Simpler Proofs of Quantumness

Abstract

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer.There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classicallyhard one-way function (e.g. using Shor's algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii).In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.)We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.

Deniable Encryption in a Quantum World

“…Since perfect unexplainability is impossible to achieve classically, it must be that the encryption algorithm is quantum, and in particular that it cannot be replaced by a classical algorithm (otherwise there would be a way to "explain" by providing the input randomness). Now, as originally pointed out in [BKVV20], a single-round proof of quantumness immediately implies a separation of the sampling classes BPP and BQP. Such a separation does not seem to be implied by the hardness of LWE, as the current state-of-the-art suggests that LWE is equally intractable for classical and quantum computers.…”

“…The scheme that makes the theorem true is a variation on the previous one, and is inspired by the follow-up work [BKVV20] to [BCM + 18], which makes use of a random oracle.…”

“…The construction is simple, and is inspired by the "proof of quantumness" construction in [BKVV20]. To obtain an encryption scheme, the idea is to use the "hardcore" bit in their construction as a one-time pad.…”

“…In this section we introduce the notion of noisy trapdoor claw-free functions (NTCFs). This section is taken almost verbatim from [BKVV20]. Let X , Y be finite sets and K a set of keys.…”

Oracle separations of hybrid quantum-classical circuits

“…In other words, the idea is to design a task (or a test) which can be solved by a quantum device having coherent control (the ability to adapt the gates it will perform based on the measurement results) but which cannot be solved by a device without coherent control (one which performs a measurement of all its qubits when providing a response). This is related to the recent notion of proofs of quantumness [Bra+18;Bra+20]. This is a test which can be passed by a BQP machine but not by a BPP one, assuming the intractability of some cryptographic task.…”