Cross-Platform Verification of Intermediate Scale Quantum Devices with Randomized Measurements
Andreas Elben (Austrian Academy of Sciences)
6049 - 6060 of 20131 Results
Format results
MIP* = RE: Putting Everything Together
Zhengfeng Ji (University of Technology Sydney)The Emperor's New Crown: What Covid-19 Reveals
Brandon Ogbunu Brown University
Self-Testing as an Approach to Certifying Quantum Systems
Andrea Coladangelo (Caltech)Non-Local Binary Games With Noisy Epr States Are Decidable
Penghui Yao (Nanjijng University)Computational Pseudorandomness and Constraints on the Ads/Cft Duality
Adam Bouland (UC Berkeley)Predicting Many Properties of a Quantum System from Very Few Measurements
Richard Kueng (Caltech)
Cross-Platform Verification of Intermediate Scale Quantum Devices with Randomized Measurements
Andreas Elben (Austrian Academy of Sciences)Recently, protocols based on statistical correlations of randomized measurements were developed for probing and verifying engineered quantum many-body systems. After a general introduction in the context of Renyi entropies, I focus in this talk on the cross-platform verification of quantum computers and simulators by means of fidelity measurements. I show how to measure the overlap between (reduced) density matrices, and thus a (mixed-state) fidelity of two quantum states prepared on separate experimental platforms. The protocol requires only local measurements in randomized product bases and classical communication between the devices. As a proof-of-principle, I present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator. To conclude, I will present further applications of randomized measurements for probing quantities beyond standard observables, such as out-of-time-ordered correlation functions.Gravitational edge modes: From Kac-Moody charges to Poincaré networks
Daniele Pranzetti University of Udine
In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand the Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes. This leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. Taking a finite dimensional truncation of this quantization yields states of quantum geometry, dubbed `Poincaré charge networks’, which carry a representation of the 3D diffeomorphism boundary charges on top of the SU(2) fluxes and gauge transformations. This opens the possibility to have for the first time a framework where spatial diffeomorphism are represented at the quantum level. Moreover, our construction leads naturally to the picture that the relevant geometrical degrees of freedom live on boundaries, that their dynamics and the fabric of quantum space itself is encoded into their entanglement, and it is designed to offer a new setting to study the coarse-graining of gravity both at the classical and the quantum levels.
MIP* = RE: Putting Everything Together
Zhengfeng Ji (University of Technology Sydney)In this talk, we will discuss the overall framework for combining many of the techniques established in previous talks of this workshop, including the quantum low-degree test, question reduction by introspection, and answer reduction by the PCP technique. Building upon these techniques, we will construct a recursive gap-preserving compression procedure for quantum two-prover interactive proofs in the normal form and use it to give a proof of MIP* = RE.MIP* = RE Part 2: PCPs and Introspection
John Wright (Caltech)Continuing in the line of MIP* = RE talks, I will discuss two of the tools involved in the result, introspection and PCP composition, which are used to compress large MIP* protocols into small MIP* protocols. I will introduce these tools in the context of prior work with Anand Natarajan showing that MIP* contains NEEXP. Joint work with Zhengfeng Ji, Anand Natarajan, Thomas Vidick, and Henry YuenThe Algebraic Side of MIP* = RE
William Slofstra (University of Waterloo)One of the most exciting consequences of the recent MIP* = RE result by Ji, Natarajan, Vidick, Wright, and Yuen is the resolution of Connes' embedding problem (CEP). Although this problem started out as a casual question about embeddings of von Neumann algebras, it has gained prominence due to its many equivalent and independently interesting formulations in operator theory and beyond. In particular, MIP* = RE resolves the CEP by resolving Tsirelson's problem, an equivalent formulation of CEP involving quantum correlation sets. In this expository talk, I'll try to explain the connection between MIP* = RE and Connes' original problem directly, using the synchronous algebras of Helton, Meyer, Paulsen, and Satriano. I'll also explain how one of the remaining open problems on the algebraic side, the existence of a non-hyperlinear group, is related to the study of variants of MIP* with lower descriptive complexity. This talk will be aimed primarily at physicists and computer scientists, although hopefully there will be something for everyone.Quantum PCPs Meet Derandomization
Alex Bredariol Grilo (CWI & QuSoft)The derandomization of MA, the probabilistic version of NP, is a long standing open question. In this work, we connect this problem to a variant of another major problem: the quantum PCP conjecture. Our connection goes through the surprising quantum characterization of MA by Bravyi and Terhal. They proved the MA-completeness of the problem of deciding whether the groundenergy of a uniform stoquastic local Hamiltonian is zero or inverse polynomial. We show that the gapped version of this problem, i.e. deciding if a given uniform stoquastic local Hamiltonian is frustration-free or has energy at least some constant ϵ, is in NP. Thus, if there exists a gap-amplification procedure for uniform stoquastic Local Hamiltonians (in analogy to the gap amplification procedure for constraint satisfaction problems in the original PCP theorem), then MA = NP (and vice versa). Furthermore, if this gap amplification procedure exhibits some additional (natural) properties, then P = RP. We feel this work opens up a rich set of new directions to explore, which might lead to progress on both quantum PCP and derandomization. Joint work with Dorit Aharonov.The Emperor's New Crown: What Covid-19 Reveals
Brandon Ogbunu Brown University
As of late March 2020, Covid-19 has already secured its status among the most expansive pandemics of the last century. Covid-19 is caused by a coronavirus--SARS-CoV-2--that causes a severe respiratory disease in a fraction of those infected, and is typified by several important features: ability to infect cells of various kinds, contagiousness prior to the onset of symptoms, and a widely varying experience with disease across patient demographics.
In this seminar, I discuss the many lessons that the scientific community has learned from Covid-19, including insight from molecular evolution, cell biology, and epidemiology. I discuss the role of mathematical and computational modeling efforts in understanding the trajectory of the epidemic, and highlight modern findings and potential research questions at the interface of virology and materials science. I will also introduce areas of inquiry that might be of interest to the physics community.
Self-Testing as an Approach to Certifying Quantum Systems
Andrea Coladangelo (Caltech)This will be an introductory talk to self-testing as an approach to certifying quantum systems. The theory of self-testing has developed significantly in recent years. It has found applications to quantum cryptography, to characterizing the complexity of multiprover interactive proofs with entangled provers, as well as connections to foundational questions about quantum correlation sets and entanglement. In this talk, I will discuss the model, the assumptions, some common techniques, applications, and open questions.Non-Local Binary Games With Noisy Epr States Are Decidable
Penghui Yao (Nanjijng University)In this talk, we consider a variant of entangled non-local games where the players are allowed to share infinitely many copies of noisy EPR states. We provide an upper bound on the copies of noisy EPR states for the players to approximate the values of games to an arbitrary precision if the games are binary. The arguments are built on the recent framework about the decidability of the non-interactive simulation of joint distributions with significant extension. A series new techniques on the Fourier analysis on random operator spaces are introduced including a quantum invariance principle and a hypercontractive inequality for random operators. These novel tools are interesting on their own right and may have further applications in quantum information theory and quantum complexity theory.Computational Pseudorandomness and Constraints on the Ads/Cft Duality
Adam Bouland (UC Berkeley)The AdS/CFT correspondence is central to efforts to reconcile gravity and quantum mechanics. It posits a duality between a quantum gravity theory and a quantum mechanical theory, embodied in a map known as the "dictionary" which is a homomorphism between the theories. This dictionary map is not well understood and has only been computed on special, structured instances. In this talk we introduce cryptographic ideas to the study of AdS/CFT, and provide evidence that either the dictionary must be exponentially hard to compute, or else the quantum Extended Church-Turing thesis must be false in quantum gravity. The basic argument is that Susskind's "wormhole growth paradox" requires the dictionary to map a quantity which is hard to compute -- essentially the circuit complexity of the dual quantum state -- to something which is easy to compute in the quantum gravity theory. Therefore the dictionary itself must be hard to compute. Our argument requires creating a custom quantum pseudorandomness construction inspired by block ciphers such as the AES and DES cryptosystems. No background in quantum gravity will be assumed. Based on joint work with Bill Fefferman and Umesh Vazirani.Predicting Many Properties of a Quantum System from Very Few Measurements
Richard Kueng (Caltech)Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods. This is joint work with Hsin-Yuan Huang and John Preskill.