Preferred Quasiclassical Structures in General Many-Body Systems

November 30 - December 2, 2021

NTT Research, Physics & Informatics Laboratories, Sunnyvale, CA

Organizers: Jess Riedel, NTT Research, and Daniel Ranard, MIT

Large quantum many-body systems often admit an effective classical description for certain preferred observables. These “quasiclassical” variables are decohered by the remaining degrees of freedom, leading to the quantum-classical transition and the objectivity of macroscopic events.

Although some characteristic features are known, the quasiclassical variables need not be manifest in the microscopic Hamiltonian and no general principle is known for reliably identifying them, nor for reliably identifying closely associated structures like preferred subsystems, bases, consistent histories, or wavefunction branches.

This two-day workshop will focus on developing a better and more abstract understanding of these preferred quasiclassical structures, especially using the tools of condensed matter, quantum information, hydrodynamics, and tensor networks.

We will address questions that include:
  • How do we systematically identify the quasiclassical variables and associated wavefunction branches in a given many-body system?
  • On what timescales will the classical description remain accurate?
  • Is this description unique, or are there alternative descriptions on equal footing?
  • Can classical descriptions be exploited to increase the computational efficiency of numerical simulations?

Participants

Scott Aaronson*
Asir Abrar
Ehud Altman
Charlie Bennett*
Adam Brown
Thibault Chervy
Jordan Cotler*
Edmund Dable-Heath
Sebastian Deffner*^
Adil Gangat
Davide Girolami*
Ryan Hamerly
Markus Hauru*

Cheryne Jonay
Satoshi Kako
Adrian Kent*
Vedika Khemani^
Noah MacAulay
Timothy McKenna
Tamra Nebabu
Fernando Pastawski*^
Hannes Pichler*
Jason Pollack
Xiaolang Qi*^
Djordje Radicevic
Tibor Rakovszky

Simone Rijavec
Ashmeet Singh
Sho Sugiura
Myoung-Gyun Suh
Lenny Susskind*^
Akram Touil
Frank Verstraete
Curt von Keyserlingk
Don Weingarten
Bin Yan*
Mike Zaletel
Wojciech Zurek*
Michael Zwolak*^
*Remote, ^Tentative

Schedule

Tuesday, November 30
  •   7:00pm  Welcome dinner      Faultline Brewing Co, 1235 Oakmead Pkwy
Wednesday, December 1
  •   8:30-  9:00  Breakfast
  •   9:00-  9:20  Jess RiedelDay 1 overview
  •   9:30-10:20  Wojciech Zurek[The predictability sieve]
  • 10:30-11:15  Jason PollackQuantum state reduction: Generalized bipartitions from observables
  • 11:30-12:20  Adrian KentThe quantum reality problem and late-time photon measurements
  • 12:20-  1:00  Discussion Block
  •   1:00-  2:15  Lunch
  •   2:15-  3:00  Ashmeet SinghQuantum mereology: Factorizing hilbert space into subsystems with quasi-classical dynamics
  •   3:20-  3:40  Adam BrownCounting and quantum circuit complexity
  •   3:50-  4:50  Don WeingartenBranching from Complexity
  •   4:50-  5:30  Discussion Block
Thursday, December 2
  •   8:30-  9:00  Breakfast
  •   9:00-  9:20  Dan RanardDay 2 overview
  •   9:40-10:40  Hannes PichlerOptimizing trajectories of many-body Markov processes
  • 11:00-12:00  Curt von KeyserlingkEffects of operator backflow on quantum transport
  • 12:00-12:45  Discussion Block
  • 12:45-  2:00   Lunch
  •   2:00-  2:20   Djordje RadicevicAn explicit lattice-continuum correspondence in quantum theories
  •   2:30-  2:50   Noah MacAulayWavefunction branching in random circuits
  •   3:00-  4:00   Ehud AltmanClassical computation of quantum thermalization dynamics
  •   4:00-  4:45   Discussion Block
  •   
  •   7:00pm         Closing dinner      Agape Grill, 845 Stewart Dr

All events are Pacific Standard Time

Schedule and Abstracts

Tuesday, November 30

Wednesday, December 1

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by "tracing out" part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state reduces given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task, we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse-grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse-grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the 1-D Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity. [1909.12851

I explain why there is a quantum reality problem and why we are motivated to seek precise solutions that are physically natural, respect fundamental symmetries and are empirically confirmable. I discuss a proposal involving late time measurements of photons or other massless particles. I also explain how this and other proposals motivate new types of physical law, involving statistical constraints, that are natural foils against which to test standard cosmological ideas. [1608.04805, 1311.0249]

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. Extensions of this paradigm to include degrees of freedom which do not form a tensor factor of Hilbert space are also discussed. [2005.12938]

We define a version of quantum complexity designed to measure, at any instant of time, the spatial structure of entanglement in a state vector. Decomposition of a state vector into branches is then found by minimizing a linear combination of the mean squared quantum complexity of a candidate set of branches and the corresponding classical entropy of the ensemble of branch weights. In a non-relativistic formulation of this proposal, branching occurs repeatedly over time, with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen randomly according to the Born rule. In a Lorentz covariant version, the real world is a single random draw from the set of branches at asymptotically late time, restored to finite time by sequentially retracing the set of branching events implied by the late time choice. [2105.04545]

Thursday, December 2

We discuss an adaptive stochastic propagator for quantum trajectories, which is designed to give low-entanglement unravelings of the solution of a many-body master equation. [2111.12048]

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by "tracing out" part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state reduces given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task, we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse-grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse-grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the 1-D Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity. [2111.09904]

In the canonical formalism, familiar classical physics arises when the operator algebra in a continuum quantum theory is restricted to an Abelian subalgebra. Continuum quantum theories can, in turn, be understood to arise as universal, low energy regimes of "lattice" quantum theories with Hilbert spaces of finite (but very large) dimension. This understanding is at the core of the modern Wilsonian paradigm. However, no precise, generally applicable method for reducing a lattice theory to its continuum subtheory was ever offered as part of this paradigm. I will explicitly propose one such method, and I will overview some applications: first-principle calculations of operator product expansions and current algebras, a generalization of Noether's theorem to discrete symmetries, and a new approach to rigorously defining continuum quantum theories. [2105.11470, 2105.12147]

The entanglement of a quantum state grows linearly in time during generic unitary evolution, leading to exponential growth of the resources needed for classical computation. On the other hand at long times the only measurable changes in the system are due to slow hydrodynamic transport of conserved quantities. Computing these precisely only requires the knowledge of a finite set of transport coefficients. It is natural to ask if there is an optimal compression of the quantum state, which captures this dynamical information without the need to keep track of the exact state. I will review two methods designed to address this problem. In the second part of the talk I will turn to discuss the distinction between classical and quantum thermalization in monitored systems.

All events are Pacific Standard Time. Click talk title for abstract.

Event Details

Workshop Location

NTT Research Inc.
940 Stewart Dr., Sunnyvale, CA 94085

Hotel Accommodations

Residence Inn by Marriott Sunnyvale Silicon Valley II
1080 Stewart Dr., Sunnyvale, CA 94086

Welcome Dinner

Faultline Brewing Company
1235 Oakmead Pkwy, Sunnyvale, CA 94085

Closing Dinner

Agape Grill
845 Stewart Dr A, Sunnyvale, CA 94085

Expense Reimbursement

Contact Kyoko Ohashi kyoko.ohashi@ntt-research.com

Reading list

Questions? Email workshops@ntt-research.com