Quantum-inspired permanent identities

Chabaud, Ulysse; Deshpande, Abhinav; Mehraban, Saeed

doi:10.22331/q-2022-12-19-877

Cited by 7 publications

(4 citation statements)

References 52 publications

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“…A generalized formula for the permanent has been found along similar lines [55,56]. Furthermore, it is worthwhile to note that different permanent identities have been proven in a quantum-inspired way in [57]. There the Glynn formula has, e.g., been proven using cat states.…”

Section: Discussionmentioning

confidence: 88%

Entanglement in the full state vector of boson sampling

Qiao

Huh

Großmann³

2023

SciPost Phys.

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The full state vector of boson sampling is generated by passing SS single photons through beam splitters of MM modes. We express the initial Fock state in terms of 2^{S-1}S−1 generalized coherent states, making possible the exact application of the unitary evolution. Due to the favorable polynomial scaling of numerical effort in MM, we can investigate Rényi entanglement entropies for moderate particle and huge mode numbers. We find symmetric Page curves with a maximum entropy at equal partition, which is almost independent on Rényi index. Furthermore, the maximum entropy as a function of mode index saturates for M\geq S^2M≥S2 in the collision-free subspace case. The asymptotic value of the entropy increases linearly with SS. In addition, we show that the build-up of the entanglement leads to a cusp in the asymmetric entanglement curve. Maximum entanglement is reached well before the mode population is distributed over the whole system.

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Section: Discussionmentioning

confidence: 88%

Entanglement in the full state vector of boson sampling

Qiao

Huh

Großmann³

2023

SciPost Phys.

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“…If one exploits the symmetry of the transition function in the phase space, there can render a nontrivial approximation algorithm for the corresponding matrix function. Since there can be several equivalent choices of circuits for the same matrix function, e.g., permanent of unitary matrix [40,41], finding the optimal circuit is still an interesting open problem. After a proper circuit choice, there are other optimization problems, such as choosing quasiprobability representation and optimizing parameters for manipulating them in the phase space.…”

Section: Discussionmentioning

confidence: 99%

Approximating outcome probabilities of linear optical circuits

Lim

2023

Preprint

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Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using $s$-parameterized quasiprobability distributions. Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the symmetry of the linear optical transformation in the phase space. Consequently, our scheme renders an efficient estimation of outcome probabilities within an additive error whose precision depends on the classicality of the circuit. When the classicality is high enough, we reach a polynomial-time estimation algorithm of a probability within a multiplicative error by an efficient sampling from the log-concave function. By choosing appropriate input states and measurements, our results provide plenty of quantum-inspired classical algorithms for approximating various matrix functions beating best-known results. Moreover, we give sufficient conditions for the classical simulability of Gaussian boson sampling using the approximating algorithm for any (marginal) outcome probability under the poly-sparse condition.

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“…One use of this framework goes beyond simulation. We can show an example of this by deriving a general (exact) equation for computing LO transitions (which is equivalent to permanent based expressions 26,27 ). Let us take two n photon states | n 1 = |n 1,1 , .…”

Section: Computing Transition Amplitudes Nmentioning

confidence: 99%

“…( 23) is a known relation called Glynn's formula, 28 and has also been derived previously using the coherent state representation. 27 Finally we comment on performing probabilistic measurement sampling in the coherent rank framework. Whilst we saw above the cost to compute a transition probability…”

Section: Computing Transition Amplitudes Nmentioning

confidence: 99%

Advancing quantum networking: some tools and protocols for ideal and noisy photonic systems

Saied,

Marshall,

Anand

et al. 2024

Quantum Computing, Communication, and Simulation IV

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Quantum networking at many scales will be critical to future quantum technologies and experiments on quantum systems. Photonic links enable quantum networking. They will connect co-located quantum processors to enable large-scale quantum computers, provide links between distant quantum computers to support distributed, delegated, and blind quantum computing, and will link distant nodes in space enabling new tests of fundamental physics. Here, we discuss recent work advancing photonic tools and protocols that support quantum networking. We provide analytical results and numerics for the effect of distinguishability errors on key photonic circuits; we considered a variety of error models and developed new metrics for benchmarking the quality of generated photonic states. We review a distillation protocol by one of the authors that mitigates distinguishability errors. We also review recent results by a subset of the authors on the efficient simulation of photonic circuits via approximation by coherent states. We study some interactions between the theory of universal sets, unitary t-designs, and photonics: while many of the results we state in this direction may be known to experts, we aim to bring them to the attention of the broader quantum information science community and to phrase them in ways that are more familiar to this community. We prove, translating a result from representation theory, that there are no non-universal infinite closed 2-designs in U (V) when dim V ≥ 2. As a consequence, we observe that linear optical unitaries form a 1-design but not a 2-design. Finally, we apply a result of Oszmaniec and Zimborás to prove that augmenting the linear optical unitaries with any nontrivial SNAP gate is sufficient to achieve universality.

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Quantum-inspired permanent identities

Cited by 7 publications

References 52 publications

Entanglement in the full state vector of boson sampling

Entanglement in the full state vector of boson sampling

Approximating outcome probabilities of linear optical circuits

Advancing quantum networking: some tools and protocols for ideal and noisy photonic systems

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