An Improved Implementation Approach for Quantum Phase Estimation on Quantum Computers

Mohammadbagherpoor, Hamed; Oh, Young-Hyun; Dreher, Patrick; Singh, Anand; Yu, Xianqing; Rindos, Andy

doi:10.1109/icrc.2019.8914702

Cited by 43 publications

(13 citation statements)

References 28 publications

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“…Quantum ground-state algorithms fall into several classes. Quantum phase estimation is a direct route to (near exact) eigenstate determination, but has been challenging to implement so far [149][150][151]. A complementary technique is to prepare the exact ground-state via a prescribed "exact" evolution path, either in real time (adiabatic state preparation), or in imaginary time (quantum imaginary time evolution) [152][153][154].…”

Section: A Overview Of Algorithmsmentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

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As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.

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Section: A Overview Of Algorithmsmentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

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“…The quantum phase estimation (QPE) algorithm is used to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. More precisely, given an arbitrary quantum operator U and a quantum state |ψ such that U |ψ = e 2iπθ |ψ , the algorithm estimates the value of θ, given an approximation error [23,38,39].…”

Section: B the Quantum Algorithmsmentioning

confidence: 99%

Quantum Computer Benchmarking via Quantum Algorithms

Γεωργόπουλος¹,

Emary²,

Zuliani³

2021

Preprint

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We present a framework that utilizes quantum algorithms, an architecture aware quantum noise model and an ideal simulator to benchmark quantum computers. The benchmark metrics highlight the difference between the quantum computer evolution and the simulated noisy and ideal quantum evolutions. We utilize our framework for benchmarking three IBMQ systems. The use of multiple algorithms, including continuous-time ones, as benchmarks stresses the computers in different ways highlighting their behaviour for a diverse set of circuits. The complexity of each quantum circuit affects the efficiency of each quantum computer, with increasing circuit size resulting in more noisy behaviour. Furthermore, the use of both a continuous-time quantum algorithm and the decomposition of its Hamiltonian also allows extracting valuable comparisons regarding the efficiency of the two methods on quantum systems. The results show that our benchmarks provide sufficient and well-rounded information regarding the performance of each quantum computer.

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“…To probe and reconstruct the band structure on quantum hardware, we perform iterative quantum phase estimation (IQPE) [115,116]. Given U |ψ = e 2πiφ |ψ for unitary U and eigenstate |ψ , IQPE estimates the eigenphase φ ∈ [0, 1), in principle to arbitrary precision.…”

Section: Persistent Boundary Modes From Topological Protectionmentioning

confidence: 99%

“…To reduce circuit breadth and depth, we use iterative quantum phase estimation (IQPE), which has only a single ancilla qubit and controlled-unitary block [115,116]; the inverse Fourier transform for a single qubit is simply a Hadamard gate. Truncating the binary expansion of φ = 0.φ 1 φ 2 .…”

Section: B Iterative Quantum Phase Estimationmentioning

confidence: 99%

Stabilizing multiple topological fermions on a quantum computer

Koh,

Tai,

Phee

et al. 2021

Preprint

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In classical and single-particle settings, non-trivial band topology always gives rise to robust boundary modes. For quantum many-body systems, however, multiple topological fermions are not always able to coexist, since Pauli exclusion prevents additional fermions from occupying the limited number of available topological modes. In this work, we show, through IBM quantum computers, how one can robustly stabilize more fermions than the number of topological modes through specially designed 2-fermion interactions. Our demonstration hinges on the realization of BDI-and D-class topological Hamiltonians of unprecedented complexity on transmon-based quantum hardware, and crucially relied on tensor network-aided circuit recompilation approaches beyond conventional trotterization. We also achieved the full reconstruction of multiple-fermion topological band structures through iterative quantum phase estimation (IQPE). All in all, our work showcases how advances in quantum algorithm implementation enables NISQ-era quantum computers to be exploited for topological stabilization beyond the context of single-particle topological invariants.

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An Improved Implementation Approach for Quantum Phase Estimation on Quantum Computers

Cited by 43 publications

References 28 publications

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

Quantum Computer Benchmarking via Quantum Algorithms

Stabilizing multiple topological fermions on a quantum computer

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