Quantum Information

Constraint satisfaction problems are known to always be "easy" or "hard", in the sense of being either solvable in P or being NP-complete, with no intermediate difficulty levels. The quantum analog of constraint problems, frustration-free Hamiltonians, are known to exhibit at least two more levels of complexity: QMA (for arbitrary local Hamiltonians) and MA (for stoquastic Hamiltonians). Wondering if other complexity classes can occur, we answer in the affirmative: there are interactions which can be freely arranged on qubits in any arrangement, such that the resulting frustration problem is BQP-complete, and captures exactly the difficulty of quantum computation. Simple modifications of this construction show that quantum constraint problems can be complete for QCMA and BPP as well. Based on https://arxiv.org/abs/2101.08381

Optical astronomical imaging looks for better imaging quality in extreme cases of weak and subdiffraction limits. I focus on the quantum enhancement of astronomical interferometric imaging, including its fundamental limit and practical issues. For the fundamental aspects, I ignore any resource limit and noise and consider the ideal imaging problems. I show that the resolution limit can be enhanced with more carefully chosen measurement strategies and the general imaging quality can be enhanced by postprocessing the stellar photons with a quantum computer. For the practical aspects, I try to overcome the transmission loss suffered by interferometric imaging using quantum network, consider the possibility to implement a local scheme with better performance, and discuss the feasibility of decomposing thermal states into temporally localized pulses.

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics.

Unscrambling this information is possible given perfect knowledge of the scrambler [ArXiv: 1710.03363].

We show that one can retrieve the scrambled information without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Surprisingly, complex quantum scramblers admit Clifford decoders: the salient properties of a scrambling unitary can be efficiently described even if exponentially complex, as long as it is not fully chaotic. This is possible because all the redundant complexity can be described as an entropy, and for non-chaotic black holes can be efficiently pushed away, just like in a refrigerator. This entropy is not due to thermal fluctuations but to the non-stabilizer behavior of the scrambler.

A large class of Λ < 0 cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

This talk is based on 2212.00050.

Zoom link:  https://pitp.zoom.us/j/93499736007?pwd=Qmw5cmZERUN3UmtwTzdKcEdXejJ5UT09

Typicality, the feature that almost any microstate living in the microcanonical subspace cannot be locally distinguished from a thermal ensemble, lies at the fundamental part of statistical physics. However, one may wonder if there exists a sufficient amount of orthogonal atypical states to account for the whole entropy. 
In this talk, we show that, in some physical systems, there exists a sufficient amount of certain orthogonal atypical states to account for the leading order of the entropy in the following two scenarios, by finding proper upper bounds of the entanglement of formation (EoF) for each case and applying other techniques from quantum information theory. 
In the first scenario, the physical system under consideration is AdS black holes at the semiclassical limit G_N —> 0. In this case, microcanonical subspace is the subspace formed by the black hole microstates, and typical states are usually considered to have a smooth horizon as well as the black hole interior. We consider a class of atypical states called disentangled states which have large entanglement deficits compared to typical states such that they cannot have smooth horizons. In this scenario, we use a geometric quantity called entanglement wedge cross section to give upper bounds to EoF. 
In the second scenario, we consider generic quantum many-body systems with short-ranged interactions at the standard thermodynamic limit V —> ∞. In this case, it is known that typical microstates have volume law entanglement. We consider area-law entangled microstates as atypical states. We use reflected entropy to give upper bounds to EoF. 
We will also discuss the relations of our results with the additivity conjectures and atypical black hole microstate counting. 
This talk is based on 2211.11787. 

Zoom link:  https://pitp.zoom.us/j/94823687961?pwd=V3QrSjUrTklheG1iU0RsckwzQmRTUT09

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09

We give a new definition of self-testing for correlations in terms of states on C*-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed under submodels and direct sums, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Mancinska and Kaniewski. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.

Zoom link: https://pitp.zoom.us/j/95783943431?pwd=SDFyQVVZR1d4WlVNSDZ4OENzSmJQUT09

Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.

Joint work with Dominik S. Wild (arXiv:2210.11490)

Zoom link:  https://pitp.zoom.us/j/97166113711?pwd=UEg4NnJlQkkxQXFnN2xXYTBxS001Zz09

We present broadly applicable nonperturbative results on the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitary operators, in finite-dimensional Hilbert spaces. To this end, we decompose these operations into elementary 1-parameter processes in which the eigenvalues move similarly to the spheres in Newton's cradle. As special cases, we recover level repulsion and Cauchy interlacing. We discuss two examples of applications. Applied to adiabatic quantum computing, we obtain new tools to relate algorithmic complexity to computational slowdown through gap narrowing. Applied to information theory, we obtain a generalization of Shannon sampling theory, the theory that establishes the equivalence of continuous and discrete representations of information. The new generalization of Shannon sampling applies to signals of varying information density and finite length.

Zoom link: https://pitp.zoom.us/j/94120657832?pwd=SmpsWFhhVCtyeXM3a0pVQU9lMGFLdz09

We revisit the problem of how interactions emerge in quantum gravity. Namely, we show that bulk scattering of multiple particles in the AdS space requires multipartite entanglement on the boundary. This statement can be proven by two totally different methods, 1) general relativity and 2) quantum cryptographic argument. Furthermore, we argue that interactions among particles in the scattering event emerge from the mechanism of entanglement-assisted quantum error-correcting codes (EAQECCs) which utilize pre-existing multipartite entanglement in CFT. We also propose a concrete protocol to implement a certain class of multi-partite unitary interactions by using transversal logical operators of quantum codes. This talk is based on a (very) recent work with Alex May and Jonathan Sorce.

Zoom Link: https://pitp.zoom.us/j/91349028320?pwd=TGF2Q2ZNdTZtZGxkQ0NiMURLdW5Zdz09

The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. Indeed, the study of quantum phase transitions has formed a central part of 20th and 21st Century physics. We examine the complexity and computability of determining the phase diagram of a general Hamiltonian. We show that in the worst case it is uncomputable and in more restricted cases, where the Hamiltonian is “better behaved”, it remains computationally intractable even for a quantum computer. Finally, we take a look at the relations between the Renormalization Group and uncomputable Hamiltonians.

Zoom Link: https://pitp.zoom.us/j/96048987715?pwd=WGtwWk1SUnFsanNIVTZVYjNmbTh3Zz09