arXiv subjects

Austin G. Fowler

Publications and source records attributed to Austin G. Fowler.

At least 73 records · Page 4Linked to original sources

arXiv2012

Towards practical classical processing for the surface code

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.

quant-ph↗

arXiv2012

Experimental demonstration of topological error correction

Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only nearest-neighbour interaction, particularly suitable for most physical systems. Here we report the first experimental demonstration of topological error correction with an 8-qubit optical cluster state. In the experiment, it is shown that a correlation can be protected against a single error on any single qubit. In addition, when all qubits are simultaneously subjected to errors with equal probability, the effective error rate is significantly reduced, clearly verifying the advantage of topological error correction. The quantum gate with the error rate below the threshold is within the current experimental technology. We believe topological error correction should be a critical ingredient for the future large-scale quantum computation.

quant-ph↗

arXiv2012

Experimental demonstration of topological error correction

Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest known tolerable error rate for a local architecture. This scheme makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the first experimental demonstration of topological error correction with an eight-photon cluster state. It is shown that a correlation can be protected against a single error on any qubit, and when all qubits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. This demonstrates the viability of topological error correction. Our work represents the first experimental effort to achieve fault-tolerant quantum information processing by exploring the topological properties of quantum states.

quant-ph↗

arXiv2011

Fault-tolerant quantum error correction code conversion

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the encoded qubit remains protected. We found, through computational search, that the method used to convert between codes given in this paper is optimal.

quant-ph↗

arXiv2011

Tunable coupling between three qubits as a building block for a superconducting quantum computer

Large scale quantum computers will consist of many interacting qubits. In this paper we expand the two flux qubit coupling scheme first devised in [Phys. Rev. B {\bf 70}, 140501 (2004)] and realized in [Science {\bf 314}, 1427 (2006)] to a three-qubit, two-coupler scenario. We study L-shaped and line-shaped coupler geometries, and show how the interaction strength between qubits changes in terms of the couplers' dimensions. We explore two cases: the "on-state" where the interaction energy between two nearest-neighbor qubits is high, and the "off-state" where it is turned off. In both situations we study the undesirable crosstalk with the third qubit. Finally, we use the GRAPE algorithm to find efficient pulse sequences for two-qubit gates subject to our calculated physical constraints on the coupling strength.

quant-ph↗

arXiv2011

2-D color code quantum computation

We describe in detail how to perform universal fault-tolerant quantum computation on a 2-D color code, making use of only nearest neighbor interactions. Three defects (holes) in the code are used to represent logical qubits. Triple defect logical qubits are deformed into isolated triangular sections of color code to enable transversal implementation of all single logical qubit Clifford group gates. CNOT is implemented between pairs of triple defect logical qubits via braiding.

quant-ph↗

arXiv2010

Constructing arbitrary Steane code single logical qubit fault-tolerant gates

We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.

quant-ph↗

arXiv2010

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.

quant-ph↗

arXiv2010

A Photonic Implementation for the Topological Cluster State Quantum Computer

A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to create a lattice of entangled photons. We give estimates of the minimum efficiencies needed for the detectors, fusion gates and quantum dots, from a numerical simulation.

quant-ph↗

arXiv2010

Surface code quantum error correction incorporating accurate error propagation

The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is obtained by repeatedly measuring each syndrome qubit after appropriate interaction with its four nearest neighbor data qubits. Changes in the measurement value indicate the presence of chains of errors in space and time. The standard method of determining operations likely to return the code to its error-free state is to use the minimum weight matching algorithm to connect pairs of measurement changes with chains of corrections such that the minimum total number of corrections is used. Prior work has not taken into account the propagation of errors in space and time by the two-qubit interactions. We show that taking this into account leads to a quadratic improvement of the logical error rate.

quant-ph↗

arXiv2010

Surface code quantum communication

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate in existing protocols is low as two-way classical communication is used. We show that, if Bell pairs are generated between neighboring stations with a probability of heralded success greater than 0.65 and fidelity greater than 0.96, two-way classical communication can be entirely avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. The number of qubits per repeater scales logarithmically with the communication distance. If the probability of heralded success is less than 0.65 and Bell pairs between neighboring stations with fidelity no less than 0.92 are generated only every T_B seconds, the logarithmic resource scaling remains and the communication rate through N links is proportional to 1/(T_B log^2 N).

quant-ph↗

arXiv2009

Distributed Quantum Computation Architecture Using Semiconductor Nanophotonics

In a large-scale quantum computer, the cost of communications will dominate the performance and resource requirements, place many severe demands on the technology, and constrain the architecture. Unfortunately, fault-tolerant computers based entirely on photons with probabilistic gates, though equipped with "built-in" communication, have very large resource overheads; likewise, computers with reliable probabilistic gates between photons or quantum memories may lack sufficient communication resources in the presence of realistic optical losses. Here, we consider a compromise architecture, in which semiconductor spin qubits are coupled by bright laser pulses through nanophotonic waveguides and cavities using a combination of frequent probabilistic and sparse determinstic entanglement mechanisms. The large photonic resource requirements incurred by the use of probabilistic gates for quantum communication are mitigated in part by the potential high-speed operation of the semiconductor nanophotonic hardware. The system employs topological cluster-state quantum error correction for achieving fault-tolerance. Our results suggest that such an architecture/technology combination has the potential to scale to a system capable of attacking classically intractable computational problems.

quant-ph↗

arXiv2009

Classical Processing Requirements for a Topological Quantum Computing System

Dedicated research into the design and construction of a large scale Quantum Information Processing (QIP) system is a complicated task. The design of an experimentally feasible quantum processor must draw upon results in multiple fields; from experimental efforts in system control and fabrication through to far more abstract areas such as quantum algorithms and error correction. Recently, the adaptation of topological coding models to physical systems in optics has illustrated a possible long term pathway to truly large scale QIP. As the topological model has well defined protocols for Quantum Error Correction (QEC) built in as part of its construction, a more grounded analysis of the {\em classical} processing requirements is possible. In this paper we analyze the requirements for a classical processing system, designed specifically for the topological cluster state model. We demonstrate that via extensive parallelization, the construction of a classical "front-end" system capable of processing error correction data for a large topological computer is possible today.

quant-ph↗

arXiv2009

Architectural design for a topological cluster state quantum computer

The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit manufacturing and control but it crucially depends on the ability to adapt advanced techniques in quantum information theory, such as error correction, to the experimental restrictions of assembling qubit arrays into the millions. In this paper we introduce a feasible architectural design for large scale quantum computation in optical systems. We combine the recent developments in topological cluster state computation with the photonic module, a simple chip based device which can be used as a fundamental building block for a large scale computer. The integration of the topological cluster model with this comparatively simple operational element addresses many significant issues in scalable computing and leads to a promising modular architecture with complete integration of active error correction exhibiting high fault-tolerant thresholds.

quant-ph↗

arXiv2009

Two-dimensional cavity grid for scalable quantum computation with superconducting circuits

Superconducting circuits are among the leading contenders for quantum information processing. This promising avenue has been strengthened with the advent of circuit quantum electrodynamics, underlined by recent experiments coupling on-chip microwave resonators to superconducting qubits. However, moving towards more qubits will require suitable novel architectures. Here, we propose a scalable setup for quantum computing where such resonators are arranged in a two-dimensional grid with a qubit at each intersection. Its versatility allows any two qubits on the grid to be coupled at a swapping overhead independent of their distance and yields an optimal balance between reducing qubit transition frequency spread and spurious cavity-induced couplings. These features make this setup unique and distinct from existing proposals in ion traps, optical lattices, or semiconductor spins. We demonstrate that this approach encompasses the fundamental elements of a scalable fault-tolerant quantum computing architecture.

cond-mat.mes-hall↗

arXiv2009

Topological cluster state quantum computing

The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only, a threshold error rate approaching 1% and low overhead arbitrarily long-range logical gates. In this work, we review the scheme in detail framing discussion solely in terms of the required 3-D cluster state and its stabilizers.

quant-ph↗

arXiv2007

Long-range coupling and scalable architecture for superconducting flux qubits

Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an underappreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described in PRB 70, 140501 (2004) and extend it to allow approximately 500 MHz coupling of square flux qubits, 50 um a side, at a distance of up to several mm. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account crosstalk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.

cond-mat.supr-con↗

arXiv2006

Robustness of Shor's algorithm

Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this subroutine when exposed to a discrete error model that acts to perturb the computational trajectory of a quantum computer. Through detailed state vector simulations of an appropriate quantum circuit, we show that the error locations within the circuit itself heavily influences the probability of success of the QPF subroutine. The results also indicate that the naive estimate of required component precision is too conservative.

quant-ph↗