| 1. |
- Bengtsson, Andreas, 1991, et al.
(författare)
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Improved Success Probability with Greater Circuit Depth for the Quantum Approximate Optimization Algorithm
- 2020
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Ingår i: Physical Review Applied. - 2331-7019. ; 14:3
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Tidskriftsartikel (refereegranskat)abstract
- Present-day, noisy, small or intermediate-scale quantum processors-although far from fault tolerant-support the execution of heuristic quantum algorithms, which might enable a quantum advantage, for example, when applied to combinatorial optimization problems. On small-scale quantum processors, validations of such algorithms serve as important technology demonstrators. We implement the quantum approximate optimization algorithm on our hardware platform, consisting of two superconducting transmon qubits and one parametrically modulated coupler. We solve small instances of the NP (nondeterministic polynomial time)-complete exact-cover problem, with 96.6% success probability, by iterating the algorithm up to level two.
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| 2. |
- Arzani, Francesco, et al.
(författare)
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Random coding for sharing bosonic quantum secrets
- 2019
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 100:2
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Tidskriftsartikel (refereegranskat)abstract
- We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.
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| 3. |
- Calcluth, Cameron, 1997, et al.
(författare)
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Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
- 2022
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Ingår i: Quantum. - 2521-327X. ; 6, s. 867-
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Tidskriftsartikel (refereegranskat)abstract
- We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable.
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| 4. |
- Calcluth, Cameron, 1997, et al.
(författare)
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Sufficient Condition for Universal Quantum Computation Using Bosonic Circuits
- 2024
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Ingår i: PRX Quantum. - 2691-3399. ; 5:2
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Tidskriftsartikel (refereegranskat)abstract
- Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained elusive. We address this gap by focusing on promoting circuits that are otherwise simulatable to computational universality. The class of simulatable, albeit non-Gaussian, circuits that we consider is composed of Gottesman-Kitaev-Preskill (GKP) states, Gaussian operations, and homodyne measurements. Based on these circuits, we first introduce a general framework for mapping a continuous-variable state into a qubit state. Subsequently, we cast existing maps into this framework, including the modular and stabilizer subsystem decompositions. By combining these findings with established results for discrete-variable systems, we formulate a sufficient condition for achieving universal quantum computation. Leveraging this, we evaluate the computational resourcefulness of a variety of states, including Gaussian states, finite-squeezing GKP states, and cat states. Furthermore, our framework reveals that both the stabilizer subsystem decomposition and the modular subsystem decomposition (of position-symmetric states) can be constructed in terms of simulatable operations. This establishes a robust resource-theoretical foundation for employing these techniques to evaluate the logical content of a generic continuous-variable state, which can be of independent interest.
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| 5. |
- Calcluth, Cameron, 1997, et al.
(författare)
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The vacuum provides quantum advantage to otherwise simulatable architectures
- 2023
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 107:6
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Tidskriftsartikel (refereegranskat)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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| 6. |
- Calcluth, Cameron, 1997, et al.
(författare)
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Vacuum provides quantum advantage to otherwise simulatable architectures
- 2023
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 107:6
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Tidskriftsartikel (refereegranskat)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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| 7. |
- Chabaud, Ulysse, et al.
(författare)
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Classical simulation of Gaussian quantum circuits with non-Gaussian input states
- 2021
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Ingår i: Physical Review Research. - 2643-1564. ; 3:3
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Tidskriftsartikel (refereegranskat)abstract
- We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of continuous-variable quantum states to the multimode setting and relate the stellar rank of the input non-Gaussian states, a recently introduced measure of non-Gaussianity, to the cost of evaluating classically the output probability densities of these circuits. Our results have consequences for the strong simulability of a large class of near-term continuous-variable quantum circuits.
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| 8. |
- Douce, Tom, et al.
(författare)
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Probabilistic fault-tolerant universal quantum computation and sampling problems in continuous variables
- 2019
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 99:1
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Tidskriftsartikel (refereegranskat)abstract
- Continuous-variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework we define a general quantum computational model based on a CV hardware. It consists of vacuum input states, a finite set of gates-including non-Gaussian elements-and homodyne detection. We show that this model incorporates encodings sufficient for probabilistic fault-tolerant universal quantum computing. Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses. This allows us to provide a simple paradigm for experiments to probe quantum advantage relying on Gaussian states, homodyne detection, and some form of non-Gaussian evolution. We finally address the recently introduced model of instantaneous quantum computing in CV, and prove that the hardness statement is robust with respect to some experimentally relevant simplifications in the definition of that model.
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| 9. |
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| 10. |
- García Álvarez, Laura, 1990, et al.
(författare)
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Efficient simulatability of continuous-variable circuits with large Wigner negativity
- 2020
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Ingår i: Physical Review Research. - 2643-1564. ; 2:4, s. 043322-
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Tidskriftsartikel (refereegranskat)abstract
- Discriminating between quantum computing architectures that can provide quantum advantage from those that cannot is of crucial importance. From the fundamental point of view, establishing such a boundary is akin to pinpointing the resources for quantum advantage; from the technological point of view, it is essential for the design of nontrivial quantum computing architectures. Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures, including those based on continuous variables (CVs). However, it is not a sufficient resource, and it is an open question under which conditions CV circuits displaying Wigner negativity offer the potential for quantum advantage. In this work we identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable, although they are not recognized as such by previously available theorems. These families of circuits employ bosonic codes based on either translational or rotational symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes) and can include both Gaussian and non-Gaussian gates and measurements. Crucially, within these encodings, the computational basis states are described by intrinsically negative Wigner functions, even though they are stabilizer states if considered as codewords belonging to a finite-dimensional Hilbert space. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
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