GraphStateVis: Interactive Visual Analysis of Qubit Graph States and their Stabilizer Groups

Miller, Matthias; Miller, Daniel

doi:10.1109/qce52317.2021.00057

Cited by 8 publications

(9 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This discovery was facilitated by a visualization tool that we report separately in Ref. [25]. While SLDs of GHZ states and alike are not generic, those of cluster states are.…”

Section: Discussionmentioning

confidence: 99%

“…The two distributions have a significant amount of overlap (lavender), which we attribute to the similarity between star graphs and Pusteblume graphs. In both cases, we observe Āk = 0 for all odd k, a property that a graph state exhibits iff all of its vertices have an odd number of neighbors [21,25]. It is well known that Ān is maximized by the GHZ state, i.e., ĀGHZ(n) n ≥ Ān [ρ] for every n-qubit state ρ [9,11].…”

mentioning

confidence: 85%

See 1 more Smart Citation

Sector length distributions of graph states

Miller¹,

Loss²,

Tavernelli³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

The sector length distribution (SLD) of a quantum state is a collection of local unitary invariants that quantify k-body correlations. We show that the SLD of graph states can be derived by solving a graph-theoretical problem. In this way, the mean and variance of the SLD are obtained as simple functions of efficiently computable graph properties. Furthermore, this formulation enables us to derive closed expressions of SLDs for some graph state families. For cluster states, we observe that the SLD is very similar to a binomial distribution, and we argue that this property is typical for graph states in general. Finally, we derive an SLD-based entanglement criterion from the majorization criterion and apply it to derive meaningful noise thresholds for entanglement.

show abstract

“…This discovery was facilitated by a visualization tool that we report separately in Ref. [25]. While SLDs of GHZ states and alike are not generic, those of cluster states are.…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 85%

Sector length distributions of graph states

Miller¹,

Loss²,

Tavernelli³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Readout pulses have a duration of 864 ns. Finally, we provide the error rate and duration of a Cnot-gate with control qubit i and target qubit j, where (i, j) ∈ { (42,43), (43,44), (44,45), (45,54), (54,64), (64,63), (63,62)…”

Section: Details About the Experimentsmentioning

confidence: 99%

“…Clicking on the name of any molecule redirects to a web-page showing the assumed connectivity graph[62].…”

mentioning

confidence: 99%

Hardware-Tailored Diagonalization Circuits

Miller¹,

Fischer²,

Sokolov³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits are reliably executable on near-term quantum computers. Generic diagonalization circuits can lead to an unaffordable Swapgate overhead on quantum devices with limited hardware connectivity. A common alternative is excluding two-qubit gates, however, this comes at the cost of restricting the class of diagonalizable sets of Pauli operators to tensor product bases (TPBs). In this letter, we introduce a theoretical framework for constructing hardware-tailored (HT) diagonalization circuits. We apply our framework to group the Pauli operators occurring in the decomposition of a given Hamiltonian into jointly-HT-diagonalizable sets. We investigate several classes of popular Hamiltonians and observe that our approach requires a smaller number of measurements than conventional TPB approaches. Finally, we experimentally demonstrate the practical applicability of our technique, which showcases the great potential of our circuits for near-term quantum computing.

show abstract

“…Researchers have attempted to explain quantum computing via visualization. Miller et al [31] proposed a node-link approach to present quantum circuits. Lin et al [28] introduced a method to reveal the parameters' dynamic change by the sequence of quantum gates.…”

Section: Visualization For Quantum Computingmentioning

confidence: 99%

VACSEN: A Visualization Approach for Noise Awareness in Quantum Computing

Ruan¹,

Wang²,

Jiang³

et al. 2022

Preprint

View full text Add to dashboard Cite

A1 C1 Fig. 1: The interface of VACSEN makes users aware of the quantum noise via three linked views (A-C). Computer Evolution View (A) allows the assessment for all quantum computers based on a temporal analysis for multiple performance metrics. Circuit Filtering View (B) supports the filtering for the potential optimal compiled circuits. Circuit Comparison View (C) supports the in-depth comparison regarding the performance of qubits or quantum gates and corresponding usages. The control panel (D) allows users to interactively configure the settings of VACSEN. Fidelity Comparison View (E) shows the fidelity distribution of each compiled circuit. Probability Distribution View (F) visualizes the results of state distribution of a quantum circuit execution.

show abstract

GraphStateVis: Interactive Visual Analysis of Qubit Graph States and their Stabilizer Groups

Cited by 8 publications

References 31 publications

Sector length distributions of graph states

Sector length distributions of graph states

Hardware-Tailored Diagonalization Circuits

VACSEN: A Visualization Approach for Noise Awareness in Quantum Computing

Contact Info

Product

Resources

About