Improved graph formalism for quantum circuit simulation

Hu, Alexander Tianlin; Khesin, Andrey Boris

doi:10.1103/physreva.105.022432

Cited by 5 publications

(14 citation statements)

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“…Theorem A (Hu and Khesin [34]). There exists a ZXCF for stabilizer quantum states, which we call HK form.…”

mentioning

confidence: 99%

“…Much room for exploration remains for the construction of such forms. Recently, Hu and Khesin [34] investigated the idea of ZXCFs on states, and showed the following.…”

mentioning

confidence: 99%

“…All that is left to manipulate are the nodes in P. For any pivot node with a non-zero phase, we use Eq. ( 9) in Hu and Khesin [34] and apply it to the input node v in associated with that pivot node. As shown there, this operation identically applies a local complementation about the input node, which notably does not change the entries of M D .…”

mentioning

confidence: 99%

“…Lastly, if there are any edges between pivots p 1 and p 2 , we can remove them by applying Eq. ( 10) from Hu and Khesin [34] to their pair of associated input nodes v 1 and v 2 . This swaps the sets of neighbours of v 1 and v 2 , denoted N 1 and N 2 (which we could always swap back at will).…”

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confidence: 99%

“…It also does not violate the Hadamard rule as there cannot be Hadamard gates on the output edges of nodes in either N 1 or N 2 ; they were removed earlier via Eq. ( 10) of Hu and Khesin [34]. We repeat until no pivot-pivot edges are found.…”

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confidence: 99%

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Graphical quantum Clifford-encoder compilers from the ZX calculus

Khesin¹,

Lu²

2023

Preprint

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We present a quantum compilation algorithm that maps Clifford encoders, an equivalence class of quantum circuits that arise universally in quantum error correction, into a representation in the ZX calculus. In particular, we develop a canonical form in the ZX calculus and prove canonicity as well as efficient reducibility of any Clifford encoder into the canonical form. The diagrams produced by our compiler explicitly visualize information propagation and entanglement structure of the encoder, revealing properties that may be obscured in the circuit or stabilizer-tableau representation.

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“…Theorem A (Hu and Khesin [34]). There exists a ZXCF for stabilizer quantum states, which we call HK form.…”

mentioning

confidence: 99%

“…Much room for exploration remains for the construction of such forms. Recently, Hu and Khesin [34] investigated the idea of ZXCFs on states, and showed the following.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Graphical quantum Clifford-encoder compilers from the ZX calculus

Khesin¹,

Lu²

2023

Preprint

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Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is ﬂourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising ﬁeld of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer signiﬁcant complex network properties. The ﬁeld features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that uniﬁes the ﬁeld of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.

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Bases for optimising stabiliser decompositions of quantum states

de Silva,

Yin,

Strelchuk

2024

Quantum Sci. Technol.

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Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers.We introduce and study the vector space of linear dependencies of $n$-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in $n$. We construct elegant bases of linear dependencies of constant size three. Critically, our sparse bases can be computed without first compiling a dictionary of all $n$-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

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Improved graph formalism for quantum circuit simulation

Cited by 5 publications

References 11 publications

Graphical quantum Clifford-encoder compilers from the ZX calculus

Graphical quantum Clifford-encoder compilers from the ZX calculus

Complex quantum networks: a topical review

Bases for optimising stabiliser decompositions of quantum states

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