Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes
We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit s...
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| Vydané v: | Physical review letters Ročník 134; číslo 7; s. 070604 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
American Physical Society (APS)
21.02.2025
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| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
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| Abstract | We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼ 8 × 10 9 modes, illustrating the power of our framework. |
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| AbstractList | We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2^{n} modes. Specifically, we encode the initial bosonic state's expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼8×10^{9} modes, illustrating the power of our framework. We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2^{n} modes. Specifically, we encode the initial bosonic state's expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼8×10^{9} modes, illustrating the power of our framework.We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2^{n} modes. Specifically, we encode the initial bosonic state's expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼8×10^{9} modes, illustrating the power of our framework. We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼ 8 × 10 9 modes, illustrating the power of our framework. We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ~8 × 109 modes, illustrating the power of our framework. |
| ArticleNumber | 070604 |
| Author | Sornborger, Andrew T. Barthe, Alice Cerezo, M. García-Martín, Diego Larocca, Martín |
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| References | PhysRevLett.134.070604Cc25R1 PhysRevLett.134.070604Cc13R1 PhysRevLett.134.070604Cc12R1 PhysRevLett.134.070604Cc23R1 PhysRevLett.134.070604Cc22R1 PhysRevLett.134.070604Cc18R1 PhysRevLett.134.070604Cc17R1 PhysRevLett.134.070604Cc16R1 PhysRevLett.134.070604Cc15R1 PhysRevLett.134.070604Cc1R1 PhysRevLett.134.070604Cc19R1 M. A. Nielsen (PhysRevLett.134.070604Cc21R1) 2000 S. Aaronson (PhysRevLett.134.070604Cc2R1) 2010 PhysRevLett.134.070604Cc6R1 PhysRevLett.134.070604Cc7R1 PhysRevLett.134.070604Cc8R1 PhysRevLett.134.070604Cc9R1 PhysRevLett.134.070604Cc3R1 PhysRevLett.134.070604Cc4R1 PhysRevLett.134.070604Cc5R1 PhysRevLett.134.070604Cc10R1 PhysRevLett.134.070604Cc20R1 |
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| Snippet | We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes.... We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2^{n} modes.... We introduce a framework for simulating, on an (n+1)-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2n modes.... |
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| SubjectTerms | bosonic systems BQP-complete computational complexity exponential advantage quantum algorithms & computation quantum circuits quantum harmonic oscillator quantum simulations |
| Title | Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes |
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