High-threshold universal quantum computation on the surface code

Fowler, Austin G.; Stephens, Ashley M.; Groszkowski, Peter

doi:10.1103/physreva.80.052312

Cited by 379 publications

(388 citation statements)

References 27 publications

(40 reference statements)

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“…More precisely, when a stabilizer eigenvalue changes in a surface code cycle, it is efficient to store the location of that stabilizer and wait several code cycles, accumulating a spacetime diagram of stabilizer errors as additional errors occur [30,59,60]. After sufficiently many code cycles, the spacetime diagram may be used to determine the most likely configuration of Wilson lines that could have generated those errors [28,29] using a minimum-weight perfect matching algorithm [64,65]. Errors may be subsequently corrected by software when performing logical qubit manipulations and readouts [28].…”

Section: B Logical Qubits and Error Correctionmentioning

confidence: 99%

“…First, stabilizer measurements in the Majorana surface code can be performed in a single step, whereas this requires several physical gate operations in the conventional surface code [28,29]. As a result, we anticipate that the Majorana surface code has a significantly higher error tolerance.…”

Section: Introductionmentioning

confidence: 99%

“…In the surface code, measurements of nontrivial commuting operators (stabilizers) are used to project onto a "code state," and logical qubits are effectively encoded in the anyon charge of a region by ceasing certain stabilizer measurements [26][27][28][29]. The logical gates necessary for universal quantum computation are realized through sequences of measurements used to move and braid the logical qubits.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Majorana Fermion Surface Code for Universal Quantum Computation

2015

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We introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

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Section: B Logical Qubits and Error Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Majorana Fermion Surface Code for Universal Quantum Computation

2015

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“…In recent years, quantum computation has presented a compelling application for quantum control, as high-fidelity control is essential to implement quantum information processors that achieve fault-tolerance [7][8][9].…”

Section: Pacs Numbersmentioning

confidence: 99%

Controlling Quantum Devices with Nonlinear Hardware

et al. 2015

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High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices. PACS numbers:The ability to coherently control the dynamics of quantum systems with high fidelity is a critical component of the development of modern quantum devices, including quantum computers [1], actuators [2,3], and sensors [4][5][6] that push beyond the capabilities of classical computation and metrology. In recent years, quantum computation has presented a compelling application for quantum control, as high-fidelity control is essential to implement quantum information processors that achieve fault-tolerance [7][8][9].The performance of numerically optimized quantum gates in laboratory applications strongly depends on the accuracy of the system model used to approximate the response of the experimental system to the applied control sequence. Here we develop a general framework whereby classical control hardware components are modelled explicitly, such that their effect on a quantum system can be computed and compensated for using numerical optimal control theory (OCT) [10] algorithms to optimize control sequences. Control sequences designed using OCT algorithms, such as the GRadient Ascent Pulse Engineering (GRAPE) [11] algorithm, can be made robust to a wide variety of inhomogenities, pulse errors and noise processes [12][13][14]. These methods are also easily extended [15][16][17][18] to other applications and may be integrated into other protocols [19]. Recently, it was demonstrated how a model of linear distortions of the control sequence, such as those arising from finite bandwidth of the classical control hardware, may also be integrated into OCT algorithms [20][21][22].Here, we improve and generalize those results beyond linear kernels to any operation that smoothly maps a list of control steps to a classical field seen by the quantum system. Importantly, our framework naturally allows for robustness against uncertainties and errors due to classical control hardware. We begin developing our method generally, without making assumptions about the device of interest, so that our results may be broadly applicable to a wide range of quantum devices. We briefly discuss how our theory is easily applied to any linear distortion, and then in more detail, demonstrate with numerics how nonlinearities in control hardware, such as those found in strongly-driven superconducting resonators used for pulsed electron spin resonance (PESR) [23][24][25], may be included in OCT algorithms.With this goal in mind, we briefly review th...

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“…Topological quantum computation [1], [2], [3] has proven to be one of the most promising ways to realize fault-tolerant quantum computation. In this paper, we focus on the computation model in Ref.…”

Section: Introductionmentioning

confidence: 99%

Logical Qubit Layout Problem for ICM Representation

Adnan

Yamashita

2018

Journal of Information Processing

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This paper formulates the qubit layout problem for ICM representation which is favorable for topological quantum computation. Observing the properties of braiding operations in a logic circuit model of ICM, we study the potential usefulness of two-dimensional qubit layouts based on this model. We compare and contrast the efficiency of one-and two-dimensional qubit layouts in reducing the logical time steps for topological quantum circuits. This leads us to an approach to find a good gate order for two-dimensional qubit layouts. Indeed, our preliminary experimental results show the effectiveness of two-dimensional qubit layouts.

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High-threshold universal quantum computation on the surface code

Cited by 379 publications

References 27 publications

Majorana Fermion Surface Code for Universal Quantum Computation

Majorana Fermion Surface Code for Universal Quantum Computation

Controlling Quantum Devices with Nonlinear Hardware

Logical Qubit Layout Problem for ICM Representation

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