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An efficient quantum algorithm for preparation of uniform quantum superposition states

Alok Shukla, Prakash Vedula

arXiv:2306.11747Quantum Information ProcessingJan 29, 202429 citations

Single-Pulse Preparation of the Uniform Superpositional State used in Quantum Algorithms

Berman, G P, Borgonovi, F, Izrailev, F M +1 more

We examine a single-pulse preparation of the uniform superpositional wave function, which includes all basis states, in a spin quantum computer. The effective energy spectrum and the errors generated by this pulse are studied in detail. We show that, in spite of the finite width of the energy spectrum bands, amplitude and phase errors can be made reasonably small.

Jun 21, 20003 citations

Automatic Uniform Quantum State Preparation Using Decision Diagrams

Fereshte Mozafari, Mathias Soeken, Heinz Riener +1 more

Most quantum algorithms assume some specific initial state in superposition of basis states before performing the desired application-specific computations. The preparation of such states itself requires a computation performed by a quantum circuit. In this paper, we investigate the automatic state preparation of a specific subset of quantum states that are uniform superpositions over a subset of basis states, called uniform quantum states. We exploit that such states can be represented using Boolean functions and present a recursive algorithm based on functional decomposition. When using binary decision diagrams as function representation, we can enable fast and scalable quantum state preparation with respect to the size of the decision diagram. We show that the algorithm can find quantum circuits for functions, where state-of-the-art algorithms cannot be applied anymore.Most quantum algorithms assume some specific initial state in superposition of basis states before performing the desired application-specific computations. The preparation of such states itself requires a computation performed by a quantum circuit. In this paper, we investigate the automatic state preparation of a specific subset of quantum states that are uniform superpositions over a subset of basis states, called uniform quantum states. We exploit that such states can be represented using Boolean functions and present a recursive algorithm based on functional decomposition. When using binary decision diagrams as function representation, we can enable fast and scalable quantum state preparation with respect to the size of the decision diagram. We show that the algorithm can find quantum circuits for functions, where state-of-the-art algorithms cannot be applied anymore.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)Nov 1, 202010 citations

Single-Atom Indexing of Quantum State Superpositions

Christopher Moon, Christopher P. Lutz, D. M. Eigler +1 more

Bulletin of the American Physical SocietyMar 14, 20060 citations

Minimum-time generation of a uniform superposition in a qubit with only transverse field control

Vasileios Evangelakos, Emmanuel Paspalakis, Dionisis Stefanatos

We consider a two-level system with a fixed energy spacing (detuning) between the two levels and a single transverse control field which can take values between zero and a maximum amplitude. Using Pontryagin's maximum principle, we completely solve the problem of generating in minimum time a uniform superposition of the two quantum states when starting from one of them, for all the values of the ratio between the maximum control amplitude and the detuning. For each value of this ratio we find the optimal pulse sequence to have the bang-bang form and calculate the durations of the pulses composing it. The suggested framework is not only restricted to the problem at hand, but it can be also exploited in the problem of fast charging a quantum battery based on a two-level system, as well as for the optimization of pulse sequences used for the controlled preparation of the excited state in a quantum emitter, which is a prerequisite for its usage as a single-photon source.We consider a two-level system with a fixed energy spacing (detuning) between the two levels and a single transverse control field which can take values between zero and a maximum amplitude. Using Pontryagin's maximum principle, we completely solve the problem of generating in minimum time a uniform superposition of the two quantum states when starting from one of them, for all the values of the ratio between the maximum control amplitude and the detuning. For each value of this ratio we find the optimal pulse sequence to have the bang-bang form and calculate the durations of the pulses composing it. The suggested framework is not only restricted to the problem at hand, but it can be also exploited in the problem of fast charging a quantum battery based on a two-level system, as well as for the optimization of pulse sequences used for the controlled preparation of the excited state in a quantum emitter, which is a prerequisite for its usage as a single-photon source.

arXiv:2312.16744Physical Review ADec 26, 202311 citations

Single-atom gating of quantum-state superpositions

Christopher Moon, Christopher P. Lutz, Hari C. Manoharan

arXiv:0904.2884Nature PhysicsApr 6, 200837 citations

Single-pulse preparation of the uniform superpositional state used in quantum algorithms

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