scholarly journals The XZZX surface code

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
J. Pablo Bonilla Ataides ◽  
David K. Tuckett ◽  
Stephen D. Bartlett ◽  
Steven T. Flammia ◽  
Benjamin J. Brown
Keyword(s):  
Quantum Computation ◽  
High Performance ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
The Common ◽  
Surface Code ◽  
Random Codes ◽  
Quantum Error ◽  
Relevant Range

AbstractPerforming large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation.

scholarly journals The XZZX surface code

2020 ◽  
Author(s):  
J. Bonilla Ataides ◽  
David Tuckett ◽  
Stephen Bartlett ◽  
Steven Flammia ◽  
Benjamin Brown
Keyword(s):  
Quantum Computation ◽  
High Performance ◽  
Fault Tolerant ◽  
Small Scale ◽  
Single Qubit ◽  
The Common ◽  
Surface Code ◽  
Random Codes ◽  
Relevant Range ◽  
Common Situation

Abstract We show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favorable sub-threshold resource scaling that can be obtained by specializing a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation. We finally suggest some small-scale experiments that could exploit noise bias to reduce qubit overhead in two-dimensional architectures

scholarly journals ERROR THRESHOLD ESTIMATION BY MEANS OF THE [[7,1,3]] CSS QUANTUM CODE

2005 ◽  
Vol 03 (02) ◽  
pp. 371-393 ◽  
Author(s):  
P. J. SALAS ◽  
A. L. SANZ
Keyword(s):  
Quantum Computation ◽  
Error Probability ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Quantum Code ◽  
Threshold Estimation ◽  
Control Error ◽  
Threshold Conditions ◽  
Quantum Error ◽  
Depolarizing Channel

The states needed in quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting codes. In this work, we estimate the threshold conditions necessary to make a long enough quantum computation. The [[7,1,3]] CSS quantum code together with the Shor method to measure the error syndrome is used. No concatenation is included. The decoherence is introduced by means of the depolarizing channel error model, obtaining several thresholds from the numerical simulation. Regarding the maintenance of a qubit stabilized in the memory, the error probability must be smaller than 2.9 × 10-5. In order to implement a one or two-qubit encoded gate in an effective fault-tolerant way, it is possible to choose an adequate non-encoded noisy gate if the memory error probability is smaller than 1.3 × 10-5. In addition, fulfilling this last condition permits us to assume a more efficient behavior compared to the equivalent non-encoded process.

scholarly journals Online scheduled execution of quantum circuits protected by surface codes

2017 ◽  
Vol 17 (15&16) ◽  
pp. 1335-1348 ◽  
Author(s):  
Alexandru Paler ◽  
Austin G. Fowler ◽  
Robert Wille
Keyword(s):  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Dynamic Structure ◽  
Quantum Circuit ◽  
Error Correcting Codes ◽  
Quantum Circuits ◽  
Static Scheduling ◽  
Surface Code ◽  
High Level ◽  
Quantum Error

Quantum circuits are the preferred formalism for expressing quantum information processing tasks. Quantum circuit design automation methods mostly use a waterfall approach and consider that high level circuit descriptions are hardware agnostic. This assumption has lead to a static circuit perspective: the number of quantum bits and quantum gates is determined before circuit execution and everything is considered reliable with zero probability of failure. Many different schemes for achieving reliable fault-tolerant quantum computation exist, with different schemes suitable for different architectures. A number of large experimental groups are developing architectures well suited to being protected by surface quantum error correcting codes. Such circuits could include unreliable logical elements, such as state distillation, whose failure can be determined only after their actual execution. Therefore, practical logical circuits, as envisaged by many groups, are likely to have a dynamic structure. This requires an online scheduling of their execution: one knows for sure what needs to be executed only after previous elements have finished executing. This work shows that scheduling shares similarities with place and route methods. The work also introduces the first online schedulers of quantum circuits protected by surface codes. The work also highlights scheduling efficiency by comparing the new methods with state of the art static scheduling of surface code protected fault-tolerant circuits.

scholarly journals The boundaries and twist defects of the color code and their applications to topological quantum computation

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 101 ◽  
Author(s):  
Markus S. Kesselring ◽  
Fernando Pastawski ◽  
Jens Eisert ◽  
Benjamin J. Brown
Keyword(s):  
Quantum Computation ◽  
Domain Walls ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Two Dimensions ◽  
Abstract Theory ◽  
Color Code ◽  
Topological Quantum ◽  
Multiple Copies ◽  
Surface Code

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

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 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 A silicon-based surface code quantum computer

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Device Fabrication ◽  
Impurity Atoms ◽  
Dipole Interactions ◽  
Total Phase ◽  
Surface Code ◽  
Silicon Based

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

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.

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