• Corpus ID: 219530931

Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

@article{Hner2020LoweringTT,
  title={Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks},
  author={Thomas H{\"a}ner and Mathias Soeken},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.03845}
}
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ 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… 

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References

SHOWING 1-10 OF 59 REFERENCES

A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits

We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute force

A Logic Synthesis Toolbox for Reducing the Multiplicative Complexity in Logic Networks

TLDR
This paper presents a logic synthesis toolbox for cryptography and security applications that consists of powerful transformations, namely resubstitution, refactoring, and rewriting, specifically designed to minimize the multiplicative complexity of an XAG.

Applying Grover's Algorithm to AES: Quantum Resource Estimates

TLDR
It is established that for all three variants of AES key size 128, 192, and 256i¾źbit that are standardized in FIPS-PUB 197, there are precise bounds for the number of qubits and thenumber of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.

A multi-start heuristic for multiplicative depth minimization of boolean circuits

TLDR
A multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits and the experimental results show that they are rather powerful.

Quantum circuits for floating-point arithmetic

TLDR
This paper provides quantum circuits for floating-point addition and multiplication which are found using two vastly different approaches: to automatically generate circuits from classical Verilog implementations using synthesis tools and to generate and optimize these circuits by hand.

Constant-optimized quantum circuits for modular multiplication and exponentiation

TLDR
In the context of modular exponentiation, this work offers several constant-factor improvements, as well as an improvement by a constant additive term that is significant for few-qubit circuits arising in ongoing laboratory experiments with Shor's algorithm.

Synthesis of reversible logic circuits

TLDR
In an application important to quantum computing, the synthesis of oracle circuits for Grover's search algorithm are synthesized, and a significant improvement over a previously proposed synthesis algorithm is shown.

Low-overhead constructions for the fault-tolerant Toffoli gate

TLDR
Two constructions for the Toffoli gate are presented which substantially reduce resource costs in fault-tolerant quantum computing and a quantum circuit is presented which can detect a single ${\ensuremath{\sigma}}^{z}$ error occurring with probability $p$ in any one of eight $T$ gates required to produce the ToFFoli gate.

Enumerating Optimal Quantum Circuits using Spectral Classification

TLDR
An automatically-generated database containing minimal-cost quantum circuits for Boolean functions up to 5 inputs is presented and it is shown that any Boolean function can be derived from the implementation of its class representative without increasing any of the stated cost functions.

Logic Minimization Techniques with Applications to Cryptology

TLDR
The technique can be applied to arbitrary combinational logic problems, and often yields improvements even after optimization by standard methods has been performed, and a special case of the corresponding decision problem is Max SNP-complete, implying limits to its approximability.
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