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Simulation of Quantum Circuits via Stabilizer Frames [article]

Héctor J. García, Igor L. Markov
2017 arXiv   pre-print
Stabilizer frames offer more compact storage than previous approaches but require more sophisticated bookkeeping.  ...  We simulate quantum Fourier transform and quantum fault-tolerant circuits using Quipu, and the results demonstrate that our stabilizer-based technique empirically outperforms QuIDDPro in all cases.  ...  A total of four cofactor states are obtained. SIMULATING QUANTUM CIRCUITS WITH STABILIZER FRAMES Let F be the stabilizer frame used to represent the nqubit state |Ψ .  ... 
arXiv:1712.03554v1 fatcat:3d7zzdnzavgxfnz7qpqzk5qk24

Quipu: High-performance simulation of quantum circuits using stabilizer frames

Hector J. Garcia, Igor L. Markov
2013 2013 IEEE 31st International Conference on Computer Design (ICCD)  
Generic quantum-circuit simulation appears intractable for conventional computers.  ...  We simulate various quantum Fourier transform and quantum fault-tolerant circuits with Quipu, and the results demonstrate that our stabilizer-based technique outperforms QuIDDPro in all cases. 1 An operator  ...  SIMULATION OF QUANTUM CIRCUITS USING STABILIZER FRAMES The stabilizer gates by themselves do not form a universal set for quantum computation [1] , [11] .  ... 
doi:10.1109/iccd.2013.6657072 dblp:conf/iccd/GarciaM13 fatcat:u6lt72bs6fgftisluf6wnubrhq

Error mitigation for universal gates on encoded qubits [article]

Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta, Kristan Temme
2021 arXiv   pre-print
We argue that such circuits can be out of reach for state-of-the-art classical simulation algorithms.  ...  Recently methods have been developed to mitigate the effect of noise in shallow quantum circuits that are not protected by error correction.  ...  -Using the schemes explained above we can simulate universal fault-tolerant quantum circuits with a total sampling overhead Γ 2 = γ 2t ε , where t denotes the T -count of the circuit.  ... 
arXiv:2103.04915v2 fatcat:g23quvamnze4rbtitqhn7sfori

Realization of real-time fault-tolerant quantum error correction [article]

C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit (+5 others)
2021 arXiv   pre-print
Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, mid-circuit measurements of subsets of qubits, real-time processing  ...  The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical SPAM error of 1.7(6) × 10^-3, compared to the average  ...  Particularly, we thank Joe Chambers and Tom Skripka for the real-time engine implementation capable of making fast control decisions based on mid-circuit measurement results, we thank Raanan Tobey and  ... 
arXiv:2107.07505v1 fatcat:jkjgo7xgkraa5onulj4yvcgoxe

Estimating Outcome Probabilities of Quantum Circuits Using Quasiprobabilities

Hakop Pashayan, Joel J. Wallman, Stephen D. Bartlett
2015 Physical Review Letters  
We present a method for estimating the probabilities of outcomes of a quantum circuit using Monte Carlo sampling techniques applied to a quasiprobability representation.  ...  Our estimate converges to the true quantum probability at a rate determined by the total negativity in the circuit, using a measure of negativity based on the 1-norm of the quasiprobability.  ...  The canonical example of such a class is that of stabilizer circuits.  ... 
doi:10.1103/physrevlett.115.070501 pmid:26317701 fatcat:fcznithvufg2timdbpfc4f3ulu

Learning quantum circuits of some T gates [article]

Ching-Yi Lai, Hao-Chung Cheng
2021 arXiv   pre-print
In this paper, we study the problem of learning quantum circuits of a certain structure.  ...  By analyzing the algebraic structure of the stabilizer pseudomixture, we can reconstruct the output state of an unknown T-depth one quantum circuit on input |0^n⟩ from the outcomes of Pauli measurements  ...  We propose the following expanded stabilizer formalism for simulating a quantum circuit U of k T gates when the input is a stabilizer state.  ... 
arXiv:2106.12524v1 fatcat:up6jv3rp4zd3jekrgs6faknrdi

Realization of Real-Time Fault-Tolerant Quantum Error Correction

C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit (+5 others)
2021 Physical Review X  
The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of 1.7ð2Þ  ...  Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.  ...  Although not shown, Y-type stabilizers are generated by the X-and Z-type stabilizers listed here. execute parallel quantum operations across three different zones, and quantum circuits are executed as  ... 
doi:10.1103/physrevx.11.041058 fatcat:7bftcvniijfdrlho2rl7ube7uu

Universal Stabilization of a Parametrically Coupled Qubit

Yao Lu, S. Chakram, N. Leung, N. Earnest, R. K. Naik, Ziwen Huang, Peter Groszkowski, Eliot Kapit, Jens Koch, David I. Schuster
2017 Physical Review Letters  
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator.  ...  The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon non-conserving sideband interactions realized by flux modulation  ...  This work made use of the Pritzker Nanofabrication Facility of the Institute for Molecular Engineering at the University of Chicago, which receives support from SHyNE, a node of the National Science Foundation's  ... 
doi:10.1103/physrevlett.119.150502 pmid:29077454 fatcat:s6qftntgtncfvb6ajwgwt7zoym

Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits

Christian Kraglund Andersen, Ants Remm, Stefania Lazar, Sebastian Krinner, Johannes Heinsoo, Jean-Claude Besse, Mihai Gabureac, Andreas Wallraff, Christopher Eichler
2019 npj Quantum Information  
We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle.  ...  By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F ≈ 74% in up to 12 cycles of  ...  We implement this parity stabilization protocol on a small superconducting quantum processor consisting of a linear array of four transmon qubits, of which each pair of nearest neighbors is coupled via  ... 
doi:10.1038/s41534-019-0185-4 fatcat:q5sxarpmnfdbpe3dsosbmyquta

Degenerate Viterbi Decoding

E. Pelchat, D. Poulin
2013 IEEE Transactions on Information Theory  
Previous decoding algorithms for quantum convolutional codes optimized the probability over individual errors instead of classes of degenerate errors.  ...  We present a decoding algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability conditioned on a given error syndrome.  ...  We refer to a given period of this circuit as a time frame of the code.  ... 
doi:10.1109/tit.2013.2246815 fatcat:k4rwvzxanvcqvkuevlo6zxqamu

Stim: a fast stabilizer circuit simulator

Craig Gidney
2021 Quantum  
This paper presents "Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools.  ...  Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.  ...  Cody Jones for useful discussions about simulation algorithms, and in particular for pointing out that randomizing the Z frame after resets and measurements was sufficient for sampling from the space of  ... 
doi:10.22331/q-2021-07-06-497 fatcat:p5dbonpd3jgbvgaovqsfha2x4m

Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras [article]

Yasunari Suzuki, Suguru Endo, Keisuke Fujii, Yuuki Tokunaga
2021 arXiv   pre-print
overheads in a wide range of quantum computing regimes.  ...  In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum  ...  Since approximation errors cannot be treated in the framework of stabilizer simulation, we simulated the quantum circuits by directly updating the state vector after each gate.  ... 
arXiv:2010.03887v6 fatcat:qnhpx2rbhza4za3awftw64zeay

Logical Majorana fermions for fault-tolerant quantum simulation [article]

Andrew J. Landahl, Benjamin C. A. Morrison
2021 arXiv   pre-print
To motivate near-term implementations, we also show how one could realize each of a universal set of logical Majorana gates on a small-scale testbed using noisy intermediate scale quantum (NISQ) technology  ...  Our approach implements a universal set of fault-tolerant gates on these logical Majorana fermions by effecting encoded measurement-based topological quantum computing with them.  ...  Acknowledgments This paper benefited from helpful conversations from a number of people, including (in alphabetical order) Andrew Baczewski, Benjamin Brown, Riley Chien, Anand  ... 
arXiv:2110.10280v1 fatcat:db76jdkarrar5pi7oozqfru2bq

Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits [article]

Christian Kraglund Andersen and Ants Remm and Stefania Balasiu and Sebastian Krinner and Johannes Heinsoo and Jean-Claude Besse and Mihai Gabureac and Andreas Wallraff and Christopher Eichler
2019 arXiv   pre-print
We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle.  ...  By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F≈ 74% in up to 12 cycles of  ...  The authors acknowledge financial support by the Office of the Director of National Intelligence (ODNI), Intelli-  ... 
arXiv:1902.06946v2 fatcat:aamgynxjgrc2vduntayb3g6qz4

Stim: a fast stabilizer circuit simulator [article]

Craig Gidney
2021 arXiv   pre-print
This paper presents "Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools.  ...  Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.  ...  Cody Jones for useful discussions about simulation algorithms, and in particular for pointing out that randomizing the Z frame after resets and measurements was sufficient for sampling from the space of  ... 
arXiv:2103.02202v3 fatcat:73k62n4xi5cbpl6iivno5zcdae
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