Quantum Physics

Quantum position verification (QPV) was first introduced, under the name quantum tagging, in a patent filed in 2004. It was first discussed in the academic literature in 2009-10. The schemes proposed to that point were shown to be breakable by teleportation attacks in 2010, and a general no-go theorem showing all schemes in this class are breakable was subsequently proved. However, in an alternative standard cryptographic security scenario, in which the tag is assumed to be able to keep classical data secret, unconditionally secure schemes were presented in 2010. The various terminologies and security scenarios highlight important points whose theoretical and practical implications still remain underexplored. In practice, one normally wants to verify the location of a person or valuable object, not of an easily replaceable tagging device, for at least two reasons: (i) the device itself is not so valuable, (ii) adversaries can easily construct a replacement device and thereby potentially spoof the scheme. This requires physical assumptions about the integrity of the tag and its attachment, and bounds on the speed with which the tag may be displaced or destroyed and replaced. QPV schemes that do not rely on such assumptions are breakable without teleportation or non-local computation attacks. In the other direction, when such significant physical assumptions are necessary, it may generally be reasonable to include tag security among them. In this overview I review the early history of QPV and describe various security scenarios and their potential applications. I give versions of the secure 2010 scheme designed for efficient practical implementation and discuss the frequency, accuracy and security of position verification attainable for these schemes with present technology. I also discuss the implied constraints on what may be attainable for QPV schemes involving real-time quantum measurement and/or quantum information processing.

 

Tsirelson’s problem involves two agents, Alice and Bob, who apply measurements on the same quantum system, K. It asks whether commutation, i.e., independence of whether Alice or Bob measures first, is sufficient to conclude that Alice and Bob’s measurements can be factorised so that they act non-trivially only on distinct subsystems of K. In this talk, I will present a “fully quantum generalisation” of this problem, where Alice and Bob’s measurements are replaced by operations on K that may depend on additional quantum inputs and produce quantum outputs. As for Tsirelson’s original problem, it turns out that commutation indeed implies factorisation, provided that all relevant systems are finite-dimensional.

This is joint work with Ramona Wolf; preprint available at arXiv:2308.05792.

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 Zoom link https://pitp.zoom.us/j/99031410183?pwd=MzVoQXpPSll6bFp1b1g3U2J4U21rZz09

Finding ground states of quantum many-body systems is one of the most important---and one of the most notoriously difficult---problems in physics, both in scientific research and in practical applications.  Indeed, we know from a complexity-theoretic perspective that all methods  (quantum or classical) must necessarily fail to find the ground state efficiently in general. The ground state energy problem is already NP-hard even for classical, frustration-free, local Hamiltonians with constant spectral gap. For general quantum Hamiltonians, the problem becomes QMA-hard.

Nonetheless, as ground state problems are of such importance, and classical algorithms are often successful despite the theoretical exponential worst-case complexity, a number of quantum algorithms for the ground state problem have been proposed and studied. From quantum phase estimation-based methods, to adiabatic state preparation, to dissipative state engineering, to the variation quantum eigensolver (VQE), to quantum/probabilistic imaginary-time evolution (QITE/PITE).

Dissipative state engineering was first introduced in 2009 by Verstraete, Cirac and Wolf and by Kraus et al. However, it only works for the restricted class of frustration-free Hamiltonians.

In this talk, I will show how to construct a dissipative state preparation dynamics that provably produces the correct ground state for arbitrary Hamiltonians, including frustrated ones. This leads to a new quantum algorithm for preparing ground states: the Dissipative Quantum Eigensolver (DQE). DQE has a number of interesting advantages over previous ground state preparation algorithms:

• The entire algorithm consists simply of iterating the same set of   simple local measurements repeatedly.
• The expected overlap with the ground state increases monotonically with the length of time this process is allowed to run.
• It converges to the ground state subspace unconditionally, without any assumptions on or prior information about the Hamiltonian (such as spectral gap or ground state energy bound).
• The algorithm does not require any variational optimisation over parameters.
• It is often able to find the ground state in low circuit depth in practice.
• It has a simple implementation on certain types of quantum hardware, in particular photonic quantum computers.
• It is immune to errors in the initial state.
• It is inherently fault-resilient, without incurring any fault-tolerance overhead. I.e.\ not only is it resilient to errors on the quantum state, but also to faulty implementations of the algorithm itself; the overlap of the output with the ground state subspace degrades smoothly with the error rate, independent of the total run-time.

I give a mathematically rigorous analysis of the DQE algorithm and proofs of all the above properties, using non-commutative generalisations of methods from classical probability theory.

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Zoom link https://pitp.zoom.us/j/96022753460?pwd=SWlUVkVta1RyY3dsWUJWckRqOHdNdz09