Symmetry, Phases of Matter, and Resources in Quantum Computing

Conference Date: 
Tuesday, November 26, 2019 (All day) to Friday, November 29, 2019 (All day)
Scientific Areas: 
Quantum Information

 

Our conference covers three related subjects: quantum fault-tolerance, magic states and resource theories, and quantum computational phases of matter. The linking elements between them are (a) on the phenomenological side, the persistence of computational power under perturbations, and (b) on the theory side, symmetry. The latter is necessary for the working of all three. The subjects are close but not identical, and we expect cross-fertilization between them.Fault tolerance is an essential component of universal scalable quantum computing.However, known practical methods of achieving fault tolerance are extremely resource intensive. Distillation of magic states is, in the current paradigm of fault-tolerance, the costliest operational component, by a large margin. It is therefore pertinent to improve the efficiency of such procedures, study theoretical limits of efficiency, and more generally, to establish a resource theory of quantum state magic. During the workshop, we will focus on a fundamental connection between fault-tolerant protocols and symmetries.``Computational phases of matter’’ are a surprising link between quantum computation and condensed matter physics. Namely, in the presence of suitable symmetries, the ground states of spin Hamiltonians have computational power within the scheme of measurement-based quantum computation, and this power is uniform across physical phases. Several computationally universal phases have to date been discovered. This subject is distinct from the above, but linked to them by the feature of persistence of computational power under deformations and deviations.

Registration for this event is now closed.

 

  • Stephen Bartlett, University of Sydney
  • Earl Campbell, University of Sheffield
  • Bartek Czech, Tsinghua University
  • David Gosset, University of Waterloo
  • Daniel Gottesman, Perimeter Institute
  • David Gross, University of Cologne
  • Anthony Leverrier, INRIA
  • Peter Love, Tufts University
  • Akimasa Miyake, University of New Mexico
  • Tomoyuki Morimae, Kyoto University
  • Naomi Nickerson, Psi Quantum
  • Sam Roberts, University of Sydney
  • Norbert  Schuch, Max Planck Institute of Quantum Optics
  • Robert Spekkens, Perimeter Institute
  • Tzu-Chieh Wei, State University of New York
  • Gabriel Wong, Fudan University
  • Alvaro Alhambra, Perimeter Institute
  • Jacob Bridgeman, Perimeter Institute
  • Christopher Chubb,. Université de Sherbrooke
  • Timothy Hsieh, Perimeter Institute
  • Nick Hunter-Jones, Perimeter Institute
  • Guldam Kwak, University of Waterloo
  • Cheng-Ju (Jacob) Lin, Perimeter Institute
  • Maria Julia Maristany, Perimeter Institute
  • Iman Marvian, Duke University
  • Cihan Okay, University of British Columbia
  • James Seddon, University College London
  • Aaron Szasz, Perimeter Institute
  • Michael Vasmer, Perimeter Institute & Institute for Quantum Computing
  • Christophe Vuilot, INRIA
  • Michael Zurel, University of British Columbia

Tuesday, November 26, 2019

Time

Event

Location

9:00 – 9:25am

Registration

Reception

9:25 – 9:30am

Welcome and Opening Remarks

Bob Room

9:30 – 10:15am

Stephen Bartlett, University of Sydney

Bob Room

10:15 – 11:00am

Akimasa Miyake, University of New Mexico

Bob Room

11:00 – 11:30am

Coffee Break

Bistro – 1st Floor

11:30 – 12:15pm

Robert Spekkens, Perimeter Institute

Bob Room

12:15 – 1:15pm

Lunch

Bistro – 2nd Floor

1:15 – 3:30pm

Discussions

Bob Room

3:30 – 4:15pm

Peter Love, Tufts University
Variational Quantum Eigensolvers and contextuality

Bob Room

4:15 – 4:45pm

Coffee Break

Bistro – 1st Floor

4:45 – 5:30pm

Earl Campbell, University of Sheffield

Bob Room


Wednesday, November 27, 2019

Time

Event

Location

9:30 – 10:15am

David Gosset, University of Waterloo

Bob Room

10:15 – 11:00am

Tomoyuki Morimae, Kyoto University
Fine-grained quantum supremacy and stabilizer rank

Bob Room

11:00 – 11:30am

Coffee Break

Bistro – 1st Floor

11:30 – 12:15pm

Naomi Nickerson, Psi Quantum

Bob Room

12:15 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:30pm

Colloquium
Robert Raussendorf, University of British Columbia

Theater

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 4:45pm

Anthony Leverrier, Inria
Towards local testability for quantum coding

Bob Room

6:00pm onwards

Banquet

Bistro – 2nd Floor


Thursday, November 28, 2019

Time

Event

Location

9:30 – 10:15am

Sam Roberts, University of Sydney

Bob Room

10:15 – 11:00am

Daniel Gottesman, Perimeter Institute

Bob Room

11:00 – 11:30am

Coffee Break

Bistro – 1st Floor

11:30 – 12:15pm

Norbert Schuch, Max Planck Institute of Quantum Optics

Bob Room

12:15 – 1:15pm

Lunch

Bistro – 2nd Floor

1:15 – 3:30pm

Discussions

Bob Room

3:30 – 4:15pm

Tzu-Chieh Wei, State University of New York
Two-dimensional AKLT states as ground states of gapped Hamiltonians and resource for universal quantum computation

Bob Room

4:15 – 4:45pm

Coffee Break

Bistro – 1st Floor

4:45 – 5:30pm

David Gross, University of Cologne

Bob Room


Friday, November 29, 2019

Time

Event

Location

9:30 – 10:15am

Gabriel Wong, Fudan University

Bob Room

10:15 – 11:00am

Bartek Czech, Tsinghua University

Bob Room

11:00 – 11:30am

Coffee Break

Bistro – 1st Floor

11:30 – 12:15pm

Aleksander Kubica, Perimeter Institute

Bob Room

12:15 – 1:15pm

Lunch

Bistro – 2nd Floor

1:15 – 3:30pm

Discussions

Bob Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

 

Anthony Leverrier, Inria

Towards local testability for quantum coding

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the  p-faces of the n-cube (for n>p) and stabilizer constraints with faces of dimension (p±1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N=2n−p−1(np) physical qubits and displays local testability with a soundness of Ω(log−2(N)) beating the current state-of-the-art of log−3(N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors.
We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be 1/log(N), similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.
(joint work with Vivien Londe and Gilles Zémor)

Peter Love, Tufts University

Variational Quantum Eigensolvers and contextuality

The variational quantum eigensolver (VQE) is the leading candidate for practical applications of Noisy Intermediate Scale Quantum (NISQ) devices. The method has been widely implemented on small NISQ machines in both superconducting and ion trap implementations. I will review progress to date and discuss two questions . Firstly, how quantum mechanical are small VQE demonstrations? We will analyze this question using strong measurement contextuality. Secondly, can VQE be implemented at the scale of devices capable of exhibiting quantum supremacy, around 50 qubits? I will discuss some recent techniques to reduce the number of measurements required, which again use the concept of contextuality.

Tomoyuki Morimae, Kyoto University

Fine-grained quantum supremacy and stabilizer rank

It is known that several sub-universal quantum computing models cannot be classically simulated unless the polynomial-time hierarchy collapses. However, these results exclude only polynomial-time classical simulations. In this talk, based on fine-grained complexity conjectures, I show more ``fine-grained" quantum supremacy results that prohibit certain exponential-time classical simulations.  I also show the stabilizer rank conjecture under fine-grained complexity conjectures.

Tzu-Chieh Wei, State University of New York

Two-dimensional AKLT states as ground states of gapped Hamiltonians and resource for universal quantum computation

Affleck, Kennedy, Lieb, and Tasaki (AKLT) constructed one-dimensional and two-dimensional spin models invariant under spin rotation. These are recognized as paradigmatic examples of symmetry-protected topological phases, including the spin-1 AKLT chain with a provable nonzero spectral gap that strongly supports Haldane’s conjecture on the spectral gap of integer chains. These states were shown to provide universal resource for quantum computation, in the framework of the measurement-based approach, including the spin-3/2 AKLT state on the honeycomb lattice and the spin-2 one on the square lattice, both of which display exponential decay in the correlation functions. However, the nonzero spectral in these 2D models had not been proved analytically for over 30 years, until very recently.  I will review briefly our understanding of the quantum computational universality in the AKLT family. Then I will focus on demonstrating the nonzero spectral gap for several 2D AKLT models, including decorated honeycomb and decorated square lattices, and the undecorated degree-3 Archimedean lattices.  In brief, we now have universal resource states that are ground states of provable gapped local Hamiltonians. Such a feature may be useful in creating the resource states by cooling the system and might further help the exploration into the quantum computational phases in generalized AKLT-Haldane phases.

 

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Turn right into the PI parking lot entrance.
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If you need accommodations while attending this workshop, we offer suggestions for lodging below.  When booking your reservation, please indicate that you will be attending an event at Perimeter in order to receive the best possible rate.

Delta Waterloo 110 Erb Street West Waterloo, ON N2L 0C6
Phone: 1-888-890-3222
Distance from PI: 450 m

Comfort Inn 190 Weber Street North Waterloo, ON N2J 3H4
Phone: 519-747-9400
Distance from PI: 2.3 km

Walper Terrace Hotel 1 King Street West Kitchener, ON N2G 1A1
Phone: 519-745-4321
Distance from PI: 3.7 km

Crowne Plaza Kitchener-Waterloo 105 King Street East Waterloo, ON N2G 2K8
Phone: 519-744-4141
Distance from PI: 3.8 km

Holiday Inn Express & Suites 14 Benjamin Road Waterloo, ON N2V 2J9
Phone:  519-772-9800
Distance from PI:  5.6 km

Homewood Suites by Hilton 45 Benjamin Road Waterloo, ON N2V 2G8
Phone:  519-514-0088
Distance from PI:  5.6 km

Courtyard by Marriott 50 Benjamin Road East Waterloo, ON N2V 2J9
Phone: 519-884-9295
Distance from PI: 5.6 km

Scientific Organizers:

  • Joseph Emerson, University of Waterloo
  • Aleksander Kubica, Perimeter Institute
  • David Poulin, Université de Sherbrooke
  • Robert Raussendorf, University of British Columbia
  • Beni Yoshida, Perimeter Institute