arXiv subjects

Agi Villanyi

Publications and source records attributed to Agi Villanyi.

4 recordsLinked to original sources

arXiv2026

Towards the Impossibility of Imperfectly Complete Key Agreement in the QROM

We make progress towards the impossibility of imperfectly complete quantum-computation, classical-communication (QCCC) key agreement by constructing the first unconditional attacks on quantum key agreement in the following restricted settings. In the two-message setting, we assume that Alice makes only classical queries to the oracle in the first round and that her message to Bob is classical, but otherwise both parties may perform arbitrary quantum computation, make quantum queries, and send a quantum state in the second round. Our attack and analysis are based on the heavy-query learning techniques from Austrin et al. (CRYPTO 2022) and the reprogramming techniques of Katz and Sela (arXiv 2401.14319). In the round-independent setting, we show that the attack of Barak and Mahmoody (CRYPTO 2009; J. Cryptology 2017) can be extended to multiple rounds when Alice and Bob share classical communication and make only classical queries in all but the final round. In both settings, the attacker is computationally unbounded and makes $poly(λ)$ queries to recover the key whenever each honest query bound is at most $poly(λ)$ and the valid agreement probability is inverse-polynomial. As a consequence, we rule out imperfectly correct quantum public-key encryption for classical messages whose length is bounded by a polynomial in $λ$ in the QROM when key generation has classical oracle access, even if encryption, decryption, and the ciphertext are quantum. In particular, the one-bit case applies to the imperfectly correct PKE obtained from two-round OSP by Bartusek and Khurana (CRYPTO 2025) whenever the classical OSP sender makes only classical random-oracle queries.

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arXiv2026

A Relativizing MIP for BQP

Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP} \not\subseteq \mathsf{IP}$. In contrast, the question of whether the containment $\mathsf{BQP} \subseteq \mathsf{IP}$ is relativizing remains wide open. In this work we make progress towards resolving this question by showing that the containment $\mathsf{BQP} \subseteq \mathsf{MIP}$ holds with respect to any classical oracle. We obtain this result by constructing, for any classical oracle $O$, a $\mathsf{PCP}$ proof system for $\mathsf{BQP}^{O}$ where the verifier makes polynomially many classical queries to an exponentially-long proof, and to the oracle $O$. Our construction is inspired by the state synthesis algorithm of Grover and Rudolph, and serves as a complement to the "exponential PCP" constructed by Aharonov, Arad, and Vidick, which achieves similar parameters but which is based on different ideas and does not relativize. We propose relativization as a proxy for prover efficiency, and hope that progress towards an $\mathsf{IP}$ for $\mathsf{BQP}$ in the oracle world will lead to a non-cryptographic interactive protocol for proving any quantum computation to a classical skeptic in the unrelativized world, which is a longstanding open problem in quantum complexity theory.

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arXiv2025

Classical Commitments to Quantum States

We define the notion of a classical commitment scheme to quantum states, which allows a quantum prover to compute a classical commitment to a quantum state, and later open each qubit of the state in either the standard or the Hadamard basis. Our notion is a strengthening of the measurement protocol from Mahadev (STOC 2018). We construct such a commitment scheme from the post-quantum Learning With Errors (LWE) assumption, and more generally from any noisy trapdoor claw-free function family that has the distributional strong adaptive hardcore bit property (a property that we define in this work). Our scheme is succinct in the sense that the running time of the verifier in the commitment phase depends only on the security parameter (independent of the size of the committed state), and its running time in the opening phase grows only with the number of qubits that are being opened (and the security parameter). As a corollary we obtain a classical succinct argument system for QMA under the post-quantum LWE assumption. Previously, this was only known assuming post-quantum secure indistinguishability obfuscation. As an additional corollary we obtain a generic way of converting any X/Z quantum PCP into a succinct argument system under the quantum hardness of LWE.

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arXiv2025

Exponential Quantum Advantage for Simulating Open Classical Systems

A recent promising arena for quantum advantage is simulating exponentially large classical systems. Here, we show how this advantage can be used to calculate the dynamics of open classical systems experiencing dissipation, including the effects of non-Markovian baths. This is a particularly interesting class of systems since dissipation plays a key role in contexts ranging from fluid dynamics to thermalization. We adopt the Caldeira-Leggett Hamiltonian, a generic model for dissipation in which the system is coupled to a bath of harmonic oscillators with a large number of degrees of freedom. To date, the most efficient classical algorithms for simulating such systems have a polynomial dependence on the size of the bath. In this work, we give a quantum algorithm with an exponential speedup, capable of simulating $d$ system degrees of freedom coupled to $N = 2^n\gg d$ bath degrees of freedom, to within error $\varepsilon$, using $O({\rm poly}(d, n, t, \varepsilon^{-1}))$ quantum gates.

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