Quantum mechanics redefines information and its fundamental properties. Researchers at Perimeter Institute work to understand the properties of quantum information and study which information processing tasks are feasible, and which are infeasible or impossible. This includes research in quantum cryptography, which studies the tradeoff between information extraction and disturbance, and its applications. It also includes research in quantum error correction, which involves the study of methods for protecting information against decoherence. Another important side of the field is studying the application of quantum information techniques and insights to other areas of physics, including quantum foundations and condensed matter.
Format results

18 talksCollection Number C17011
Talk

Hyperinvariant tensor networks and holography
Glen Evenbly Georgia Institute of Technology

Tensor network and (padic) AdS/CFT
LingYan Hung Fudan University  Physics Department

Dynamics for holographic codes
Tobias Osborne Leibniz Universität Hannover

Random tensor networks and holographic coherent states
Xiaoliang Qi Stanford University


Complexity, Holography & Quantum Field Theory
Robert Myers Perimeter Institute for Theoretical Physics

Two Continous Approaches to AdS/Tensor Network duality
Tadashi Takayanagi Yukawa Institute for Theoretical Physics

Tensor Networks and Holography
James Sully McGill University


The Story of Anyons
Steve Simon University of Oxford  Rudolf Peierls Centre for Theoretical Physics

Predicting many properties of quantum systems with chaotic dynamics
HongYe Hu University of California

Quantum Scientific Computation
JinPeng Liu University of New Mexico

Probing topological invariants from a ground state wave function
ZePei Cian University of New Mexico

Matrixvalued logarithmic Sobolev inequalities
Haojian Li Baylor University

Spectral analysis of product formulas for quantum simulation
Changhao Yi University of New Mexico

Quantum Algorithms for Classical Sampling Problems
Dominik Wild Max Planck Institute of Quantum Optics

Contracting Arbitrary Tensor Networks: Approximate and Exact Approach with Applications in Graphical Models and Quantum Circuit Simulations
Feng Pan Perimeter Institute for Theoretical Physics

The Markov gap for geometric reflected entropy
Jonathan Sorce Stanford University

Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
Charles Cao University of Maryland

Exponential Error Suppression for NearTerm Quantum Devices
Balint Koczor University of Oxford

Tensor Networks for Quantum Field Theories II
18 talksCollection Number C17011Tensor Networks for Quantum Field Theories II 
The Story of Anyons
Steve Simon University of Oxford  Rudolf Peierls Centre for Theoretical Physics
I will review the history of anyons, particles that are neither bosons nor fermions, starting with their theoretical proposal all the way to their definitive experimental observation over 40 years later. I will further discuss why the more general idea of nonabelian anyons is of intense interest for quantum computation. If time permits I will give a status report on some of the current nonabelian anyon experiments.
Zoom Link: https://pitp.zoom.us/j/98698779123?pwd=SWIyak9OZ0dud2ZGcWdoazdkVURHQT09

Predicting many properties of quantum systems with chaotic dynamics
HongYe Hu University of California
Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. However, it is quite challenging to realize deep unitary circuits on nearterm quantum devices, and an unbiased reconstruction map is nontrivial to find for arbitrary random unitary ensembles. In this talk, I will discuss our recent progress on combining classical shadow tomography with quantum chaotic dynamics. Particularly, I will introduce two new families of shadow tomography schemes: 1) Hamiltoniandriven shadow tomography and 2) Classical shadow tomography with locally scrambled quantum dynamics. In both works, I’ll derive the unbiased reconstruction map, and analyze the sample complexity. In the Hamiltoniandriven scheme, I will illustrate how to use proper time windows to achieve a more efficient tomography. In the second work, I will demonstrate advantages of shadow tomography in the shallow circuit region. Then I’ll conclude by discussing approximate shadow tomography with local Hamiltonian dynamics, and demonstrate that a single quenchdisordered quantum spin chain can be used for approximate shadow tomography.
References:
[1] HongYe Hu, YiZhuang You. “HamiltonianDriven Shadow Tomography of Quantum States”. arXiv:2102.10132 (2021)
[2] HongYe Hu, Soonwon Choi, YiZhuang You. “Classical Shadow Tomography with Locally Scrambled Quantum Dynamics”. arXiv: 2107.04817 (2021)Zoom Link: https://pitp.zoom.us/j/99011187936?pwd=OVU3VkpyZ21YcXRCOW5DOHlnSWlVQT09

Quantum Scientific Computation
JinPeng Liu University of New Mexico
Quantum computers are expected to dramatically outperform classical computers for certain computational problems. While there has been extensive previous work for linear dynamics and discrete models, for more complex realistic problems arising in physical and social science, engineering, and medicine, the capability of quantum computing is far from well understood. One fundamental challenge is the substantial difference between the linear dynamics of a system of qubits and realworld systems with continuum, stochastic, and nonlinear behaviors. Utilizing advanced linear algebra techniques and nonlinear analysis, I attempt to build a bridge between classical and quantum mechanics, understand and optimize the power of quantum computation, and discover new quantum speedups over classical algorithms with provable guarantees. In this talk, I would like to cover quantum algorithms for scientific computational problems, including topics such as linear, nonlinear, and stochastic differential equations, with applications in areas such as quantum dynamics, biology and epidemiology, fluid dynamics, and finance.
Reference:
Quantum spectral methods for differential equations, Communications in Mathematical Physics 375, 14271457 (2020), https://arxiv.org/abs/1901.00961
Highprecision quantum algorithms for partial differential equations, Quantum 5, 574 (2021), https://arxiv.org/abs/2002.07868
Efficient quantum algorithm for dissipative nonlinear differential equations, Proceedings of the National Academy of Sciences 118, 35 (2021), https://arxiv.org/abs/2011.03185
Quantumaccelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance, Quantum 5, 481 (2021), https://arxiv.org/abs/2012.06283 
Probing topological invariants from a ground state wave function
ZePei Cian University of New Mexico
With the rapid development of programmable quantum simulators, the quantum states can be controlled with unprecedented precision. Thus, it opens a new opportunity to explore the strongly correlated phase of matter with new quantum technology platforms. In quantum simulators, one can engineer interactions between the microscopic degree of freedom and create exotic phases of matter that presumably are beyond the reach of natural materials. Moreover, quantum states can be directly measured instead of probing physical properties indirectly via optical and electrical responses of material as done in traditional condensed matter. Therefore, it is pressing to develop new approaches to efficiently prepare and characterize desired quantum states in the novel quantum technology platforms.
In this talk, I will introduce our recent works on the characterization of the topological invariants from a ground state wave function of the topological order phase and the implementation in noisy intermediate quantum devices. First, using topological field theory and tensor network simulations, we demonstrate how to extract the manybody Chern number (MBCN) given a bulk of a fractional quantum Hall wave function [1]. We then propose an ancillafree experimental scheme for measuring the MBCN without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function [2]. Finally, I will present an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a ground state wave function of a gapped, translationally invariant Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We then use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully characterize topological order from the bulk of a ground state wave function [3].
[1] H. Dehghani, Z.P. Cian, M. Hafezi, and M. Barkeshl, Phys. Rev. B 103, 075102
[2] Z.P. Cian, H. Dehghani, A. Elben, B. Vermersch, G. Zhu, M. Barkeshli, P. Zoller, and M. Hafezi, Phys. Rev. Lett. 126, 050501
[3] Z.P. Cian, M. Hafezi, and M. Barkeshl, Manuscript in preparation. 
Matrixvalued logarithmic Sobolev inequalities
Haojian Li Baylor University
Logarithmic Sobolev inequalities (LSI) were first introduced by Gross in the 1970s as an equivalent formulation of hypercontractivity. LSI have been well studied in the past few decades and found applications to information theory, optimal transport, and graph theory. Recently matrixvalued LSI have been an active area of research. Matrixvalued LSI of Lindblad operators are closely related to decoherence of open quantum systems. In this talk, I will present recent results on matrixvalued LSI, in particular a geometric approach to matrixvalued LSI of Lindblad operators. This talk is based on joint work with Li Gao, Marius Junge, and Nicholas LaRacuente.

Spectral analysis of product formulas for quantum simulation
Changhao Yi University of New Mexico
TrotterSuzuki formula is a practical and efficient algorithm for Hamiltonian simulation. It has been widely used in quantum chemistry, quantum field theory and condensed matter physics. Usually, its error is quantified by the operator norm distance between the ideal evolution operator and the digital evolution operator. However, recently more and more papers discovered that, even in large Trotter step region, the quantity of interest can still be accurately simulated. These robustness phenomena imply a different approach of analyzing TrotterSuzuki formulas. In our previous paper, by analyzing the spectral analysis of the effective Hamiltonian, we successfully established refined estimations of digital errors, and thus improved the circuit complexity of quantum phase estimation and digital adiabatic simulation.

Quantum Algorithms for Classical Sampling Problems
Dominik Wild Max Planck Institute of Quantum Optics
Sampling from classical probability distributions is an important task with applications in a wide range of fields, including computational science, statistical physics, and machine learning. In this seminar, I will present a general strategy of solving sampling problems on a quantum computer. The entire probability distribution is encoded in a quantum state such that a measurement of the state yields an unbiased sample. I will discuss the complexity of preparing such states in the context of several toy models, where a polynomial quantum speedup is achieved. The speedup can be understood in terms of the properties of classical and quantum phase transitions, which establishes a connection between computational complexity and phases of matter. To conclude, I will comment on the prospects of applying this approach to challenging, realworld tasks.

Contracting Arbitrary Tensor Networks: Approximate and Exact Approach with Applications in Graphical Models and Quantum Circuit Simulations
Feng Pan Perimeter Institute for Theoretical Physics
Tensor network algorithms are numerical tools widely used in physical research. But traditionally they are only applied to lattice systems with specific structure. In this talk, tensor network algorithms to deal with physical systems with arbitrary topology will be discussed. Theoretical framework will firstly be constructed to analyze the difficulty of contracting an arbitrary tensor network. Then both approximate and exact contraction approaches will be involved according to computational tasks of interest. Finally two applications, one in graphical models and the other in quantum circuit simulations, will be introduced to demonstrate the performance and potential of arbitrary tensor network algorithms.

The Markov gap for geometric reflected entropy
Jonathan Sorce Stanford University
This talk concerns the "Markov gap," a tripartiteentanglement measure with a simple geometric dual in holographic quantum gravity. I will prove a new inequality constraining the Markov gap of classical states in quantum gravity, and interpret this inequality as a lesson about multipartite entanglement in holography. I will also speculate about signatures of the inequality in nonholographic field theories, and conjecture a new universal entanglement feature of twodimensional CFTs.
Zoom Link: https://pitp.zoom.us/j/98327637522?pwd=TUJOQ0d1aU5Gc0RLTlJLd3B3Ty9LUT09 
Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
Charles Cao University of Maryland
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal nonClifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as nonstabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework's range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct nontrivial codes. These examples include the toric code and its variants, a holographic code with transversal nonClifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d BaconShor code after "dualizing" its tensor network encoding map.

Exponential Error Suppression for NearTerm Quantum Devices
Balint Koczor University of Oxford
Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediatescale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. We take n independently prepared circuit outputs to create a state whose symmetries prevent errors from contributing bias to the expected value. The approach is very well suited for current and nearterm quantum devices as it is modular in the main computation and requires only a shallow circuit that bridges the n copies immediately prior to measurement. Using no more than four circuit copies, we confirm error suppression below 10−6 for circuits consisting of several hundred noisy gates (2qubit gate error 0.5%) in numerical simulations validating our approach. This talk is based on [B. Koczor, Phys. Rev. X 11, 031057] and [B. Koczor, New J. Phys. (accepted), arXiv:2104.00608].
Zoom Link: https://pitp.zoom.us/j/91654758635?pwd=TEtPMmZMNGZya1JOc05KbGt6OUpjdz09