Sevag Gharibian

Georgios Karaiskos, Dorian Rudolph, Johannes Jakob Meyer et al.

Classical shadows are succinct classical representations of quantum states which allow one to encode a set of properties P of a quantum state rho, while only requiring measurements on logarithmically many copies of rho in the size of P. In this work, we initiate the study of verification of classical shadows, denoted classical shadow validity (CSV), from the perspective of computational complexity, which asks: Given a classical shadow S, how hard is it to verify that S predicts the measurement statistics of a quantum state? We first show that even for the elegantly simple classical shadow protocol of [Huang, Kueng, Preskill, Nature Physics 2020] utilizing local Clifford measurements, CSV is QMA-complete. This hardness continues to hold for the high-dimensional extension of said protocol due to [Mao, Yi, and Zhu, PRL 2025]. In contrast, we show that for the HKP and MYZ protocols utilizing global Clifford measurements, CSV can be "dequantized" for low-Frobenius norm observables, i.e., solved in randomized poly-time with standard sampling assumptions. Among other results, we also show that CSV for exponentially many observables is complete for a quantum generalization of the second level of the polynomial hierarchy, yielding the first natural complete problem for such a class.

Sevag Gharibian, Jonas Kamminga

Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of estimating ground state entanglement, and more generally entropy estimation for low energy states and Gibbs states. We find, in particular, that the classes qq-QAM [Kobayashi, le Gall, Nishimura, SICOMP 2019] (a quantum analogue of public-coin AM) and QMA(2) (QMA with unentangled proofs) play a crucial role for such problems, showing: (1) Detecting a high-entanglement ground state is qq-QAM-complete, (2) computing an additive error approximation to the Helmholtz free energy (equivalently, a multiplicative error approximation to the partition function) is in qq-QAM, (3) detecting a low-entanglement ground state is QMA(2)-hard, and (4) detecting low energy states which are close to product states can range from QMA-complete to QMA(2)-complete. Our results make progress on an open question of [Bravyi, Chowdhury, Gosset and Wocjan, Nature Physics 2022] on free energy, and yield the first QMA(2)-complete Hamiltonian problem using local Hamiltonians (cf. the sparse QMA(2)-complete Hamiltonian problem of [Chailloux, Sattath, CCC 2012]).

Harry Buhrman, Sevag Gharibian, Zeph Landau et al.

We present an extremely simple polynomial-space exponential-time $(1-\varepsilon)$-approximation algorithm for MAX-k-SAT that is (slightly) faster than the previous known polynomial-space $(1-\varepsilon)$-approximation algorithms by Hirsch (Discrete Applied Mathematics, 2003) and Escoffier, Paschos and Tourniaire (Theoretical Computer Science, 2014). Our algorithm repeatedly samples an assignment uniformly at random until finding an assignment that satisfies a large enough fraction of clauses. Surprisingly, we can show the efficiency of this simpler approach by proving that in any instance of MAX-k-SAT (or more generally any instance of MAXCSP), an exponential number of assignments satisfy a fraction of clauses close to the optimal value.

Anne Broadbent, Sevag Gharibian, Hong-Sheng Zhou

A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we show how to use quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. This is in sharp contrast with the classical case, where stateless hardware tokens alone cannot yield OTMs. In addition, our scheme is technologically simple. We prove security in the quantum universal composability framework, employing semi-definite programming results of Molina, Vidick and Watrous [TQC 2013] and combinatorial techniques of Pastawski et al. [Proc. Natl. Acad. Sci. 2012].