Adaptive algorithm for quantum circuit simulation

Schutski, Roman; Lykov, D. I.; Oseledets, Ivan

doi:10.1103/physreva.101.042335

Cited by 26 publications

(15 citation statements)

References 24 publications

(31 reference statements)

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“…This approach has multiple benefits. The only disadvantage of the line graph approach is that it has limited usability to simulate sub-tensors of amplitudes, which was resolved in the work by Schutski et al [46].…”

Section: Contraction Complexity and Relation To Tensor-network Simulamentioning

confidence: 99%

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

et al. 2021

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Our recent work (Ayral et al. in Proceedings of IEEE computer society annual symposium on VLSI, ISVLSI, pp 138–140, 2020. 10.1109/ISVLSI49217.2020.00034) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. This accommodates the limited number of qubits and short coherence times of quantum processors. This article investigates the impact of different noise sources—readout error, gate error and decoherence—on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We also describe in detail the noise models we used to reproduce experimental runs on IBM’s Johannesburg processor. This article also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.

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Section: Contraction Complexity and Relation To Tensor-network Simulamentioning

confidence: 99%

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

et al. 2021

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“…Each of these expressions has a tensor network analog, where the operator Û is represented by a tensor network that is composed of elementary gates acting on subsets of qubits. For more details on how a quantum circuit is converted to a tensor network, see [14], [15].…”

Section: Tensor Network Qaoa Simulatormentioning

confidence: 99%

Transferability of optimal QAOA parameters between random graphs

Galda¹,

Liu²,

Lykov³

et al. 2021

Preprint

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The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. In a typical QAOA setup, a set of quantum circuit parameters is optimized to prepare a quantum state used to find the optimal solution of a combinatorial optimization problem. Several empirical observations about optimal parameter concentration effects for special QAOA MaxCut problem instances have been made in recent literature, however, a rigorous study of the subject is still lacking. We show that convergence of the optimal QAOA parameters around specific values and, consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on the local properties of the graphs, specifically the types of subgraphs (lightcones) from which the graphs are composed. We apply this approach to random regular and general random graphs. For example, we demonstrate how optimized parameters calculated for a 6-node random graph can be successfully used without modification as nearly optimal parameters for a 64-node random graph, with less than 1% reduction in approximation ratio as a result. This work presents a pathway to identifying classes of combinatorial optimization instances for which such variational quantum algorithms as QAOA can be substantially accelerated.

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“…In the context of random circuit C simulation with TNs, previous works [8,9,14,15,17] focused mostly on the efficiency in the evaluation of a single amplitude/probability p C (s) = | s|C|0 n | 2 or one batch of amplitudes associated with a given bitstring s. For example, in [14] a batch of size 2 37 is calculated for a universal ran-dom circuit of depth 23 in a 2D lattice of 8 × 7 qubits. Furthermore, the idea of using large batches in quantum simulations as a trade-off between the single-amplitude and the full-state simulators is discussed in [17].…”

mentioning

confidence: 99%

“…way. If we are given a quantum circuit C, then we can convert it into a tensor network N C in a standard way (see, for example, [17]). We also suppose that standard TN simplification techniques like gate fusion are already applied [8,26].…”

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confidence: 99%