| 1. |
- Calcluth, Cameron, 1997, et al.
(author)
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The vacuum provides quantum advantage to otherwise simulatable architectures
- 2023
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In: Physical Review A. - 2469-9934 .- 2469-9926. ; 107:6
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Journal article (peer-reviewed)abstract
- We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states, Gaussian operations - including all rational symplectic operations and all real displacements -, and homodyne measurement. We prove that such architecture is classically efficiently simulatable, by explicitly providing an algorithm to calculate the probability density function of the measurement outcomes of the computation. We also provide a method to sample when the circuits contain conditional operations. This result is based on an extension of the celebrated Gottesman-Knill theorem, via introducing proper stabilizer operators for the code at hand. We conclude that the resource enabling quantum advantage in the universal computational model considered by B.Q. Baragiola et al [Phys. Rev. Lett. 123, 200502 (2019)], composed of a subset of the elements given above augmented with a provision of vacuum states, is indeed the vacuum state.
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| 2. |
- Calcluth, Cameron, 1997, et al.
(author)
-
Vacuum provides quantum advantage to otherwise simulatable architectures
- 2023
-
In: Physical Review A. - 2469-9934 .- 2469-9926. ; 107:6
-
Journal article (peer-reviewed)abstract
- We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states, Gaussian operations including all rational symplectic operations and all real displacements, and homodyne measurement. We prove that such architecture is classically efficiently simulatable by explicitly providing an algorithm to calculate the probability density function of the measurement outcomes of the computation. We also provide a method to sample when the circuits contain conditional operations. This result is based on an extension of the celebrated Gottesman-Knill theorem, via introducing proper stabilizer operators for the code at hand. We conclude that the resource enabling quantum advantage in the universal computational model considered by Baragiola et al. [Phys. Rev. Lett. 123, 200502 (2019)0031-900710.1103/PhysRevLett.123.200502], composed of a subset of the elements given above augmented with a provision of vacuum states, is indeed the vacuum state.
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| 3. |
- Svensson, Marika, 1989, et al.
(author)
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Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs
- 2023
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In: Physical Review Applied. - 2331-7019. ; 20:3
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Journal article (peer-reviewed)abstract
- We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the branch-and-price algorithm, which is regularly used to solve large-scale integer linear programs with a specific structure. The role of the quantum algorithm is to find integer solutions to subproblems appearing in branch-and-price. Obtaining optimal or near-optimal integer solutions to these subproblems can increase the quality of solutions and reduce the depth and branching factor of the branch-and-price algorithm and hence reduce the overall running time. We investigate the viability of the approach by considering the tail assignment problem and the quantum approximate optimization algorithm (QAOA). Here, the master problem is the optimization problem set partitioning or its decision version exact cover and can be expressed as finding the ground state of an Ising spin glass Hamiltonian. For exact cover, our numerical results indicate that the required algorithm depth decreases with the number of feasible solutions for a given success probability of finding a feasible solution. For set partitioning, on the other hand, we find that for a given success probability of finding the optimal solution, the required algorithm depth can increase with the number of feasible solutions if the Hamiltonian is balanced poorly, which in the worst case is exponential in the problem size. We therefore address the significance of properly balancing the objective and constraint parts of the Hamiltonian. We empirically find that the approach is viable with QAOA if polynomial algorithm depth can be realized on quantum devices.
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| 4. |
- Zheng, Yu, 1992, et al.
(author)
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Gaussian conversion protocol for heralded generation of generalized Gottesman-Kitaev-Preskill states
- 2023
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In: Physical Review A. - 2469-9934 .- 2469-9926. ; 108:1
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Journal article (peer-reviewed)abstract
- In the field of fault-tolerant quantum computing, continuous-variable systems can be utilized to protect quantum information from noise through the use of bosonic codes. These codes map qubit-type quantum information onto the larger bosonic Hilbert space, and can be divided into two main categories: translational-symmetric codes, such as Gottesman-Kitaev-Preskill (GKP) codes, and rotational-symmetric codes, including cat and binomial codes. The relationship between these families of codes has not yet been fully understood. We present an iterative protocol for converting between two instances of these codes - generalized GKP (so-called qunaught) states and fourfold-symmetric binomial states corresponding to a zero-logical encoded qubit - using only Gaussian operations. This conversion demonstrates the potential for universality of binomial states for all-Gaussian quantum computation and provides a method for the heralded preparation of GKP states. Through numerical simulation, we obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%, after only two steps of our iterative protocol, though higher fidelities can be achieved with additional iterations at the cost of lower success probabilities.
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