scholarly journals Deterministic generation of a two-dimensional cluster state

Science ◽  
2019 ◽  
Vol 366 (6463) ◽  
pp. 369-372 ◽  
Author(s):  
Mikkel V. Larsen ◽  
Xueshi Guo ◽  
Casper R. Breum ◽  
Jonas S. Neergaard-Nielsen ◽  
Ulrik L. Andersen
Keyword(s):  
Quantum Computation ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Cluster State ◽  
Two Dimensional ◽  
Cluster States ◽  
Squeezed Light ◽  
Universal Quantum ◽  
Speed Up ◽  
Quantum Error

Measurement-based quantum computation offers exponential computational speed-up through simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30,000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of two-dimensional cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.

scholarly journals Bounds on universal quantum computation with perturbed two-dimensional cluster states

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Román Orús ◽  
Henning Kalis ◽  
Marcel Bornemann ◽  
Kai Phillip Schmidt
Keyword(s):  
Quantum Computation ◽  
Two Dimensional ◽  
Cluster States ◽  
Universal Quantum

scholarly journals Cost-optimal single-qubit gate synthesis in the Clifford hierarchy

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 396
Author(s):  
Gary J. Mooney ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Error Correction ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Practical Implementation ◽  
Error Correction Code ◽  
Universal Quantum ◽  
Arbitrary Precision ◽  
Qubit Gate ◽  
Quantum Error

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra’s pathfinding algorithm for the canonical Clifford+T set of base gates and compared them to when additionally including Z-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced to T-counts by recursively applying a Z-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to 54±3% when using the Z-rotation catalyst circuit approach and by up to 33±2% when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets of Z-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.

scholarly journals Generating Fault-Tolerant Cluster States from Crystal Structures

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 295 ◽  
Author(s):  
Michael Newman ◽  
Leonardo Andreta de Castro ◽  
Kenneth R. Brown
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Crystal Structures ◽  
Fault Tolerant ◽  
Cluster State ◽  
Error Correcting Codes ◽  
Noise Model ◽  
Cluster States ◽  
Promising Alternative ◽  
Quantum Error

Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-3 connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

scholarly journals MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES

2009 ◽  
Vol 07 (06) ◽  
pp. 1053-1203 ◽  
Author(s):  
ROBERT RAUßENDORF
Keyword(s):  
Computational Model ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Network Model ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Cluster State ◽  
Building Blocks ◽  
Network Simulator ◽  
Classical Level

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

scholarly journals Roads towards fault-tolerant universal quantum computation

Nature ◽  
2017 ◽  
Vol 549 (7671) ◽  
pp. 172-179 ◽  
Author(s):  
Earl T. Campbell ◽  
Barbara M. Terhal ◽  
Christophe Vuillot
Keyword(s):  
Quantum Computation ◽  
Fault Tolerant ◽  
Universal Quantum

scholarly journals Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

2021 ◽  
Author(s):  
Dongsheng Wang ◽  
Yunjiang Wang ◽  
Ningping Cao ◽  
Bei Zeng ◽  
Raymond Lafflamme
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Valence Bond ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Exact Quantum ◽  
Valence Bond Solid ◽  
Quantum Error

Abstract In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

scholarly journals Universal quantum computation and quantum error correction with ultracold atomic mixtures

2021 ◽  
Author(s):  
Valentin Kasper ◽  
Daniel González-Cuadra ◽  
Apoorva Hegde ◽  
Andy Xia ◽  
Alexandre Dauphin ◽  
...  
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Quantum Error Correction ◽  
Universal Quantum ◽  
Quantum Error

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals Generation of time-domain-multiplexed two-dimensional cluster state

Science ◽  
2019 ◽  
Vol 366 (6463) ◽  
pp. 373-376 ◽  
Author(s):  
Warit Asavanant ◽  
Yu Shiozawa ◽  
Shota Yokoyama ◽  
Baramee Charoensombutamon ◽  
Hiroki Emura ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Large Scale ◽  
Cluster State ◽  
Continuous Variable ◽  
Error Correcting Codes ◽  
Square Lattice ◽  
Two Dimensional ◽  
Report Generation ◽  
Cluster States ◽  
Variable Cluster

Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states—based on bosonic modes rather than qubits—have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.

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