees on the circuit depth for compiling
parallel operations when compared to related compilation methods based on swaps
and network coding. EDPC also shows a quadratic depth improvement over
sequential Pauli-based compilation for parallel rotations requiring magic
resources. We implement EDPC and find significantly improved performance for
circuits built from parallel cnots, and for circuits which implement the
multi-controlled gate.Comment: 48 pages, 20 figures. Published version in PRX Quantum. Includes new
comparison table, tightened Theorem 3.3/3.4, and source cod
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