Saachi Mutreja

A classical obfuscator for quantum circuits is a classical program that, given the classical description of a quantum circuit Q, outputs the classical description of a functionally equivalent quantum circuit Q' that hides as much as possible about Q. Previously, the only known feasibility result for classical obfuscation of quantum circuits (Bartusek and Malavolta, ITCS 2022) was limited to "nul" security, which is only meaningful for circuits that always reject. On the other hand, if the obfuscator is allowed to compile the quantum circuit Q into a quantum state |Q'>, there exist feasibility results for obfuscating much more expressive classes of circuits: All pseudo-deterministic quantum circuits (Bartusek, Kitagawa, Nishimaki and Yamakawa, STOC 2023, Bartusek, Brakerski and Vaikuntanathan, STOC 2024), and even all unitaries (Huang and Tang, FOCS 2025). We show that (relative to a classical oracle) there exists a classical obfuscator for all pseudo-deterministic quantum circuits. As our main technical step, we give the first construction of a compact quantum fully-homomorphic encryption (QFHE) scheme that supports public verification of (pseudo-deterministic) quantum evaluation, relative to a classical oracle. To construct our QFHE scheme, we improve on an approach introduced by Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023), which previously required ciphertexts that are both quantum and non-compact due to a heavy use of quantum coset states and their publicly-verifiable properties. As part of our core technical contribution, we introduce new techniques for analyzing coset states that can be generated "on the fly", by proving new cryptographic properties of the one-shot signature scheme of Shmueli and Zhandry (CRYPTO 2025). Our techniques allow us to produce QFHE ciphertexts that are purely classical, compact, and publicly-verifiable. This additionally yields the first classical verification of quantum computation protocol for BQP that simultaneously satisfies blindness and public-verifiability.

Quantum learning from remotely accessed and a priori unknown quantum data must address two key challenges: verifying the correctness of data and ensuring the privacy of the learner’s data-collection strategies and resulting conclusions. The covert (verifiable) learning model of Canetti and Karchmer (TCC 2021) provides a framework for endowing classical learning algorithms with such guarantees, protecting against computationally bounded adversaries who observe and tamper with public oracle queries. However, their framework has two drawbacks: it relies on computational hardness assumptions and does not flexibly accommodate richer data-access models, such as quantum ones. In this work, we propose models of covert verifiable learning in quantum learning theory and realize them without computational hardness assumptions for remote data access scenarios motivated by established quantum data advantages. We consider two privacy notions: (i) strategy-covertness, where the eavesdropper does not gain information about the learner's strategy; and (ii) target-covertness, where the eavesdropper does not gain information about the unknown object being learned. We show: - Strategy-covert algorithms for making quantum statistical queries via classical shadows; - Target-covert algorithms for: - learning quadratic functions from public quantum examples and private quantum statistical queries; - Pauli shadow tomography and stabilizer state learning from public multi-copy and private single-copy quantum measurements; - solving Forrelation and Simon's problem from public quantum queries and private classical queries, where the adversary is an i.i.d. ancilla-free eavesdropper. The lattermost results in particular establish that the exponential separation between classical and quantum queries for Forrelation and Simon’s problem survives under covertness constraints. Along the way, we design covert verifiable protocols for quantum data acquisition from public quantum queries which may be of independent interest. Overall, our models and corresponding algorithms demonstrate that quantum advantages are privately and verifiably achievable even with untrusted, remote data.

It is well-known that digital signatures can be constructed from one-way functions in a black-box way. While one-way functions are essentially the minimal assumption in classical cryptography, this is not the case in the quantum setting. A variety of qualitatively weaker and inherently quantum assumptions (e.g. EFI pairs, one-way state generators, and pseudorandom states) are known to be sufficient for non-trivial quantum cryptography. While it is known that commitments, zero-knowledge proofs, and even multiparty computation can be constructed from these assumptions, it has remained an open question whether the same is true for quantum digital signatures schemes (QDS). In this work, we show that there does not exist a black-box construction of a QDS scheme with classical signatures from pseudorandom states with linear, or greater, output length. Our result complements that of Morimae and Yamakawa (2022), who described a one-time secure QDS scheme with classical signatures, but left open the question of constructing a standard multi-time secure one.