| 1. |
- Allan, Dan, et al.
(author)
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Time-optimal quantum transformations with bounded bandwidth
- 2021
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In: Quantum. - : Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 5, s. 1-19
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Journal article (peer-reviewed)abstract
- In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.
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| 2. |
- Andreasson, Philip, et al.
(author)
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Quantum error correction for the toric code using deep reinforcement learning
- 2019
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In: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 3
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Journal article (peer-reviewed)abstract
- We implement a quantum error correction algorithm for bit-flip errors on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Q-function is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which significantly simplifies the state space representation independently of the number of defect pairs. The training is done using experience replay, where data from the algorithm being played out is stored and used for mini-batch upgrade of the Q-network. We find performance which is close to, and for small error rates asymptotically equivalent to, that achieved by the Minimum Weight Perfect Matching algorithm for code distances up to d=7. Our results show that it is possible for a self-trained agent without supervision or support algorithms to find a decoding scheme that performs on par with hand-made algorithms, opening up for future machine engineered decoders for more general error models and error correcting codes.
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| 3. |
- Calcluth, Cameron, 1997, et al.
(author)
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Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
- 2022
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In: Quantum. - 2521-327X. ; 6, s. 867-
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Journal article (peer-reviewed)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. |
- Fitzek, David, 1993, et al.
(author)
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Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
- 2024
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In: Quantum. - 2521-327X. ; 8
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Journal article (peer-reviewed)abstract
- Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. VQAs are based on a parameterized quantum circuit optimized in a closed loop via a classical algorithm. This hybrid approach reduces the quantum processing unit load but comes at the cost of a classical optimization that can feature a flat energy landscape. Existing optimization techniques, including either imaginary time -propagation, natural gradient, or momentum -based approaches, are promising candidates but place either a significant burden on the quantum device or suffer frequently from slow convergence. In this work, we propose the quantum Broyden adaptive natural gradient (qBang) approach, a novel optimizer that aims to distill the best aspects of existing approaches. By employing the Broyden approach to approximate updates in the Fisher information matrix and combining it with a momentumbased algorithm, qBang reduces quantumresource requirements while performing better than more resource -demanding alternatives. Benchmarks for the barren plateau, quantum chemistry, and the maxcut problem demonstrate an overall stable performance with a clear improvement over existing techniques in the case of flat (but not exponentially flat) optimization landscapes. qBang introduces a new development strategy for gradient -based VQAs with a plethora of possible improvements.
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| 5. |
- Gidney, Craig, et al.
(author)
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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
- 2021
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In: QUANTUM. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 5, s. 433-
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Journal article (peer-reviewed)abstract
- We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Niu 1996, Zalka 2006, Fowler 2012, Ekera-Hastad 2017, Ekerg, 2017, EkerS, 2018, Gidney-Fowler 2019, Gidney 2019. We estimate the approximate cost of our construction using plausible physical assumptions for large-scale superconducting qubit platforms: a planar grid of qubits with nearest-neighbor connectivity, a characteristic physical gate error rate of 10(-3), a surface code cycle time of 1. microsecond, and a reaction time of 1.0 microseconds. We account for factors that are normally ignored such as noise, the need to make repeated attempts, and the spacetime layout of the computation. When factoring 2048 bit RSA integers, our construction's spacetime volume is a hundredfold less than comparable estimates from earlier works (Van Meter et al. 2009, Jones et al. 2010, Fowler et al. 2012, Gheorghiu et al. 2019). In the abstract circuit model (which ignores overheads from distillation, routing, and error correction) our construction uses 3n + 0.002n lg n logical qubits, 0.3n(3) + 0.0005n(3) lg n Toffolis, and 500n(2) +n(2) lg n measurement depth to factor n-bit RSA integers. We quantify the cryptographic implications of our work, both for RSA and for schemes based on the DLP in finite fields.
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| 6. |
- Li, Boxi, et al.
(author)
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Pulse-level noisy quantum circuits with QuTiP
- 2022
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In: Quantum. - 2521-327X. ; 6
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Journal article (peer-reviewed)abstract
- The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate- Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip, QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad densitymatrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch- Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce exper- imental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.
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| 7. |
- Mackel, Naim E., et al.
(author)
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Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
- 2023
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In: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 7
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Journal article (peer-reviewed)abstract
- Many-particle quantum systems with intermediate anyonic exchange statistics are supported in one spatial dimension. In this context, the anyon-anyon mapping is recast as a continuous transformation that generates shifts of the statistical parameter K. We characterize the geometry of quantum states associated with different values of K, i.e., different quantum statistics. While states in the bosonic and fermionic subspaces are always orthogonal, overlaps between anyonic states are generally finite and exhibit a universal form of the orthogonality catastrophe governed by a fundamental statistical factor, indespeed limits on the flow of K, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.
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| 8. |
- Paczos, Jerzy, 1999-, et al.
(author)
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Quantum time dilation in a gravitational field
- 2024
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In: Quantum. - 2521-327X. ; 8
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Journal article (peer-reviewed)abstract
- According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.
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| 9. |
- Sanz, Mikel, et al.
(author)
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Electro-mechanical Casimir effect
- 2018
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In: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 2
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Journal article (peer-reviewed)abstract
- The dynamical Casimir effect is an intriguing phenomenon in which photons are generated from vacuum due to a non-adiabatic change in some boundary conditions. In particular, it connects the motion of an accelerated mechanical mirror to the generation of photons. While pioneering experiments demonstrating this effect exist, a conclusive measurement involving a mechanical generation is still missing. We show that a hybrid system consisting of a piezoelectric mechanical resonator coupled to a superconducting cavity may allow to electro-mechanically generate measurable photons from vacuum, intrinsically associated to the dynamical Casimir effect. Such an experiment may be achieved with current technology, based on film bulk acoustic resonators directly coupled to a superconducting cavity. Our results predict a measurable photon generation rate, which can he further increased through additional improvements such as using superconducting metamaterials.
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| 10. |
- Sowa, Artur, et al.
(author)
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Solving the Bose-Hubbard model in new ways
- 2022
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In: QUANTUM. - : VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF. - 2521-327X. ; 6
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Journal article (peer-reviewed)abstract
- We introduce a new method for analysing the Bose-Hubbard model for an array of boson sites with nearest neighbor interactions. It is based on a number-theoretic implementation of the creation and annihilation operators that constitute the model. One of the advantages of this approach is that it facilitates accurate computations involving multi-particle states. In particular, we provide a rigorous computer assisted proof of quantum phase transitions in finite systems of this type. Furthermore, we investigate properties of the infinite array via harmonic analysis on the multiplicative group of positive rationals. This furnishes an isomorphism that recasts the underlying Fock space as an infinite tensor product of Hecke spaces, i.e., spaces of square-integrable periodic functions that are a superposition of non-negative frequency harmonics. Under this isomorphism, the number-theoretic creation and annihilation operators are mapped into the Kastrup model of the harmonic oscillator on the circle. It also enables us to highlight a kinship of the model at hand with an array of spin moments with a local anisotropy field. This identifies an interesting physical system that can be mapped into the model at hand.
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| 11. |
- Srivastava, Basudha, 1996, et al.
(author)
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The XYZ^2 hexagonal stabilizer code
- 2022
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In: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 6
-
Journal article (peer-reviewed)abstract
- We consider a topological stabilizer code on a honeycomb grid, the "XYZ2" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302 (2015)], with a specific implementation of the boundary. It utilizes weight-six (XYZXYZ) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d2 qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y, or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50%. In contrast to the rotated surface code and the XZZX code, which have code distance d2 only for pure Y noise, here the code distance is 2d2 for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.
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| 12. |
- Srivastava, Basudha, et al.
(author)
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The XYZ(2) hexagonal stabilizer code
- 2022
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In: Quantum. - 2521-327X. ; 6, s. 698-
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Journal article (peer-reviewed)abstract
- We consider a topological stabilizer code on a honeycomb grid, the "XYZ(2) " code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [1], with a specific implementation of the boundary. It utilizes weight-six (XYZXYZ) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d(2) qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y, or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50 %. In contrast to the rotated surface code and the XZZX code, which have code distance d(2) only for pure Y noise, here the code distance is 2d(2) for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.
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| 13. |
- Tang, W., et al.
(author)
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Non-ergodic delocalized phase with Poisson level statistics
- 2022
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In: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 6
-
Journal article (peer-reviewed)abstract
- Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space. On the above example, we formulate general conditions to a single-particle and random-matrix models in order to carry such states, based on the transparent generalization of the Anderson localization of single-particle states and multiple resonances.
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