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Lloyd C L Hollenberg - One of the best experts on this subject based on the ideXlab platform.
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cost optimal single qubit gate synthesis in the clifford hierarchy
Quantum, 2021Co-Authors: Gary J Mooney, Charles D Hill, Lloyd C L HollenbergAbstract:For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error Correction Code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates, which are fault-tolerantly performable while enCoded in a quantum error-Correction Code. However, current procedures do not yet support individual assignment of base gate cost values and many do not support extended sets of universal base gates. We study cost-optimal sequences synthesised from sets of base gates which include Clifford gates and $Z$-rotation gates from higher orders of the Clifford hierarchy, which can be performed fault-tolerantly on error-Correction Codes using magic state distillation protocols. The individual costs assigned are the average numbers of raw (i.e. physical level) magic states required to implement the gates fault-tolerantly. By including the $Z$-rotation gates from the fourth order of the Clifford hierarchy as base gates in addition to the canonical Clifford+$T$ gates, we find that the average cost decreases by up to $30\%$. The gate synthesis algorithm introduced in this work, based on Dijkstra's algorithm, generates cost-optimal sequences for single-qubit target gates and supports arbitrary universal sets of single-qubit base gates with individually assigned cost values. In addition, we develop an analytic model to estimate the proportion of sets of $Z$-rotation gates from higher orders of the Clifford hierarchy among gates within sequences approximating random target gates, which can be used to estimate each order's effectiveness for the purpose of gate synthesis.
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towards practical classical processing for the surface Code
Physical Review Letters, 2012Co-Authors: Austin G Fowler, Adam C Whiteside, Lloyd C L HollenbergAbstract:The surface Code is unarguably the leading quantum error Correction Code for 2D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an $n\ifmmode\times\else\texttimes\fi{}n$ lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in $O({n}^{2})$ average time per round of error Correction. We also describe how to parallelize the algorithm to achieve $O(1)$ average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.
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towards practical classical processing for the surface Code
Physical Review Letters, 2012Co-Authors: Austin G Fowler, Adam C Whiteside, Lloyd C L HollenbergAbstract:The surface Code is unarguably the leading quantum error Correction Code for 2D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an n×n lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n2) average time per round of error Correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.
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fault tolerant quantum error Correction Code conversion
arXiv: Quantum Physics, 2011Co-Authors: Charles D Hill, Austin G Fowler, David Wang, Lloyd C L HollenbergAbstract:In this paper we demonstrate how data enCoded in a five-qubit quantum error Correction Code can be converted, fault-tolerantly, into a seven-qubit Steane Code. This is achieved by progressing through a series of Codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the enCoded qubit remains protected. We found, through computational search, that the method used to convert between Codes given in this paper is optimal.
Yaakov S. Weinstein - One of the best experts on this subject based on the ideXlab platform.
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syndrome measurement order for the 7 1 3 quantum error Correction Code
arXiv: Quantum Physics, 2013Co-Authors: Yaakov S. WeinsteinAbstract:In this work we explore the accuracy of quantum error Correction depending of the order of the implemented syndrome measurements. CSS Codes require bit-flip and phase flip-syndromes be measured separately. To comply with fault tolerant demands and to maximize accuracy this set of syndrome measurements should be repeated allowing for flexibility in the order of their implementation. We examine different possible orders of Shor state and Steane state syndrome measurements for the [[7,1,3]] quantum error Correction Code. We find that the best choice of syndrome order, determined by the fidelity of the state after noisy error Correction, will depend on the error environment. We also compare the fidelity when syndrome measurements are done with Shor states versus Steane states and find that Steane states generally, but not always, lead to final states with higher fidelity. Together, these results allow a quantum computer programmer to choose the optimal syndrome measurement scheme based on the system's error environment.
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Encoding an arbitrary state in a [7,1,3] quantum error Correction Code
Quantum Information Processing, 2013Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. WeinsteinAbstract:We calculate the fidelity with which an arbitrary state can be enCoded into a [7, 1, 3] Calderbank-Shor-Steane quantum error Correction Code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. The determination of usability is accomplished by applying ideal error Correction to the enCoded state which demonstrates the correctability of errors that occurred during the encoding process. We also apply single-qubit Clifford gates to the enCoded state and determine the accuracy with which these gates can be implemented. Finally, fault tolerant noisy error Correction is applied to the enCoded states allowing us to compare noisy (realistic) and perfect error Correction implementations. We find the encoding to be usable for the states $${|0\rangle, |1\rangle}$$ , and $${|\pm\rangle = |0\rangle\pm|1\rangle}$$ . These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error Correction must be applied at every step in a quantum protocol.
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encoding an arbitrary state in a 7 1 3 quantum error Correction Code
arXiv: Quantum Physics, 2011Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. WeinsteinAbstract:We calculate the fidelity with which an arbitrary state can be enCoded into a [7,1,3] CSS quantum error Correction Code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. This determination is accomplished by applying ideal error Correction to the enCoded state which demonstrates the correctability of errors that occurred during the encoding process. We then apply single-qubit Clifford gates to the enCoded state and determine the accuracy with which these gates can be applied. Finally, fault tolerant noisy error Correction is applied to the enCoded states in the non-equiprobable Pauli operator error environment allowing us to compare noisy (realistic) and perfect error Correction implementations. We note that this maintains the fidelity of the enCoded state for certain error-probability values. These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error Correction should be applied at every step in a quantum protocol.
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logical zeros for the seven qubit quantum error Correction Code
Proceedings of SPIE, 2011Co-Authors: Gerald Gilbert, Yaakov S. WeinsteinAbstract:ABSTRACT Inthisworkwecomparetheaccuracyoftwomethodsusedtocon structa logicalzerostate appropriateforthe [7;1;3] CSSquantum error Correction Code in a non-equiprobablePauli o perator error environment. The r st method is to apply errorCorrection, via syndrome measurement, on seven physical qu bits all in the state zero. To do the syndrome measurementsin a fault-tolerant fashion requires the construction of fo ur qubit Shor states. These Shor states are also assumed to beconstructedin anon-equiprobablePaulioperatorerrorenv ironmentandit is these thatareusedtoimplementthe syndro memeasurement. The second construction method is to implemen t the [7;1;3] encoding gate sequence, also in the non-equiprobable Pauli operator error environment. The d elit y of the output states is calculated for each of these methods .With respect to the Shor state construction we n d that the im plementation of (noisy) parity based veric ations does notnecessarily raise the d elity of the resulting Shor state. W e also n d that the second logical zero construction methodoutputs a seven qubit state with a respectfully higher d eli ty than the r st (fault tolerant) method. However, the d eli ty ofthe single qubit of stored informationhas almost equivalen td elity from the two constructionmethods.Keywords: cluster state, entanglement,decoherence,superoperator
Wojciech H. Zurek - One of the best experts on this subject based on the ideXlab platform.
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perfect quantum error correcting Code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a quantum error Correction Code which protects a qubit of information against general one qubit errors. To accomplish this, we enCode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state {vert_bar}0{r_angle} to the enCoded state. It can also be converted into a deCoder by running it backward. The original state of the enCoded qubit can then be restored by a simple unitary transformation. {copyright} {ital 1996 The American Physical Society.}
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perfect quantum error correcting Code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a quantum error Correction Code which protects a qubit of information against general one qubit errors. To accomplish this, we enCode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$ to the enCoded state. It can also be converted into a deCoder by running it backward. The original state of the enCoded qubit can then be restored by a simple unitary transformation.
Sahar Daraeizadeh - One of the best experts on this subject based on the ideXlab platform.
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machine learning based three qubit gate design for the toffoli gate and parity check in transmon systems
Physical Review A, 2020Co-Authors: Sahar Daraeizadeh, S P Premaratne, Nader Khammassi, Xiaoyu Song, Marek Perkowski, A Y MatsuuraAbstract:We use machine-learning techniques to design three-qubit entangling gates with fidelities of g99.9% and duration of 50 ns for nearest-neighbor coupled flux-tunable transmons in circuit quantum electrodynamics architectures. The gate design procedure enforces realistic constraints and analyzes the robustness of the new gates under decoherence, distortion, and random noise. The controlled-controlled-phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, and quantum error Correction. We also introduce a three-qubit entangling Parity Checker gate which has applications in quantum arithmetic circuits and quantum error Correction schemes. Using these three-qubit gates, we design a circuit for Shor's nine-qubit quantum error Correction Code and compare its performance to conventional realizations.
Raymond Laflamme - One of the best experts on this subject based on the ideXlab platform.
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perfect quantum error correcting Code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a quantum error Correction Code which protects a qubit of information against general one qubit errors. To accomplish this, we enCode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state {vert_bar}0{r_angle} to the enCoded state. It can also be converted into a deCoder by running it backward. The original state of the enCoded qubit can then be restored by a simple unitary transformation. {copyright} {ital 1996 The American Physical Society.}
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perfect quantum error correcting Code
Physical Review Letters, 1996Co-Authors: Raymond Laflamme, Cesar Miquel, Juan Pablo Paz, Wojciech H. ZurekAbstract:We present a quantum error Correction Code which protects a qubit of information against general one qubit errors. To accomplish this, we enCode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$ to the enCoded state. It can also be converted into a deCoder by running it backward. The original state of the enCoded qubit can then be restored by a simple unitary transformation.