Closing Gaps of a Quantum Advantage with Short-Time Hamiltonian Dynamics

Haferkamp, Jonas; Hangleiter, Dominik; Bouland, Adam; Fefferman, Bill; Eisert, Jens; Bermejo-Vega, Juan

doi:10.1103/physrevlett.125.250501

Cited by 27 publications

(29 citation statements)

References 53 publications

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“…Moreover, this conjecture was recently proven for a uniform random choice of angles of the input state (see Eq. 11) from the set Θ = [0, 2π] [78]. Furthermore, positive evidence for conjecture (C2) is given by approximate worst-case hardness results in [24] (case Θ = {0, π/4}), as well as by recent proofs of exact average-case hardness and anticoncentration theorems given in [78] for the larger set of angles (case Θ = [0, 2π]).…”

Section: Complexity Theoretic Assumptions Needed For Quantum Advantage Via Sampling Problemsmentioning

confidence: 91%

“…Furthermore, positive evidence for conjecture (C2) is given by approximate worst-case hardness results in [24] (case Θ = {0, π/4}), as well as by recent proofs of exact average-case hardness and anticoncentration theorems given in [78] for the larger set of angles (case Θ = [0, 2π]). The results in [24,78] are analogous to approximate worst-case hardness results in [20][21][22]; proofs of anti-concentration of the output distribution in [21,72]; and exact average-case hardness results in [31,79]. For all known quantum advantage proposals, including ours, proving approximate average-case hardness remains an open question.…”

Section: Complexity Theoretic Assumptions Needed For Quantum Advantage Via Sampling Problemsmentioning

confidence: 96%

“…However, in order to develop higher confidence against the classical simulability of the REM Test, it would be required to develop new tools to study average-case complexity of problems in BQP. This is because known polynomial-interpolation techniques used in worst-to-average reductions are rather sensitive to noise [31,78,91,92] and cannot be readily applied in the standard-resolution regime.…”

Section: A Classical User Picks a Random Many-body Localmentioning

confidence: 99%

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Quantum advantage from energy measurements of many-body quantum systems

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2021

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The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state – a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

show abstract

Section: Complexity Theoretic Assumptions Needed For Quantum Advantage Via Sampling Problemsmentioning

confidence: 91%

Section: Complexity Theoretic Assumptions Needed For Quantum Advantage Via Sampling Problemsmentioning

confidence: 96%

Section: A Classical User Picks a Random Many-body Localmentioning

confidence: 99%

See 1 more Smart Citation

Quantum advantage from energy measurements of many-body quantum systems

Novo

Bermejo-Vega

García−Patrón

2021

Quantum

View full text Add to dashboard Cite

show abstract

“…In this endeavor, the first major intermediate goal is the demonstration of a scalable quantum advantage or quantum computational supremacy over classical computers [1,2,3]. Among the different approaches for demonstrating quantum advantage [4,5,6,7,8,9], photonics provides a promising track as it enables fast gate operations, room-temperature functioning and significant potential for scalability [10,11,12]. The most well-known and feasible photonic advantage scheme is Boson Sampling formulated by Aaronson and Arkhipov [4] and its extended variant known as Gaussian Boson Sampling (GBS) [13,14,15], which are shown to be classically intractable under certain assumptions [4,16].…”

Section: Introductionmentioning

confidence: 99%

Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Kaposi¹,

Kolarovszki²,

Kozsik³

et al. 2021

Preprint

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Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact calculation of the Torontonian compared to stateof-the-art algorithms. According to our numerical analysis the complexity of the algorithm is proportional to N 1.0691 2 N/2 with N being the size of the problem. We also show that the recursive algorithm can be scaled up to HPC use cases making feasible the simulation of threshold GBS up to 35 − 40 photon clicks without the needs of large-scale computational capacities.

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“…of the distribution of projected states over H A . We note that understanding statistical properties of ensembles of quantum states or unitaries (specifically quantifying the degree of randomness) forms the basis of many applications in quantum information science such as cryptography, tomography, or machine learning, as well as sampling-based computational-advantage tests for near-term quantum devices [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Eq.…”

mentioning

confidence: 99%

Exact emergent quantum state designs from quantum chaotic dynamics

Ho,

Choi

2021

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We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking.

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Closing Gaps of a Quantum Advantage with Short-Time Hamiltonian Dynamics

Cited by 27 publications

References 53 publications

Quantum advantage from energy measurements of many-body quantum systems

Quantum advantage from energy measurements of many-body quantum systems

Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

Exact emergent quantum state designs from quantum chaotic dynamics

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