QECOOL: On-Line Quantum Error Correction with a Superconducting Decoder for Surface Code

Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a reinforcement learning framework for optimizing and fault-tolerantly adapting quantum error correction codes. We consider a reinforcement learning agent tasked with modifying a family of surface code quantum memories until a desired logical error rate is reached. Using efficient simulations with about 70 data qubits with arbitrary connectivity, we demonstrate that such a reinforcement learning agent can determine near-optimal solutions, in terms of the number of data qubits, for various error models of interest. Moreover, we show that agents trained on one setting are able to successfully transfer their experience to different settings. This ability for transfer learning showcases the inherent strengths of reinforcement learning and the applicability of our approach for optimization from off-line simulations to on-line laboratory settings.

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Fault-tolerant thresholds for quantum error correction with the surface code

Physical Review A ◽

10.1103/physreva.89.022321 ◽

2014 ◽

Vol 89 (2) ◽

Cited By ~ 38

Author(s):

Ashley M. Stephens

Keyword(s):

Error Correction ◽

Fault Tolerant ◽

Quantum Error Correction ◽

Surface Code ◽

Quantum Error

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Decoding surface code with a distributed neural network–based decoder

Quantum Machine Intelligence ◽

10.1007/s42484-020-00015-9 ◽

2020 ◽

Vol 2 (1) ◽

Cited By ~ 2

Author(s):

Savvas Varsamopoulos ◽

Koen Bertels ◽

Carmen G. Almudever

Keyword(s):

Neural Network ◽

Renormalization Group ◽

Error Correction ◽

Quantum Error Correction ◽

Noise Model ◽

Error Correction Codes ◽

Exponential Increase ◽

Main Challenge ◽

Surface Code ◽

Quantum Error

Abstract There has been a rise in decoding quantum error correction codes with neural network–based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network–based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the renormalization group (RG) decoders. In this paper, we introduce a decoding algorithm that combines the concept of RG decoding and neural network–based decoders. We tested the decoding performance under depolarizing noise with noiseless error syndrome measurements for the rotated surface code and compared against the blossom algorithm and a neural network–based decoder. We show that a similar level of decoding performance can be achieved between all tested decoders while providing a solution to the scalability issues of neural network–based decoders.

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Qubit parity measurement by parametric driving in circuit QED

Science Advances ◽

10.1126/sciadv.aau1695 ◽

2018 ◽

Vol 4 (11) ◽

pp. eaau1695 ◽

Cited By ~ 4

Author(s):

Baptiste Royer ◽

Shruti Puri ◽

Alexandre Blais

Keyword(s):

Error Correction ◽

Quantum Electrodynamics ◽

High Amplitude ◽

Quantum Error Correction ◽

Parametric Oscillation ◽

Circuit Qed ◽

Experimental Implementation ◽

Parity Measurement ◽

Surface Code ◽

Quantum Error

Multiqubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and that requires notable experimental overhead. We propose a hardware-efficient multiqubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator’s parametric oscillation threshold, which depends on the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for one parity subspace and no oscillation for the other. We present analytical and numerical results for two- and four-qubit parity measurements, with high-fidelity readout preserving the parity eigenpaces. Moreover, we discuss a possible realization that can be readily implemented with the current circuit quantum electrodynamics (QED) experimental toolbox. These results could lead to substantial simplifications in the experimental implementation of quantum error correction and notably of the surface code.

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Non-Pauli topological stabilizer codes from twisted quantum doubles

Quantum ◽

10.22331/q-2021-02-17-398 ◽

2021 ◽

Vol 5 ◽

pp. 398

Author(s):

Julio Carlos Magdalena de la Fuente ◽

Nicolas Tarantino ◽

Jens Eisert

Keyword(s):

Quantum Information ◽

Error Correction ◽

Lattice Models ◽

Full Rank ◽

Error Correcting Codes ◽

Quantum Error Correction ◽

Topological Order ◽

Topological Quantum ◽

Surface Code ◽

Quantum Error

It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.

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A Silicon Surface Code Architecture Resilient Against Leakage Errors

Quantum ◽

10.22331/q-2019-12-09-212 ◽

2019 ◽

Vol 3 ◽

pp. 212 ◽

Cited By ~ 4

Author(s):

Zhenyu Cai ◽

Michael A. Fogarty ◽

Simon Schaal ◽

Sofia Patomäki ◽

Simon C. Benjamin ◽

...

Keyword(s):

Quantum Dot ◽

Error Correction ◽

Large Scale ◽

Building Blocks ◽

Quantum Error Correction ◽

Error Correction Codes ◽

Relaxation Processes ◽

Spin Qubits ◽

Surface Code ◽

Quantum Error

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98% fidelity and are improving rapidly. However, there are other types of error --- such as charge leakage and propagation --- that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design.

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Surface code continuous quantum error correction using feedback

2015 54th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2015.7403339 ◽

2015 ◽

Cited By ~ 2

Author(s):

Thien Nguyen ◽

Charles D. Hill ◽

Lloyd C. L. Hollenberg ◽

Matthew R. James

Keyword(s):

Error Correction ◽

Quantum Error Correction ◽

Surface Code ◽

Quantum Error

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A surface code quantum computer in silicon

Science Advances ◽

10.1126/sciadv.1500707 ◽

2015 ◽

Vol 1 (9) ◽

pp. e1500707 ◽

Cited By ~ 112

Author(s):

Charles D. Hill ◽

Eldad Peretz ◽

Samuel J. Hile ◽

Matthew G. House ◽

Martin Fuechsle ◽

...

Keyword(s):

Error Correction ◽

Nuclear Spin ◽

Quantum Coherence ◽

Large Scale ◽

Quantum Error Correction ◽

Shared Control ◽

Two Dimensional ◽

Surface Code ◽

Quantum Error ◽

And Control

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

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Machine-learning-assisted correction of correlated qubit errors in a topological code

Quantum ◽

10.22331/q-2018-01-29-48 ◽

2018 ◽

Vol 2 ◽

pp. 48 ◽

Cited By ~ 37

Author(s):

Paul Baireuther ◽

Thomas E. O'Brien ◽

Brian Tarasinski ◽

Carlo W. J. Beenakker

Keyword(s):

Neural Network ◽

Machine Learning ◽

Error Correction ◽

Recurrent Neural Network ◽

Learning Algorithm ◽

Minimum Weight ◽

Quantum Error Correction ◽

Noise Model ◽

Surface Code ◽

Quantum Error

A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.

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Removing leakage-induced correlated errors in superconducting quantum error correction

Nature Communications ◽

10.1038/s41467-021-21982-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

M. McEwen ◽

D. Kafri ◽

Z. Chen ◽

J. Atalaya ◽

K. J. Satzinger ◽

...

Keyword(s):

Quantum Computing ◽

Error Correction ◽

Energy Levels ◽

System Size ◽

High Energy ◽

Error Rates ◽

Quantum Error Correction ◽

Correlated Errors ◽

Surface Code ◽

Quantum Error

AbstractQuantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.

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