Quantum Garbled Circuits

06/01/2020
βˆ™
by   Zvika Brakerski, et al.
βˆ™
0
βˆ™

We present a garbling scheme for quantum circuits, thus achieving a decomposable randomized encoding scheme for quantum computation. Specifically, given a quantum circuit and a quantum input, we show how to compute an encoding 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. The properties of our scheme are analogous to ones achieved in the classical setting (in particular to the so-called point-and-permute garbling method). Our scheme has perfect correctness, and has perfect information-theoretic security if we allow the encoding size to grow exponentially with the depth of the circuit. This exponential blowup can be avoided via computational assumptions (specifically, the existence of quantum-secure pseudorandom generators). The encoding process is decomposable: each input qubit can be encoded independently, when given access to a string of classical randomness and EPR pairs. The complexity of the encoding is comparable to that of classical garbled circuits in terms of dependence on the size and depth of the encoded circuit (and on the security parameter in the computational setting). Furthermore, the encoding can be computed via a constant-depth quantum circuit with bounded-arity gates as well as quantum fan-out gates (which come "for free" in the classical setting). Formally this is captured by the complexity class 𝐐𝐍𝐂^0_f.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 35

page 38

βˆ™ 11/05/2020

Quantum randomized encoding, verification of quantum computing, no-cloning, and blind quantum computing

Randomized encoding is a powerful cryptographic primitive with various a...
βˆ™ 06/20/2019

Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

Recently, Bravyi, Gosset, and KΓΆnig (Science, 2018) exhibited a search p...
βˆ™ 10/30/2018

Average-Case Quantum Advantage with Shallow Circuits

Recently Bravyi, Gosset and KΓΆnig (Science 2018) proved an unconditional...
βˆ™ 01/31/2019

Input Redundancy for Parameterized Quantum Circuits

The topic area of this paper parameterized quantum circuits (quantum neu...
βˆ™ 03/01/2022

Towards a SAT Encoding for Quantum Circuits: A Journey From Classical Circuits to Clifford Circuits and Beyond

Satisfiability Testing (SAT) techniques are well-established in classica...
βˆ™ 05/09/2020

Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions

Effective quantum computation relies upon making good use of the exponen...
βˆ™ 01/10/2022

EP-PQM: Efficient Parametric Probabilistic Quantum Memory with Fewer Qubits and Gates

Machine learning (ML) classification tasks can be carried out on a quant...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.