Pradeep Book Physics Class 12 Pdf

[Munir Junker]

Iam mainly interested in applying tools from quantum information to apply to other areas of physics, such as condensed matter and many-body physics of atomic, molecular and optical systems. A major theme of my research is that of computational complexity theory, and what statements we can make about physical systems using complexity theory.

(with Brayden Ware, Dominik Hangleiter, Pradeep Niroula, Bill Fefferman, Alexey V. Gorshkov, and Michael Gullans)

The linear cross-entropy benchmark (XEB) is a popular measure used to estimate the fidelity of a random quantum circuit subject to noise. Recent work has showed that in an $n$-qubit circuit, the XEB approximates the fidelity well in certain regimes of noise strengths, namely if the noise strength per qubit is $\epsilon \ll 1/n$. In this work, we show that as the noise strength increases, the correspondence between the fidelity and the XEB breaks down sharply at a critical value of the noise strength. This critical value depends on the geometry of the random circuit architecture and the choice of gate set.

(with Soumik Ghosh, Dominik Hangleiter, Alexey V. Gorshkov and Bill Fefferman)

Entanglement is necessary, but not always sufficient, for the classical hardness of simulating quantum dynamics. But how much entanglement is needed in general? A quantitative link is missing. Here, we study a family of states, k-regular graph states, and show that both the entanglement and complexity of this class of states are linked. They display transitions as a function of k at the same points. Far from being a coincidence, the entanglement transition can be said to cause the complexity transition.

(with Joseph T. Iosue, Adam Ehrenberg, Dominik Hangleiter, and Alexey V. Gorshkov)

In this work, we derive the bosonic analogue of the Page curve for qudits, namely the average entanglement as a function of subsystem size for a family of random Gaussian states. We also obtain typicality results for the entanglement. The states considered are precisely those that are outputs of Gaussian Boson Sampling (GBS) experiments.

(with Ulysse Chabaud and Saeed Mehraban)

The permanent is a fascinating mathematical object that appears very naturally in linear optics. The permanent vs. the determinant dichotomy is also related to the boson vs. fermion dichotomy in physics. In this work, we build on this connection with linear optics to derive several identities for the permanent, some previously known and some unknown. These include generalisations of the MacMahon master theorem, an identity relating the permanent to the determinant. We also obtain new results for the hardness of simulating linear optics with cat states as input.

(with Mathias Van Regemortel, Oles Shtanko, Luis Pedro Garcia-Pintos, Hossein Dehghani, Alexey Gorshkov, and Mohammad Hafezi)

We looked at a simple system of emitters described by a master equation and considered different unravellings of the same underlying master equation. The different unravellings correspond to different ways of monitoring emitted photons. These unravellings differ with respect to the entanglement they generate. There is a direct relation between the entanglement generated and the complexity of the monitoring scheme, a.k.a. the complexity of the linear optical network through which the photons pass before being measured.

(with Pradeep Niroula, Oles Shtanko, Alexey Gorshkov, Bill Fefferman, and Michael Gullans)

In this work, we considered how fast noisy random circuits converge to the uniform distribution. We prove that for an $n$-qubit system evolving under Haar-random local gates for depth $d$ and subject to local Pauli noise, the average total variation distance from the uniform distribution scales as $\delta \sim \exp[-\tilde\Theta(d)]$. This has implications for proof techniques purporting to show a quantum computational advantage via approximate sampling.

(with Arthur Mehta, Trevor Vincent, Nicolas Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, Dominik Hangleiter, Bill Fefferman, and Ish Dhand)

In this paper, we propose a new architecture we call high-dimensional Gaussian Boson Sampling. We show that this architecture has many of the hardness properties shared by other schemes (such as random circuit sampling) for exhibiting a quantum computational advantage over classical computers. Along the way, we also give improved evidence for the asymptotic hardness of the original Gaussian Boson Sampling proposal. We also give concrete estimates of the classical cost of simulating a finite-size experiment using known algorithms.

(with Andrew Guo, Su-Kuan Chu, Zachary Eldredge, Przemyslaw Bienias, Dhruv Devulapalli, Yuan Su, Andrew Childs, and Alexey Gorshkov)

In this work, we give a way of implementing fast fanout gates that take time at most logarithmic in the system size in a system with power-law interactions. We also devise a new technique based on the Frobenius-norm light-cone developed in arXiv:2001.11509 (paper #9 below) to lower-bound the time required to build the fanout and QFT gates.

(with Oles Shtanko, Paul Julienne, and Alexey Gorshkov)

This work deals with classical simulability of fermionic open systems with quadratic Hamiltonians and quadratic-linear Lindblad operators (corresponding to quartic terms in the Liouvillian). We classify the set of Lindblad operators based on whether they give rise to simulable dynamics or lead to dynamics that are equivalent in computational power to universal quantum computation. This also suggests a scheme for quantum computing with fermionic atoms coupled to an environment.

(with Zachary Eldredge, Leo Zhou, Aniruddha Bapat, James Garrison, Frederic Chong, and Alexey Gorshkov)

This work has the same motivation as arXiv:1808.07876, where we evaluate graphs that prescribe how to wire up different modules of a quantum computer. We deal with the more general case of measurements and feedback here and show a lower bound on the time required to create highly-entangled states on graphs. We also show that this bound can be saturated up to a logarithmic factor in the number of qubits.

(with Venkata Vikram Orre, Elizabeth Goldschmidt, Alexey Gorshkov, Vincenzo Tamma, Mohammad Hafezi, and Sunil Mittal)

In this experimental work, we demonstrate the interference of two and three a priori distinguishable photons by stretching the photons in time to remove their distinguishability. We also give a theoretical outline of why a scaled-up version of this setup may be hard to simulate on a classical computer.

Also see coverage here: Stretched Photons Recover Lost Interference.

(with Anne Nielsen)

Here we derive the analogue of Laughlin wavefunctions for lattices with periodic boundary conditions, and derive various properties of these states, such as the modular S-matrix (which describes the phases picked up by anyons upon braiding them around each other).

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