Quantum Information

We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals A, B and C on a spatial slice, where we can view these quantities as measuring correlations between A and C that are not mediated by the region B that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where A and C are close using the OPE expansion. We also compare the mutual information between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.

We describe supersymmetric SYK models which display a scaling similarity at low temperatures, rather than the usual conformal behavior. We discuss the large N equations, which were studied previously as uncontrolled approximations to other models. We also present a picture for the physics of the model which suggest that the relevant low energy degrees of freedom are almost free. We also searched for a spin glass phase but we found no replica symmetry breaking solutions.

We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) horizon, the mere presence of the horizon will eventually destroy the coherence of the superposition in a finite time. This occurs because, in effect, the long-range fields sourced by the superposition register on the black hole horizon which forces the emission of entangling “soft gravitons/photons” through the horizon. This enables the horizon to harvest “which path” information about the superposition. We provide estimates of the decoherence time for such quantum superpositions in the presence of a black hole and cosmological horizon. Finally, we further sharpen and generalize this mechanism by recasting the gedankenexperiment in the language of (approximate) quantum error correction. This yields a complementary picture where the decoherence is due to an “eavesdropper” (Eve) in the black hole attempting to obtain "which path" information by measuring the long-range fields of the superposed body. We explicitly compute the quantum fidelity to determine the amount of information such an Eve can obtain and show, by the information-disturbance tradeoff, a direct relationship between the information gained by Eve and the decoherence of the superposition in the exterior. In particular, we show that the decoherence of the superposition corresponds to the "optimal" measurement made by Eve in the black hole interior.

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II infinity factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit.

We argue that generic local subregions in semiclassical quantum gravity are associated with von Neumann algebras of type II_1, extending recent work by Chandrasekaran et.al. beyond subregions bounded by Killing horizons. The subregion algebra arises as a crossed product of the type III_1 algebra of quantum fields in the subregion by the flow generated by a gravitational constraint operator. We conjecture that this flow agrees with the vacuum modular flow sufficiently well to conclude that the resulting algebra is type II_\infty, which projects to a type II_1 algebra after imposing a positive energy condition. The entropy of semiclassical states on this algebra can be computed and shown to agree with the generalized entropy by appealing to a first law of local subregions. The existence of a maximal entropy state for the type II_1 algebra is further shown to imply a version of Jacobson’s entanglement equilibrium hypothesis. We discuss other applications of this construction to quantum gravity and holography, including the quantum extremal surface prescription and the quantum focusing conjecture.

In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

Systems in thermal equilibrium at non-zero temperature are described by their Gibbs state. For classical many-body systems, the Metropolis-Hastings algorithm gives a Markov process with a local update rule that samples from the Gibbs distribution. For quantum systems, sampling from the Gibbs state is significantly more challenging. Many algorithms have been proposed, but these are more complex than the simple local update rule of classical Metropolis sampling, requiring non-trivial quantum algorithms such as phase estimation as a subroutine.

Here, we show that a dissipative quantum algorithm with a simple, local update rule is able to sample from the quantum Gibbs state. In contrast to the classical case, the quantum Gibbs state is not generated by converging to the fixed point of a Markov process, but by the states generated at the stopping time of a conditionally stopped process. This gives a new answer to the long-sought-after quantum analogue of Metropolis sampling. Compared to previous quantum Gibbs sampling algorithms, the local update rule of the process has a simple implementation, which may make it more amenable to near-term implementation on suitable quantum hardware. We also show how this can be used to estimate partition functions using the stopping statistics of an ensemble of runs of the dissipative Gibbs sampler. This dissipative Gibbs sampler works for arbitrary quantum Hamiltonians, without any assumptions on or knowledge of its properties, and comes with certifiable precision and run-time bounds.
This talk is based on 2304.04526, completed in collaboration with Jan-Lukas Bosse and Toby Cubitt.

Zoom Link: https://pitp.zoom.us/j/96780945341?pwd=NG9SUjE4SkVia3VqazNXUFNUamhRdz09

 

 

In this talk, I will present three algorithms that address distinct variants of the problem of testing quantum states. First, I will discuss the problem of statistically testing whether an unknown quantum state is a matrix product state of certain bond dimension or it is far from all such states. Next, I will demonstrate a method for testing whether a bipartite quantum state, shared between two parties, corresponds to the ground state of a given gapped local Hamiltonian. Finally, I will present a scheme for verifying that a machine learning model of an unknown quantum state has high overlap with the actual state.

Zoom Link: https://pitp.zoom.us/j/99250127489?pwd=UCtXUi9zMzJZamppT29DbWtJcWU3Zz09

We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local reversibility in context of measurement circuits, which allows us to treat finite depth measurement circuits on a similar footing to finite depth unitary circuits. In contrast to the unitary case, a finite depth locally reversible measurement sequence can implement a translation in one dimension. A locally reversible measurement sequence in two dimensions may also induce a flow of logical information along the boundary. We introduce "measurement quantum cellular automata" which unifies these ideas and define an index in one dimension to characterize the flow of logical operators. We find a Z_2 bulk invariant for Floquet topological codes which indicates an obstruction to having a trivial boundary. We prove that the Hastings-Haah honeycomb code belong to a class with such obstruction, which means that any boundary must have either non-local dynamics, period doubled, or admits boundary flow of quantum information.

Zoom Link: https://pitp.zoom.us/j/96083249406?pwd=MnhYbTEyU05ybVdyUlE3UGZrdEhPdz09

A key subroutine in quantum computing, especially in quantum simulation, is to prepare thermal states or ground states of Hamiltonians. Today, I will talk about a new family of quantum algorithms for this task. Physically, our algorithms distill the essence of system-bath interaction by simulating an effective Lindbladian; computationally, our algorithms are quantum analogs of classical Markov chain Monte Carlo sampling. Given the ubiquity of thermodynamics and the triumph of classical Monte Carlo methods, we anticipate that quantum thermal state preparation will become indispensable in quantum computing. 

Joint work with Michael J. Kastoryano, Fernando G.S.L. Brandão, and András Gilyén. https://arxiv.org/abs/2303.18224 

Zoom Link: https://pitp.zoom.us/j/91641127738?pwd=cExPM3Bvd3BaYnJYS0U0UlBiVTJ0QT09

I will introduce a family of dual-unitary circuits in 1+1 dimensions which are invariant under the joint action of Lorentz and scale transformations. With the same dual unitaries I will construct tensor-network states for this 1+1 model and interpret them as spatial slices of curved 2+1 discrete geometries. These tensor-network states satisfy the Ryu-Takayanagi conjecture outside event horizons, but the geometry of the network is also well defined inside the horizon. The dynamics of the circuit induces a natural dynamics on these geometries which reproduces GR phenomena like the gravitational redshift, the formation of black holes and the growth of their throat.

Zoom link:  https://pitp.zoom.us/j/92034586204?pwd=eEo0NzVjeFkxWVJnY0hjOUhodXNWdz09

We study the behavior of errors in the quantum simulation of  spin systems with long-range multibody interactions resulting from the  Trotter-Suzuki decomposition of the time evolution operator. We  identify a regime where the Floquet operator underlying the Trotter  decomposition undergoes sharp changes even for small variations in the  simulation step size. This results in a time evolution operator that  is very different from the dynamics generated by the targeted  Hamiltonian, which leads to a proliferation of errors in the quantum  simulation. These regions of sharp change in the Floquet operator,  referred to as structural instability regions, appear typically at  intermediate Trotter step sizes and in the weakly interacting regime,  and are thus complementary to recently revealed quantum chaotic  regimes of the Trotterized evolution [L. M. Sieberer et al. npj  Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv.  5, eaau8342 (2019)]. We characterize these structural instability  regimes in p-spin models, transverse-field Ising models with  all-to-all p-body interactions, and analytically predict their  occurrence based on unitary perturbation theory. We further show that  the effective Hamiltonian associated with the Trotter decomposition of  the unitary time-evolution operator, when the Trotter step size is  chosen to be in the structural instability region, is very different  from the target Hamiltonian, which explains the large errors that can  occur in the simulation in the regions of instability. These results  have implications for the reliability of near-term gate based quantum  simulators, and reveal an important interplay between errors and the  physical properties of the system being simulated.

Zoom link:  https://pitp.zoom.us/j/92045582127?pwd=WDUxcnlIeXdnVWM3WGJoSFVMNDE2dz09