Midterm strategic meeting - Granada, November 2019 - QuantERA

Midterm strategic meeting
             Granada, November 2019

QCDA: Quantum code design and architecture

         Project co-ordinator: Earl Campbell

                                 This project has received funding from the European Union’s
                                           Horizon 2020 research and innovation programme
                                                           under grant agreement No 731473.

Q               C             D             A
    Delft         London         Paris      Sheffield       Munich
The Netherlands United Kingdom   France   United Kingdom    Germany

Meet the PIs

               3

Kick-off meeting Paris
Winter 2018

Goal

                    Beat the surface code

Google’s Symcamore processor is designed to realise the surface code.
Expensive: Need over 1 million qubits for useful fault-tolerant algorithms.

                                                                         5

Objectives

               Beat the surface code

Objective 1 Develop Low-Density Parity Check (LDPC)
coding architectures, which assume only low connectivity
between qubits and exhibit their possible benefits;

Objective 2 Develop continuous-variable (CV) error correction
as a viable alternative coding architecture as compared to
qubit-based schemes.

                                                                6

Workpackages

WP1 qubit codes and decoders (Paris lead)

WP2 Universal logic & compiling (London Lead)

WP3 Implementing QEC (Delft lead)

WP4 Continuous variable architectures (Munich lead)

WP5 Management & dissemination (Sheffield lead)

                                                      7

Seven significant results

 Significant results in midterm report

WP1
1: Decoders for quantum expander code.
2: Golden & hyperbolic codes and decoders.
3: General theory of single-shot error correction
WP2
4: Invention of PIN codes.
5: Transversal control-control-Z gate in 3D toric code.
WP4
6: Concatenating the toric code with the Gottesman-Kitaev-Preskill.
7: Universal Uhrig Dynamical Decoupling for Bosonic Systems.

Note: WP3 at early stage                                              8

Seven significant results

 Significant results in midterm report

WP1
1: Decoders for quantum expander code.
2: Golden & hyperbolic codes and decoders.
3: General theory of single-shot error correction
WP2
4: Invention of PIN codes.
5: Transversal control-control-Z gate in 3D toric code.
WP4
6: Concatenating the toric code with the Gottesman-Kitaev-Preskill.
7: Universal Uhrig Dynamical Decoupling for Bosonic Systems.

Note: WP3 at early stage                                              9

Decoders for quantum expander code.

First ever proof that constant overhead fault-tolerance is possible;
  Paris group developed small-set flip decoder for quantum-expander
  codes [FGL18, GK18]
  o 4.6% threshold for an LDPC code family with check-weight 11;
Important advance, but need faster/better and lower check weights

Decoders for quantum expander code.

Writing up results Sheffield, London & Paris
o Developed hybrid family between surface-expander LDPC codes;
o Improvement of Ordered Statistics Decoder (OSD) – poorly
   understood but gets best numerical performance (in prep)
o Reshape decoder provably decodes adversial errors (in prep)

Decoders for quantum expander code.

First high-rate LDPC code family with non-Clifford transversal
gates – important for performing fault-tolerant logic
                           PIN codes:
                           [VB19] Collaboration between London,
                           a postdoc who moved Delft->Paris

                           Codes defined using ”pinned” paths
                           through a chain complex.

                           Includes many colour codes,
                           and can be regarded as a
                           generalization of this family.

Towards objective 2

[VAWPT19]: First work which shows that
bosonic error correction can be made
scalable and can thus serve as the blueprint
of a quantum computer architecture.
o Concatenating GKP with the 2D toric
  code and modelling all sources of errors;
o found threshold corresponding to GKP
  states with 4-6 photons.
                                                  GKP: grid states use 1 CV
Initial work in Delft, but postdoc relocated to   mode to encode a logical
Paris node with followup work in progress.        qubit.

Munich & Sheffield collaborating on devising
fault-tolerant gadgets for CV codes.
                                                                              13

Towards objective 2

[HK19]: First work showing dynamical decoupling in bosonic setting
Munich group

o Unwanted Gaussian interactions can be efficiently suppressed
  to any given order;
o This can be achieved using rather simple pulses: single-mode
  passive Gaussians & two mode swaps.

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Brought QEC (quantum error correction) to London!
Summer 2019

Thanks for listening

     Visit our website www.qcda.eu

Contact me at: e.campbell@sheffield.ac.uk

                         This project has received funding from the European Union’s
                                   Horizon 2020 research and innovation programme
                                                   under grant agreement No 731473.