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Dziemba, Friederike Anna

doi:10.26421/qic17.13-14

Cited by 21 publications

(12 citation statements)

References 21 publications

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“…The output amplitudes of a quantum circuit, as a quantum mechanical system, can likewise be described as the sum over all trajectories of the system. However, as quantum gates are typically modelled as operators on a finite dimensional Hilbert space, a discrete sum rather than integral is typically used [8,12,21,24].…”

Section: The Path-sum Frameworkmentioning

confidence: 99%

“…In this work we propose a novel framework for the formal specification and functional verification of unitary (i.e., measurement-free) quantum circuits over a universal gate set -specifically, the Clifford group extended with Z-axis rotations taken from the Clifford hierarchy [17]. Our framework is built around Richard Feynman's path integral technique, which has been used recently to prove results in complexity theory [12,24], and to perform circuit simulation [10,21] and optimization [1,2,4]. Specifically, we develop a concrete representation of quantum operators as path-sums -exponential sums of basis states over a finite set of Boolean path variables.…”

Section: Introductionmentioning

confidence: 99%

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Towards Large-scale Functional Verification of Universal Quantum Circuits

Amy

2019

Electron. Proc. Theor. Comput. Sci.

124

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We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions. Verification of circuits over all levels of the Clifford hierarchy with respect to either a specification or reference circuit is enabled by a novel rewrite system for exponential sums with free variables. Our algorithm is further shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits. We evaluate our methods by performing automated verification of optimized Clifford+T circuits with up to 100 qubits and thousands of T gates, as well as the functional verification of quantum algorithms using hundreds of qubits. Our experiments culminate in the automated verification of the Hidden Shift algorithm for a class of Boolean functions in a fraction of the time it has taken recent algorithms to simulate.

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Section: The Path-sum Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Towards Large-scale Functional Verification of Universal Quantum Circuits

Amy

2019

Electron. Proc. Theor. Comput. Sci.

124

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“…As there are three stabilizers, we need three rounds of checks. By symmetry, it suffices to explain how to measure (CZ) 12 [27][28][29].) Take k independent output CCZ states from the quadratic protocol in the previous subsection, and separate a single qubit from each of the CCZ states.…”

Section: Quartic Error Reductionmentioning

confidence: 99%

Codes and Protocols for DistillingT, controlled-S, and Toffoli Gates

Haah

Hastings

2018

Quantum

101

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We present several different codes and protocols to distill T , controlled-S, and Toffoli (or CCZ) gates. One construction is based on codes that generalize the triorthogonal codes of Ref.[1], allowing any of these gates to be induced at the logical level by transversal T . We present a randomized construction of generalized triorthogonal codes obtaining an asymptotic distillation efficiency γ → 1. We also present a Reed-Muller based construction of these codes which obtains a worse γ but performs well at small sizes. Additionally, we present protocols based on checking the stabilizers of CCZ magic states at the logical level by transversal gates applied to codes; these protocols generalize the protocols of Ref. [2]. Several examples, including a Reed-Muller code for T -to-Toffoli distillation, punctured Reed-Muller codes for T -gate distillation, and some of the check based protocols, require a lower ratio of input gates to output gates than other known protocols at the given order of error correction for the given code size. In particular, we find a code with parameters [[512, 30, 8]] that distills 512 T-gates to 10 Toffoli gates as well as triorthogonal codes with parameters [[887, 137, 5]], [[912, 112, 6]], [[937, 87, 7]] with very low prefactors in front of the leading order error terms in those codes.

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“…Proof of Proposition 7. It has been shown that there exists some quantum channel N * ∈ MIO but not IO, i.e, there exists some quantum state ρ such that N * (ρ) = M(ρ) for any M ∈ IO [61], which implies that max…”

Section: Appendix D: Improvement From Coherent States In Channel Disc...mentioning

confidence: 99%

Quantifying the resource content of quantum channels: An operational approach

Liu

2020

Phys. Rev. A

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We propose a general method to operationally quantify the "resourcefulness" of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a given channel from the set of free channels by free probe states is exactly characterized by the resource generating power, i.e. the maximum amount of resource produced by the action of the channel, given by the trace distance to the set of free states. We apply this framework to the resource theory of quantum coherence, as an informative example. The general results can also be easily applied to other resource theories such as entanglement, magic states, and asymmetry.

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Untitled

Cited by 21 publications

References 21 publications

Towards Large-scale Functional Verification of Universal Quantum Circuits

Towards Large-scale Functional Verification of Universal Quantum Circuits

Codes and Protocols for DistillingT, controlled-S, and Toffoli Gates

Quantifying the resource content of quantum channels: An operational approach

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