Summary Phase transition in Random Circuit Sampling arxiv.org
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Google Quantum AI and its collaborators conducted a study on Random Circuit Sampling (RCS), identifying phase boundaries through cross-entropy benchmarking to observe distinct phases influenced by the interaction of quantum dynamics and noise.
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Key Points
- Google Quantum AI and collaborators conducted experiments on Random Circuit Sampling (RCS) to study the interplay between quantum dynamics and noise.
- They observed distinct phases driven by this interplay and identified phase boundaries using cross-entropy benchmarking.
- A noise-induced phase transition was observed in a 2D random circuit sampling experiment.
- The study presents a new RCS experiment, demonstrating the computational hardness and memory requirements of the process.
- The authors aim to characterize quantum supremacy in near-term devices.
- Platt et al. (2019) and Wu et al. (2021) demonstrated quantum computational advantage with superconducting processors.
- The phase transition in Random Circuit Sampling is different from the quantum to classical transition discussed in a previous reference.
- The document discusses the benchmarking of a random circuit sampling device and presents an ISWAP-like characterization.
Summaries
40 word summary
Google Quantum AI and collaborators studied Random Circuit Sampling (RCS), observing distinct phases driven by the interplay of quantum dynamics and noise. Phase boundaries were identified using cross-entropy benchmarking. The algorithm for sampling from a quantum circuit's output distribution was
82 word summary
Google Quantum AI and its collaborators conducted experiments on Random Circuit Sampling (RCS) to study the interplay between quantum dynamics and noise. They observed distinct phases driven by this interplay and identified phase boundaries using cross-entropy benchmarking. In a
In the document "Phase transition in Random Circuit Sampling," the authors discuss the algorithm for sampling from the output distribution of a quantum circuit. They explain that frugal rejection sampling requires computing only about 10 probabilities per bitstring. The distribution of normalized singular
1075 word summary
Google Quantum AI and collaborators conducted experiments on Random Circuit Sampling (RCS) to study the interplay between quantum dynamics and noise. They observed distinct phases driven by this interplay and identified phase boundaries using cross-entropy benchmarking. The results showed a
In a 2D random circuit sampling experiment, a noise-induced phase transition was observed. The order parameter increased with increasing depth for noise rates below 0.17, but decreased for noise rates above 0.17. At the critical point of
The study presents a new Random Circuit Sampling (RCS) experiment, demonstrating the computational hardness and memory requirements of the process. The experiment estimates the XEB fidelity using a discrete gate set and sampling circuit instances. The results show a sharp transition to maximum
The authors of the document "Phase transition in Random Circuit Sampling" include Arya, J. Atalaya, J. C. Bardin, A. Bilmes, G. Bortoli, A. Bourassa, J. Bov
This document is a collaboration between multiple authors from various research institutions and companies. It discusses the phase transition in random circuit sampling and its implications in quantum computing. The authors aim to characterize quantum supremacy in near-term devices. The document includes references to previous research
The summary of the text excerpt is as follows:
The text excerpt consists of a list of references to various scientific papers and articles related to quantum circuits, information scrambling, computational complexity, and quantum supremacy. These references include works by authors such as Quintana
Platt et al. (2019) demonstrated quantum supremacy using a superconducting processor. Wu et al. (2021) also achieved strong quantum computational advantage with a superconducting quantum processor. Both studies are relevant to the phase transition in
Phase transition in Random Circuit Sampling is a study conducted by Qian, D. Qiao, H. Rong, H. Su, L. Sun, L. Wang, S. Wang, D. Wu, Y. Wu, Y.
The transition discussed in this paper is different from the quantum to classical transition discussed in a previous reference. It is a competition between the convergence rate to the overall ergodic state and the fidelity per cycle. The authors validate quantum supremacy experiments using tensor network contraction
The summary of the text excerpt is as follows: The text includes references to various research papers on quantum computational advantage and certified randomness from quantum advantage experiments. It also discusses the phase transition in random circuit sampling and provides additional experimental data. The appendix explores the
Treating the sum over j as a sum of i.i.d variables, the averaged effect of noise can be approximated as a totally depolarizing channel. The same result is obtained for log XEB. Numerical checks show that the output distribution
The document discusses the benchmarking of a random circuit sampling device, measuring error rates and echo times. It also presents an ISWAP-like characterization and validates an error model with 2-patches and 3-patches XEB. The document includes
The text discusses a Markov process with an update matrix that corresponds to a two-qubit gate. The matrix elements represent transition probabilities between different configurations. The text also mentions the contribution of each configuration to the XEB, which is determined by individual in
The critical depth in Random Circuit Sampling depends on the error per qubit per unit time. The scaling of linear cross-entropy benchmark (XEB) changes from growth to decay at the transition point, which is approximately size independent. This transition can be
An algorithm for sampling from the output distribution of a quantum circuit involves sampling bitstrings randomly, calculating ideal probabilities for those bitstrings, and using rejection sampling to select a subset as the output. Frugal rejection sampling requires computing only about 10 probabilities per
The distribution of normalized singular values in random circuit sampling follows the Marc?enko-Pastur distribution. The fidelity of a Schmidt-decomposed state can be expressed as a product of partial fidelities. Approximated tensor representations can be used to sample bit
The summary of the text excerpt is as follows:
The fidelity for close simulations is compared to the exact fidelity. The bond dimension is fixed at 8. The circuits are split into three parts. The pattern ABCDCDAB is used and the q
In the document "Phase transition in Random Circuit Sampling," the authors discuss the case when ? = ? = c = d and compute the desired result using equations (F29) and (F30). They also consider the special case when ? =
The document discusses the phase transition in Random Circuit Sampling and its implications for entropy estimation and randomness generation. The average purity of the reduced state is the same for both ensembles, and entanglement is typically measured with the von Neumann entropy. The
We assume distinct values in a set and denote the set of sequences missing a particular value. The probability of one bitstring from the Porter-Thomas distribution is calculated using minus log of the probability. The inclusion-exclusion principle is used to calculate the probability
The probability of measuring a certain state is calculated and the bias of the experimental readout measurement error is taken into account. Bitstrings with small Hamming distance between them are eliminated to prevent potential attacks. A truncated XEB fidelity estimator is proposed as a
The authors of the document include K. Drozdov, J. Chau, G. Laun, R. Movassagh, A. Asfaw, L. T.A.N. Branda?o, R. Peralta
This is an excerpt from the document "Phase transition in Random Circuit Sampling" and it contains a list of authors and their affiliations. The authors are from various research institutions including Google Research Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, University of Connecticut
The summary is not clear as it is simply a list of references and does not provide any information about the main ideas or key points of the document.
The article cited various authors and studies related to diabatic gates for frequency-tunable superconducting qubits. These authors include Gid-29, Neill, McCourt, Mi, Jiang, Niu, Mruczkiewicz,
This excerpt contains a list of references to various scientific papers on the topic of quantum circuits and their simulation. The papers cover a range of subjects including quantum computation, quantum supremacy, tensor networks, and classical simulation of quantum circuits. These references provide a comprehensive
The following papers were cited in the document: L. Markov, A. Fatima, S. V. Isakov, and S. Boixo, "Quantum supremacy is both closer and farther than it appears" (2018), B
We study a circuit ensemble consisting of random choices of one-qubit gates and the two-qubit gate iSWAP ?1. We can move Z gates between layers as we transform iSWAP ?1's to iSWAP's. This has