Resource theory of quantum uncomplexity

Halpern, Nicole Yunger; Kothakonda, Naga B. T.; Haferkamp, Jonas; Munson, Anthony; Eisert, Jens; Faist, Philippe

doi:10.1103/physreva.106.062417

Cited by 8 publications

(4 citation statements)

References 103 publications

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“…Moreover, it provides a natural set of resource states for studying chaotic dynamics, for which both magic and entanglement are necessary. Resource theories based on the complexity associated with quantum information scrambling were recently introduced [55,56]. Here we will be interested in estimating numerically how many, and what type, of cat states need to be injected into a non-entangling Clifford circuit to achieve quantum information scrambling, a topic we review next.…”

Section: Doping Random Quantum Circuits With Magical Resourcesmentioning

confidence: 99%

Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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Recently, cat states have been used to heuristically improve the runtime of a classical simulator of quantum circuits based on the diagrammatic ZX-calculus. Here we investigate the use of cat-state injection within the quantum circuit model. We explore a family of cat states, $\left| \mathrm{cat}_m^* \right>$, and describe circuit gadgets using them to concurrently inject non-stabilizerness (also known as magic) and entanglement into any quantum circuit. We provide numerical evidence that cat-state injection does not lead to speed-up in classical simulation. On the other hand, we show that our gadgets can be used to widen the scope of compelling applications of cat states. Specifically, we show how to leverage them to achieve savings in the number of injected qubits, and also to induce scrambling dynamics in otherwise non-entangling Clifford circuits in a controlled manner.

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Section: Doping Random Quantum Circuits With Magical Resourcesmentioning

confidence: 99%

Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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“…The landscape of quantum processes is of interest for both foundational and practical aspects of quantum information. On the foundational side, quantum complexity theory [57,58], quantum resource theories [59], categorical quantum mechanics [60] and quantum formal logic [61] rely on the properties of this landscape. The transition to practical aspects is orchestrated by the geometric formulation of quantum computation [44,62].…”

Section: Geometric Quantum Machine Learningmentioning

confidence: 99%

Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis

Gia

Kundu

Acharya

et al. 2023

Entropy

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This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities.

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“…This new form of information, based on the principles of quantum mechanics, aims to explore the transmission and processing of information and is considered an invaluable physical resource. Quantum resource theory [6][7][8][9] provides a broad and effective theoretical framework for investigating the quantum properties of quantum mechanics, such as quantum entanglement [10][11][12][13][14][15], quantum discord [16][17][18][19][20][21][22], and quantum coherence [23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Optimal convex approximations of qubit states under Pauli distance

Zhang,

Shi,

2024

Laser Phys.

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Utilizing the l 1 norm as the quantum state distance metric, we consider the Pauli distance of arbitrary target quantum states, that is, the optimal convex approximation of any qubit mixed states relative to the available state of pairs of eigenstates in three Pauli matrices. We get the complete analytical expressions for B 1 -distance, B 2 -distance and B 3 -distance. We determine the parameter range for the optimal approximation of each B 2 -distance in eight distinct scenarios. Furthermore, some trade-off relations about B 2 -distances are also studied.

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Resource theory of quantum uncomplexity

Cited by 8 publications

References 103 publications

Non-stabilizerness and entanglement from cat-state injection

Non-stabilizerness and entanglement from cat-state injection

Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis

Optimal convex approximations of qubit states under Pauli distance

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