Algebraic and Logical Emulations of Quantum Circuits

Regan, Kenneth W.; Chakrabarti, Amlan; Guan, Chaowen

doi:10.1007/978-3-662-56499-8_4

Cited by 2 publications

(5 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nevertheless, perhaps these techniques can apply to heuristic or approximative methods on general quantum circuits. The polynomial translation in [RCG18] applies to quantum circuits of all common gate types. There are questions about analyzing circuits that are "mostly Clifford" or those from the Clifford plus T libraries that try to minimize the latter gates, of which we mention[BG16, MFIB18, BBC + 19].…”

Section: Discussionmentioning

confidence: 99%

“…We employ the theory of classical quadratic forms over Z 4 as developed by Schmidt [Sch09] and more recently by Cai, Guo, and Williams [CGW18]. The quadratic forms are built using the real-time algorithm of [RC09,RCG18] for computing what we call the additive partition polynomials q C for quantum circuits C that meet a mild "balance" condition. Related works involving low-degree polynomials and counting complexity include [BvDR08,BJS10,Mon17,KPS17].…”

Section: Quantum Stabilizer Circuitsmentioning

confidence: 99%

“…Here step 1 from [RCG18] takes time linear in the number s of quantum gates in C, which for standard-basis inputs can be bounded above by O(n 2 / log n) with O(n) quantum Hadamard gates [AG04].…”

Section: Introductionmentioning

confidence: 99%

“…The connections used in our proof run through the real-time conversion of quantum circuits C to "phase polynomials" q C over Z K for K = 2 k , k ≥ 1 in [RC09,RCG18], which extended results by [DHH + 04] for k = 1, and the analysis of quadratic forms over Z 4 by Schmidt [Sch09] drawing on [Alb38,Bro72]. In the case of graph-state circuits and stabilizer circuits more generally, q C becomes a classical quadratic form over Z 4 , as treated also in [CGW18].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank

Guan,

Regan

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We show that a form of strong simulation for n-qubit quantum stabilizer circuits C is computable in O(s + n ω ) time, where ω is the exponent of matrix multiplication. Solution counting for quadratic forms over F 2 is also placed into O(n ω ) time. This improves previous O(n 3 ) bounds. Our methods in fact show an O(n 2 )-time reduction from matrix rank over F 2 to computing p = | 0 n | C |0 n | 2 (hence also to solution counting) and a converse reduction that is O(s + n 2 ) except for matrix multiplications used to decide whether p > 0. The current best-known worst-case time for matrix rank is O(n ω ) over F 2 , indeed over any field, while ω is currently upper-bounded by 2.3728 . . . Our methods draw on properties of classical quadratic forms over Z 4 . We study possible distributions of Feynman paths in the circuits and prove that the differences in +1 vs. −1 counts and +i vs. −i counts are always 0 or a power of 2. Further properties of quantum graph states and connections to graph and matroid theory are discussed.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Quantum Stabilizer Circuitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank

Guan,

Regan

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…While all quantum circuits have a unitary representation, they may also be represented differently. For example, an algebraic representation is better suited for distributed quantum computing [35]. We focus on the quantum gate unitary model in the paper as it is the most pertinent to Quest's mathematical reasoning.…”

Section: Quest-relevant Terms and Definitionsmentioning

confidence: 99%

QUEST: systematically approximating Quantum circuits for higher output fidelity

Patel

Younis

Iancu

et al. 2022

Proceedings of the 27th ACM International Conference on Architectural Support for Programming Languages and Operating Systems

View full text Add to dashboard Cite

We present Quest, a procedure to systematically generate approximations for quantum circuits to reduce their CNOT gate count. Our approach employs circuit partitioning for scalability with procedures to 1) reduce circuit length using approximate synthesis, 2) improve fidelity by running circuits that represent key samples in the approximation space, and 3) reason about approximation upper bound. Our evaluation results indicate that our approach of łdissimilarž approximations provides close fidelity to the original circuit. Overall, the results indicate that Quest can reduce CNOT gate count by 30-80% on ideal systems and decrease the impact of noise on existing and near-future quantum systems.

show abstract

Algebraic and Logical Emulations of Quantum Circuits

Cited by 2 publications

References 31 publications

Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank

Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank

QUEST: systematically approximating Quantum circuits for higher output fidelity

Contact Info

Product

Resources

About