| 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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| 11. |
- Hahn, Oliver, 1993, et al.
(författare)
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Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources
- 2022
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Ingår i: Physical Review A. - : American Physical Society. - 2469-9934 .- 2469-9926. ; 105:6
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Tidskriftsartikel (refereegranskat)abstract
- In the context of quantum technologies over continuous variables, Gaussian states and operations are typically regarded as freely available, as they are relatively easily accessible experimentally. In contrast, the generation of non-Gaussian states, as well as the implementation of non-Gaussian operations, pose significant challenges. This divide has motivated the introduction of resource theories of non-Gaussianity. As for any resource theory, it is of practical relevance to identify free conversion protocols between resources, namely, Gaussian conversion protocols between non-Gaussian states. Via systematic numerical investigations, we address the approximate conversion between experimentally relevant single-mode non-Gaussian states via arbitrary deterministic one-to-one mode Gaussian maps. First we show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit. Then we consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations. The numerical tools that we develop also allow one to devise conversions of trisqueezed into cubic-phase states beyond previously reported performances. Finally, we identify various other conversions which instead are not viable.
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| 12. |
- Hahn, Oliver, 1993, et al.
(författare)
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Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
- 2022
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 128:21
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Tidskriftsartikel (refereegranskat)abstract
- Quantum resource theories are a powerful framework for characterizing and quantifying relevant quantum phenomena and identifying processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation. Particularly, we use the Gottesman-Kitaev-Preskill code to represent multiqubit states and consider the resource theory for the Wigner negativity. Our techniques are useful in finding resource lower bounds for different applications as state conversion and gate synthesis. The analytical expression of our magic measure allows us to extend current analysis limited to small dimensions, easily addressing systems of up to 12 qubits.
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| 13. |
- Hillmann, Timo, 1995, et al.
(författare)
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Performance of Teleportation-Based Error-Correction Circuits for Bosonic Codes with Noisy Measurements
- 2022
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Ingår i: PRX Quantum. - 2691-3399. ; 3:2
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Tidskriftsartikel (refereegranskat)abstract
- Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware over-head required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit. Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential. In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes. In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.
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| 14. |
- Hillmann, Timo, 1995, et al.
(författare)
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Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
- 2020
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 125:16
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Tidskriftsartikel (refereegranskat)abstract
- We provide an explicit construction of a universal gate set for continuous-variable quantum computation with microwave circuits. Such a universal set has been first proposed in quantum-optical setups, but its experimental implementation has remained elusive in that domain due to the difficulties in engineering strong nonlinearities. Here, we show that a realistic three-wave mixing microwave architecture based on the superconducting nonlinear asymmetric inductive element [Frattini et al. , Appl. Phys. Lett. 110 , 222603 (2017)] allows us to overcome this difficulty. As an application, we show that this architecture allows for the generation of a cubic phase state with an experimentally feasible procedure. This work highlights a practical advantage of microwave circuits with respect to optical systems for the purpose of engineering non-Gaussian states and opens the quest for continuous-variable algorithms based on few repetitions of elementary gates from the continuous-variable universal set
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| 15. |
- Kudra, Marina, 1992, et al.
(författare)
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Robust Preparation of Wigner-Negative States with Optimized SNAP-Displacement Sequences
- 2022
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Ingår i: PRX Quantum. - : AMER PHYSICAL SOC. - 2691-3399. ; 3:3
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Tidskriftsartikel (refereegranskat)abstract
- Hosting nonclassical states of light in three-dimensional microwave cavities has emerged as a promising paradigm for continuous-variable quantum information processing. Here we experimentally demonstrate high-fidelity generation of a range of Wigner-negative states useful for quantum computation, such as Schrodinger-cat states, binomial states, Gottesman-Kitaev-Preskill states, as well as cubic phase states. The latter states have been long sought after in quantum optics and have never been achieved experimentally before. We use a sequence of interleaved selective number-dependent arbitrary phase (SNAP) gates and displacements. We optimize the state preparation in two steps. First we use a gradient-descent algorithm to optimize the parameters of the SNAP and displacement gates. Then we optimize the envelope of the pulses implementing the SNAP gates. Our results show that this way of creating highly nonclassical states in a harmonic oscillator is robust to fluctuations of the system parameters such as the qubit frequency and the dispersive shift.
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| 16. |
- Svensson, Marika, 1989, et al.
(författare)
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Hybrid Quantum-Classical Heuristic to Solve Large-Scale Integer Linear Programs
- 2023
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Ingår i: Physical Review Applied. - 2331-7019. ; 20:3
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Tidskriftsartikel (refereegranskat)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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| 17. |
- Vikstål, Pontus, 1993, et al.
(författare)
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Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem
- 2020
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Ingår i: Physical Review Applied. - 2331-7019. ; 14:3
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Tidskriftsartikel (refereegranskat)abstract
- Airlines today are faced with a number of large-scale scheduling problems. One such problem is the tail-assignment problem, which is the task of assigning individual aircraft to a given set of flights, minimizing the overall cost. Each aircraft is identified by the registration number on its tail fin. In this paper, we simulate the quantum approximate optimization algorithm (QAOA) applied to instances of this problem derived from real-world data. The QAOA is a variational hybrid quantum-classical algorithm recently introduced and likely to run on near-term quantum devices. The instances are reduced to fit on quantum devices with 8, 15, and 25 qubits. The reduction procedure leaves only one feasible solution per instance, which allows us to map the tail-assignment problem onto the exact-cover problem. We find that repeated runs of the QAOA identify the feasible solution with close to unit probability for all instances. Furthermore, we observe patterns in the variational parameters such that an interpolation strategy can be employed, which significantly simplifies the classical optimization part of the QAOA. Finally, we empirically find a relation between the connectivity of the problem graph and the single-shot success probability of the algorithm.
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| 18. |
- Zheng, Yu, 1992, et al.
(författare)
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Gaussian conversion protocol for heralded generation of generalized Gottesman-Kitaev-Preskill states
- 2023
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 108:1
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Tidskriftsartikel (refereegranskat)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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| 19. |
- Zheng, Yu, 1992, et al.
(författare)
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Gaussian Conversion Protocols for Cubic Phase State Generation
- 2021
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Ingår i: PRX Quantum. - 2691-3399. ; 2:1
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Tidskriftsartikel (refereegranskat)abstract
- Universal quantum computing with continuous variables requires non-Gaussian resources, in addition to a Gaussian set of operations. A known resource enabling universal quantum computation is the cubic phase state, a non-Gaussian state whose experimental implementation has so far remained elusive. In this paper, we introduce two Gaussian conversion protocols that allow for the conversion of a non-Gaussian state that has been achieved experimentally, namely the trisqueezed state [Chang et al., Phys. Rev. X 10, 011011 (2020)], to a cubic phase state. The first protocol is deterministic and it involves active (inline) squeezing, achieving large fidelities that saturate the bound for deterministic Gaussian protocols. The second protocol is probabilistic and it involves an auxiliary squeezed state, thus removing the necessity of inline squeezing but still maintaining significant success probabilities and fidelities even larger than for the deterministic case. The success of these protocols provides strong evidence for using trisqueezed states as resources for universal quantum computation.
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