The State Hidden Subgroup Problem and How to Efficiently Locate Unentanglement
We introduce the “hidden cut problem:” given as input which is product across an unknown bipartition, the goal is to learn precisely where the state is unentangled, i.e. to find the hidden cut. We give a polynomial time quantum algorithm for the hidden cut problem, which consumes O(n/ε^2) many copies of the state, and show that this asymptotic is optimal. In the special case of Haar-random states, the circuits involved are of merely constant depth, which could prove relevant to experimental implementations.
Optimization by Decoded Quantum Interferometry
In this talk I will describe Decoded Quantum Interferometry (DQI), a quantum algorithm for reducing classical optimization problems to classical decoding problems by exploiting structure in the Fourier spectrum of the objective function. (See: https://arxiv.org/abs/2408.08292.) For a regression problem called optimal polynomial intersection, which has been previously studied in the contexts of coding theory and cryptanalysis, we believe DQI achieves an exponential quantum speedup.
Quantum Sensing, with Applications to Fundamental Physics
Quantum sensing leverages the principles of quantum mechanics to provide ``quantum-enhanced'' measurement sensitivity, thereby amplifying our ability to observe interesting physical phenomena. It employs a rich arsenal of techniques, including squeezing, photon counting, entanglement assistance, and distributed quantum sensing to achieve unprecedented sensitivity.
A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire
Aaronson, Atia, and Susskind established that swapping quantum states |ψ〉 and |ϕ〉 is computationally equivalent to distinguishing their superpositions |ψ〉 ± |ϕ〉. We extend this to a general duality principle: manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. Formally, for any group, implementing a unitary representation is computationally equivalent to Fourier subspace extraction from its irreducible representations.
Quantum Simulation of Spin-Boson Models with Structure Bath
The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems that describe many dissipative processes in physical, chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models, by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons, respectively.
Entanglement witness for combined atom interferometer-mechanical oscillator system
D. Carney et al. [https://doi.org/10.1103/PRXQuantum.2.030330] suggest the use of a trapped atom interferometer combined with a mechanical oscillator to test certain theories combining quantum mechanics with gravity. We construct an entanglement witness applicable to the stated interferometer-oscillator setup. We also investigate the effects of atomic dephasing and thermal noise on the practical use of this entanglement witness in an experimental implementation of such a system.
Quantum complexity in many-body physics: random circuits and thermodynamics
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. I will discuss two approaches to better understand the role of quantum complexity in many-body physics. First, we'll consider random circuits, a model for chaotic dynamics. In such circuits, the quantum complexity grows linearly until it saturates at a value exponential in the system size.
Instability of steady-state mixed symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
We address the question of whether open quantum system dynamics which host mixed symmetry-protected topological (SPT) states as steady states continue to do so after introducing symmetric perturbations. In particular, we discuss the characteristics of the decohered cluster state --- a mixed SPT protected by a combined strong and weak symmetry --- and construct a parent Lindbladian which hosts it as a steady state. The parent Lindbladian can be mapped onto reaction-diffusion dynamics, which is exactly solvable, even in the presence of certain perturbations.
Polynomial-Time Classical Simulation of Noisy IQP Circuits with Constant Depth
Abstract: Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, whose depth is greater than a critical O(1)threshold, the output distribution can be efficiently sampled by a classical computer.
Order-by-disorder in the antiferromagnetic J1-J2-J3 transverse-field Ising model on the ruby lattice
Extensively degenerate ground-state spaces due to frustration pose a formidable resource for emergent quantum phenomena. Perturbing extensively degenerate ground-state spaces may result in several distinct scenarios lifting the ground-state degeneracy. First, an infinitesimal perturbation can lead to a symmetry-broken order (order-by-disorder) or second the perturbation can result in a symmetry-unbroken phase (disorder-by-disorder), which can be either trivial or an exotic quantum spin liquid.