Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis

Sun, Xiaoming; Tian, Guojing; Yang, Shuai; Yuan, Pei; Zhang, Shengyu

doi:10.1109/tcad.2023.3244885

Cited by 30 publications

(9 citation statements)

References 31 publications

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“…DI is a more straightforward method of state preparation, which entails loading the CI vectors of each individual fragment onto fragment circuits of size N frag , where N frag represents the number of spin orbitals in each fragment’s active space. Improving these initialization algorithms is an ongoing field of research, with multiple methods of circuit synthesis, with their cost still lower-bounded by an exponential-scaling number of CNOTs. − The DI method used in this work, as implemented in Qiskit, involves the use of quantum multiplexors to generate an arbitrary n -qubit quantum state. This is done by resetting the fragment qubits to |0⟩ and subsequently applying combinations of one- and two-qubit gates.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

D’Cunha,

Otten,

Hermes

et al. 2024

J. Chem. Theory Comput.

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State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space−unitary coupled cluster (LAS−UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. In this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We test the two state preparation methods on three systems, ranging from a model system, a set of interacting hydrogen molecules, to more realistic chemical problems, like the C−C double bond breaking in transbutadiene and the spin ladder in a bimetallic system. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits that can be used for realistic chemical applications.

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Section: Theoretical Backgroundmentioning

confidence: 99%

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

D’Cunha,

Otten,

Hermes

et al. 2024

J. Chem. Theory Comput.

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“…Ideally, the database of hit-pattern templates would be loaded onto the device from Quantum Random-Access Memory (QRAM; Giovannetti et al, 2008 ), however limitations on the ability to realize QRAM mean that, currently, the database must be prepared via state preparation. State preparation is a highly non-trivial task, and has been shown to necessitate exponential circuit depths to construct an arbitrary quantum state (Sun et al, 2023 ). By leveraging ancillary qubits, this scaling can be reduced to polynomial scaling in circuit depth, though at the potential cost of an exponentially growing number of ancillary qubits (Plesch and Brukner, 2011 ; Zhang et al, 2021 , 2022 ; Rosenthal, 2023 ).…”

Section: Quantum Template Matching For Track Findingmentioning

confidence: 99%

Quantum pathways for charged track finding in high-energy collisions

Brown,

Spannowsky,

Tapper

et al. 2024

Front. Artif. Intell.

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In high-energy particle collisions, charged track finding is a complex yet crucial endeavor. We propose a quantum algorithm, specifically quantum template matching, to enhance the accuracy and efficiency of track finding. Abstracting the Quantum Amplitude Amplification routine by introducing a data register, and utilizing a novel oracle construction, allows data to be parsed to the circuit and matched with a hit-pattern template, without prior knowledge of the input data. Furthermore, we address the challenges posed by missing hit data, demonstrating the ability of the quantum template matching algorithm to successfully identify charged-particle tracks from hit patterns with missing hits. Our findings therefore propose quantum methodologies tailored for real-world applications and underline the potential of quantum computing in collider physics.

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“…This state can be generated using poly(ℓ(x)) gates, where poly(ℓ(x)) indicates a term at most polynomial in ℓ(x). This follows since the encoding of x to |x⟩ needs O(ℓ(x)) gates [25], [26] and unitary U ℓ(x) uses poly(ℓ(x)) gates by definition. Next, note that the empirical mean deviates from the expected value ⟨x| U…”

Section: A F (X) Is Quantum 1-computablementioning

confidence: 99%

Relation Between Quantum Advantage in Supervised Learning and Quantum Computational Advantage

Pérez-Guijarro,

Pagés-Zamora,

Fonollosa

2024

IEEE Trans. Quantum Eng.

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The widespread use of machine learning has raised the question of quantum supremacy for supervised learning as compared to quantum computational advantage. In fact, a recent work shows that computational and learning advantage are, in general, not equivalent, i.e., the additional information provided by a training set can reduce the hardness of some problems. This paper investigates under which conditions they are found to be equivalent or, at least, highly related. This relation is analyzed by considering two definitions of learning speed-up: one tied to the distribution and another that is distribution-independent. In both cases, the existence of efficient algorithms to generate training sets emerges as the cornerstone of such conditions, although, for the distribution-independent definition, additional mild conditions must also be met. Finally, these results are applied to prove that there is a quantum speed-up for some learning tasks based on the prime factorization problem, assuming the classical intractability of this problem.

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Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis

Cited by 30 publications

References 31 publications

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

Quantum pathways for charged track finding in high-energy collisions

Relation Between Quantum Advantage in Supervised Learning and Quantum Computational Advantage

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