Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum Garbled Circuits
118
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a garbling scheme for quantum circuits, thus achieving a decomposable randomized encoding scheme for quantum computation. Specifically, we show how to compute an encoding of a given quantum circuit and quantum input, from which it is possible to derive the output of the computation and nothing else. In the classical setting, garbled circuits (and randomized encodings in general) are a versatile cryptographic tool with many applications such as secure multiparty computation, delegated computation, depth-reduction of cryptographic primitives, complexity lower-bounds, and more. However, a quantum analogue for garbling general circuits was not known prior to this work. We hope that our quantum randomized encoding scheme can similarly be useful for applications in quantum computing and cryptography. To illustrate the usefulness of quantum randomized encoding, we use it to design a conceptually-simple zero-knowledge (ZK) proof system for the complexity class $mathbf{QMA}$. Our protocol has the so-called $Sigma$ format with a single-bit challenge, and allows the inputs to be delayed to the last round. The only previously-known ZK $Sigma$-protocol for $mathbf{QMA}$ is due to Broadbent and Grilo (FOCS 2020), which does not have the aforementioned properties.
rate research
Read More
We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of dual-mode classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.
Virtual black-box obfuscation is a strong cryptographic primitive: it encrypts a circuit while maintaining its full input/output functionality. A remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator that obfuscates classical circuits into classical circuits cannot exist. A promising direction that circumvents this impossibility result is to obfuscate classical circuits into quantum states, which would potentially be better capable of hiding information about the obfuscated circuit. We show that, under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant of virtual black-box obfuscation of classical circuits is generally impossible. On the way, we show that under the presence of dependent classical auxiliary input, even the small class of classical point functions cannot be quantum virtual black-box obfuscated.
The multiplicative depth of a logic network over the gate basis ${land, oplus, eg}$ is the largest number of $land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth in logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a reduction in the multiplicative depth directly translates to a lower $T$-depth of the corresponding quantum circuit. Our experimental results show improvements in $T$-depth over state-of-the-art methods and over several hand-optimized quantum circuits for instances of AES, SHA, and floating-point arithmetic.
In a recent breakthrough, Bravyi, Gosset and K{o}nig (BGK) [Science, 2018] proved that simulating constant depth quantum circuits takes classical circuits $Omega(log n)$ depth. In our paper, we first formalise their notion of simulation, which we call possibilistic simulation. Then, from well-known results, we deduce that their circuits can be simulated in depth $O(log^{2} n)$. Separately, we construct explicit classical circuits that can simulate any depth-$d$ quantum circuit with Clifford and $t$ $T$-gates in depth $O(d+t)$. Our classical circuits use ${text{NOT, AND, OR}}$ gates of fan-in $leq 2$.
We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly velocity $v_{B} = 1$. Using a transfer matrix approach, we present analytic results for the long-time value of the OTOC on and inside the light cone. First, we consider `dual-unitary circuits with various levels of ergodicity, including the integrable and non-integrable kicked Ising model, where we show exponential decay away from the light cone and relate both the decay rate and the long-time value to those of the correlation functions. Second, we consider a class of kicked XY models similar to the integrable kicked Ising model, again satisfying $v_{B}=1$, highlighting that maximal butterfly velocity is not exclusive to dual-unitary circuits.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
