Quantum Physics

We develop the theory of quantum scars for quantum fields. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum fields, we find that unstable periodic classical solutions of the field equations imprint themselves in a precise manner on bands of energy eigenfunctions. This indicates a breakdown of thermalization at certain energy scales, in a manner that can be characterized via semiclassics. As an explicit example, we consider time-periodic non-topological solitons in complex scalar field theories. We find that an unstable variant of Q-balls, called Q-clouds, induce quantum scars. Some technical contributions of our work include methods for characterizing moduli spaces of periodic orbits in field theories, which are essential for formulating our quantum scar formula. We further discuss potential connections with quantum many-body scars in Rydberg atom arrays. Based on work in arXiv:2212.01637 with Jordan Cotler.

---

Zoom link https://pitp.zoom.us/j/91572728134?pwd=Q0Jzb0lwQW5VU0ptRnRWL2tOTTdLdz09

Measuring the temperature of your coffee should not change the amount of coffee in your cup. This holds because the operators representing the coffee’s energy and volume commute. The intuitive assumption that conserved quantities, also known as charges, commute, underpins basic physics derivations, like that of the thermal state's form and Onsager coefficients. Yet, operators' failure to commute plays a key role in quantum theory, e.g. underlying uncertainty relations. Lifting this assumption has spawned a growing subfield of quantum many-body physics [1].

How can one argue that charges’ noncommutation caused a result? To isolate the effects of charges’ noncommutation, we created analogous models that differ in whether their charges commute and discovered more entanglement in the noncommuting-charge model [2]. We further introduce noncommuting charges (an SU(2) symmetry) into monitored quantum circuits, circuits with unitary evolutions and mid-circuit projective measurements. Numerically, we find that the SU(2)-symmetric model has a critical phase in place of the area-law phase typically found in these circuits [3]. I will focus on the results from Ref 2 and 3. Time permitting, I'll briefly explain how one can use Lie Algebra theory to build the Hamiltonians necessary for testing the predictions of noncommuting charge physics [4].

[1] Majidy et al. "Noncommuting conserved charges in quantum thermodynamics and beyond." Nat Rev Phys (2023)
[2] Majidy et al. "Non-Abelian symmetry can increase entanglement entropy.” PRB (2023)
[3] Majidy et al. "Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits." PRB (2023)
[4] Yunger Halpern and Majidy “How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics” npj QI (2022)

---

Zoom link https://pitp.zoom.us/j/97193579200?pwd=MkdmbWo1S2lUcUZtUFpORk5VbnFBdz09

Squeezing has proven to be a powerful tool for suppressing noise in bosonic quantum sensing and communication. However, it is fragile and the resulting quantum advantage is extremely vulnerable to loss and noise. In this seminar, I will first overview the method of formulating loss and noise and thereby characterizing the practical quantum advantages. Then I will present our recent progress on entanglement-assisted protocols using two-mode squeezed-vacuum states, which are robust to loss and noise. I will demonstrate the quantum advantages in three scenarios: dark matter search, absorption spectroscopy, and telecommunication. Notably, we derived the ultimate precision limit of noise sensing and dark matter search. As a result, we found the two-mode squeezed vacuum is the optimal quantum source for dark matter search at the limit of strong squeezing. This optimality extends to entanglement-assisted communication. In each of the presented scenarios, entanglement-assisted protocols yield quantum advantages of orders of magnitude over classical protocols.

---

Zoom link https://pitp.zoom.us/j/94873478582?pwd=c1dxNEVtMGx0ZU4vZjRvTU5OakZoUT09

Network nonlocality, and more specifically, triangle network nonlocality, is a basic feature of modern causal modelling when going beyond Bell scenarios. However, despite the apparent simplicity of the problems one may formulate, relatively little is known due to the hardness of certifying nonlocality in networks. In this talk, I will describe a motivating example of a quantum triangle distribution, the Elegant Joint Measurement due to Nicolas Gisin, that is strongly believed to be nonlocal even in the presence of experimental noise. I will then present the ongoing effort to produce a computer-assisted proof of nonlocality for this distribution, thereby developing a toolkit to tackle general nonlocality problems. This effort is based on the inflation technique for causal inference, but taken to higher levels than what was generally considered tractable. This is made possible by a number of optimization techniques, involving symmetry reductions, branch-and-bound optimization, and most importantly, the use of a Frank-Wolfe algorithm to bypass the need to call a standard linear program solver.

---

Zoom link https://pitp.zoom.us/j/97499052021?pwd=R1EyU2pmc1hFSzJ1UEpJQ1h0RnQzdz09

In the usual operational picture, operations are represented by boxes having inputs and outputs. Further, we usually consider the causally simple case where the inputs are prior to the outputs for each such operation. In this talk (motivated by an attempt to formulate an operational probabilistic field theory) I will consider what I call the "causally complex" situation. Operations are represented by circles. These circles have wires going in and out. Each such wire can represent an input and an output. Further, each operation will have a causal diagram associated with it. The causal structure can be more complicated than the simple case. These circles can be joined together to create new operations. I will discuss conditions on these causally complex operations so that we have positivity (probabilities are non-negative) and causality (to be understood in a time symmetric manner). I will also discuss how these properties compose when we join causally complex operations. Causally complex operations are related to objects in the causaloid formalism as well as to quantum combs.

---

Zoom link https://pitp.zoom.us/j/99425886198?pwd=ODR0VVFzQUJHeER4OVJ2cEo3cVdDQT09

We will present a teleportation protocol which uses the properties of superoscillatory wavefunctions. Then we will briefly introduce a different protocol, the port based teleportation. We will use it to study teleportation over infinitesimally small distances, where the vacuum of a quantum field serves as the source of entanglement. We find that the resulting motion is equivalent to a quantum teleportation-induced Brownian motion. Purifying the interactions, from measurements to unitary operations, leads to motion described by Schrodinger’s equation. Therefore, we find that the notions of teleportation and continuous quantum and classical motion are unified in this sense.

--- 

Zoom link https://pitp.zoom.us/j/93504138534?pwd=VUFPSXpRd2g0TVNxVTNlY3Rxa1ZjUT09

Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this talk, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that causality of a radially propagating excitation should be an induced one originating from a fictitious boundary behind the brane/cutoff surface. We present its consistency by checking the connected wedge theorem supported from quantum cryptography and (strong) subadditivity of holographic entanglement entropies. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation in our picture. This talk is based on 2308.00739 [10.1007/JHEP10(2023)104] with Beni Yoshida.

---

Zoom link https://pitp.zoom.us/j/98252951858?pwd=RVNZUjNVM2JkZXRlSXJVbEZ6cUpsUT09

Obtaining a description of cosmology is a central open problem in holography. Studying simple models can help us gain insight on the generic properties of holographic cosmologies. In this talk I will describe the construction of entangled microstates of a pair of holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement of two auxiliary AdS spacetimes. In generic settings, the cosmology is an entanglement island contained in the entanglement wedge of one of the two CFTs. I will then describe the properties of the non-isometric bulk-to-boundary encoding map and comment on an explicit, state-dependent boundary representation of operators acting on the cosmology. Finally, if time allows, I will argue for a non-isometric to approximately-isometric transition of the encoding of "simple" cosmological states as a function of the bulk entanglement, with tensor network toy models of the setup as a guide.

---

Zoom link https://pitp.zoom.us/j/93483219872?pwd=TGpJVVlaNDVGWTN5ZHpkTHp6a2hTZz09

Out of the many lessons quantum mechanics seems to teach us, one is that it seems there are things we cannot experimentally have access to. There is, indeed, a fundamental limit to our ability to experimentally explore the world. In this work we accept this lesson as a fact and we build a general theory based on this principle. We start by assuming the existence of statements whose truth value is not experimentally accessible. That is, there is no way, not even in theory, to directly test if these statements are true or false. We further develop a theory in which experimentally accessible statements are a union of a fixed minimum number of inaccessible statements. For example, the value of truth of the statements a and b is not accessible, but the value of truth of the statement “a or b" is accessible. We do not directly assume probability theory, we exclusively define experimentally accessible and inaccessible statements and build on these notions using the rules of classical logic. We find that an interesting structure emerges. Developing this theory, we relax the logical structure, naturally obtaining a derivation of a constrained quasi-probabilistic theory rich in structure that we name theory of inaccessible information. Surprisingly, the simplest model of theory of inaccessible information is the qubit in quantum mechanics. Along the path for the construction of this theory, we characterise and study a family of multiplicative information measures that we call inaccessibility measures. arXiv:https://arxiv.org/abs/2305.05734

---

Zoom link https://pitp.zoom.us/j/91350754706?pwd=V1dVdGM3Zk9MNkp4VlpCYUoxbXg3UT09

Classical simulation techniques are widely used in quantum computation and condensed matter physics. In this talk I will describe algorithms for classically simulating measurement of an n-qubit quantum state in the standard basis, that is, sampling a bit string from the probability distribution determined by the Born rule. Our algorithms reduce the sampling task (known as weak simulation) to computing poly(n) amplitudes of n-qubit states (strong simulation). Two classes of quantum states are considered: output states of polynomial-size quantum circuits and ground states of local Hamiltonians with an inverse polynomial energy gap. We show that our algorithm can significantly accelerate quantum circuit simulations based on tensor network contraction and low-rank stabilizer decompositions. To sample ground state probability distributions we employ the fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. 

Joint work with Giuseppe Carleo, David Gosset, and Yinchen Liu

---

Zoom link https://pitp.zoom.us/j/93297869296?pwd=TVpRdVJmU3lWZjVQM3NNKzBucVVRUT09

We report a deterministic and exact protocol to reverse any unknown qubit-unitary and qubit-encoding isometry operations. To avoid known no-go results on universal deterministic exact unitary inversion, we consider the most general class of protocols transforming unknown unitary operations within the quantum circuit model, where the input unitary operation is called multiple times in sequence and fixed quantum circuits are inserted between the calls. In the proposed protocol, the input qubit-unitary operation is called 4 times to achieve the inverse operation, and the output state in an auxiliary system can be reused as a catalyst state in another run of the unitary inversion. This protocol only applies only for qubit-unitary operations, but we extend this protocol to any qubit-encoding isometry operations. We also present the simplification of the semidefinite programming for searching the optimal deterministic unitary inversion protocol for an arbitrary dimension presented by M. T. Quintino and D. Ebler [Quantum 6, 679 (2022)]. We show a method to reduce the large search space representing all possible protocols, which provides a useful tool for analyzing higher-order quantum transformations for unitary operations.

---

Zoom link https://pitp.zoom.us/j/92900413520?pwd=a1JqU1IzMVdSRGQreWJIbEFCT2hWUT09

Quantum systems typically reach thermal equilibrium rather quickly when coupled to an external thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However, the gap, by itself, does not always yield a reasonable estimate for the thermalization time in many-body systems: without further structure, a uniform lower bound on it only constraints the thermalization time to be polynomially growing with system size. In this talk, we will discuss that for all 2-local models with commuting Hamiltonians, the thermalization time that one can estimate from the gap is in fact much smaller than direct estimates suggest: at most logarithmic in the system size. This yields the so-called rapid mixing of dissipative dynamics. We will show this result by proving that a finite gap directly implies a lower bound on the modified logarithmic Sobolev inequality (MLSI) for the class of models we consider. The result is particularly relevant for 1D systems, for which we can prove rapid thermalization with a constant decay rate, giving a qualitative improvement over all previous results. It also applies to hypercubic lattices, graphs with exponential growth rate, and trees with sufficiently fast decaying correlations in the Gibbs state. This has consequences for the rate of thermalization towards Gibbs states, and also for their relevant Wasserstein distances and transportation cost inequalities.

---

Zoom link https://pitp.zoom.us/j/91315419731?pwd=TGpFTjlHWEJZVWZkdTh6bDFKMjhQZz09