Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error

Fujii, Keisuke; Kobayashi, Hirotada; Morimae, Tomoyuki; Nishimura, Harumichi; Tamate, Shuhei; Tani, Seiichiro

doi:10.1103/physrevlett.120.200502

Cited by 58 publications

(64 citation statements)

References 55 publications

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“…As a consequence of these results, it then follows from [27] that there is no classical algorithm to efficiently approximate our cost functions, C HST or C LHST , with inverse polynomial precision, unless the polynomial hierarchy collapses to the second level.…”

Section: Approximating C Lhst Is Dqc1-hardmentioning

confidence: 93%

“…Our results build on the fact that evaluating either of our cost functions is, in some sense, as hard as trace estimation. Using the results from [27], it then immediately follows that no classical algorithm can efficiently approximate our cost functions under certain complexity assumptions.…”

Section: One-clean-qubit Model Of Computationmentioning

confidence: 99%

“…We prove that computing our cost function is DQC1hard, where DQC1 is the class of problems that can be efficiently solved in the one-clean-qubit model of computation [26]. Since DQC1 is classically hard to simulate [27], this implies that no classical algorithm can efficiently compute our cost function. We remark that an alternative cost function might be a worst-case distance measure (such as diamond distance), but such measures are known to be QIP-complete [28] and hence would violate criterion 2 in our list above.…”

Section: Introductionmentioning

confidence: 96%

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Quantum-assisted quantum compiling

Khatri

LaRose

Poremba

et al. 2019

Quantum

347

437

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Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary U and a trainable unitary V as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap Tr(V † U ) but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking. arXiv:1807.00800v5 [quant-ph]

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Section: Approximating C Lhst Is Dqc1-hardmentioning

confidence: 93%

Section: One-clean-qubit Model Of Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Quantum-assisted quantum compiling

Khatri

LaRose

Poremba

et al. 2019

Quantum

347

437

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“…A natural question is to ask at what point this decoherence renders the quantum computation classically simulateable. There is a large amount of literature surrounding classical simulation of mixed state quantum computing [38,39,40], and the role of entanglement [41,42,43,44,45]. We've already seen that when the input is completely distinguishable, the output distribution is given by the permanents of positive matrices, Eq.…”

Section: Distinguishability and Simulateabilitymentioning

confidence: 99%

Quantum simulation of partially distinguishable boson sampling

Moylett

Turner

2018

Phys. Rev. A

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Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.

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“…If an appropriately designed quantum computing model can be efficiently simulated by a classical computer, an unlikely consequence in computer science can be obtained under some unproven conjectures (for details, see section 8.2). So far, to demonstrate the quantum supremacy, several quantum computing models have been proposed [10][11][12][13][14][15][16][17][18][19][20]. As an advantage of this approach, the quantum computing model do not have to be universal one.…”

Section: Introductionmentioning

confidence: 99%

Verifying commuting quantum computations via fidelity estimation of weighted graph states

Hayashi

Takeuchi²

2019

New J. Phys.

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The instantaneous quantum polynomial time (IQP) model is one of promising models to demonstrate a quantum computational advantage over classical computers. If the IQP model can be efficiently simulated by a classical computer, an unlikely consequence in computer science can be obtained (under some unproven conjectures). In order to experimentally demonstrate the advantage using medium or large-scale IQP circuits, it is inevitable to efficiently verify whether the constructed IQP circuits faithfully work. There exist two types of IQP models, each of which is the sampling on hypergraph states or weighted graph states. For the first-type IQP model, polynomial-time verification protocols have already been proposed. In this paper, we propose verification protocols for the secondtype IQP model. To this end, we propose polynomial-time fidelity estimation protocols of weighted graph states for each of the following four situations where a verifier can (i) choose any measurement basis and perform adaptive measurements, (ii) only choose restricted measurement bases and perform adaptive measurements, (iii) choose any measurement basis and only perform non-adaptive measurements, and (iv) only choose restricted measurement bases and only perform non-adaptive measurements. In all of our verification protocols, the verifier's quantum operations are only singlequbit measurements. Since we assume no independent and identically distributed property on quantum states, our protocols work in any situation.

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Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error

Cited by 58 publications

References 55 publications

Quantum-assisted quantum compiling

Quantum-assisted quantum compiling

Quantum simulation of partially distinguishable boson sampling

Verifying commuting quantum computations via fidelity estimation of weighted graph states

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