Efficient state preparation for a register of quantum bits (13 pages)

@article{Soklakov2004EfficientSP,
  title={Efficient state preparation for a register of quantum bits (13 pages)},
  author={Andrei N. Soklakov and R. Schack},
  journal={Physical Review A},
  year={2004},
  volume={73},
  pages={12307}
}
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register. 
Double sparse quantum state preparation
TLDR
This work proposes a quantum state preparation algorithm called CVO-QRAM with computational cost O(kM), where M is the number of nonzero probability amplitudes and k is the maximum number of bits with value 1 in the patterns to be stored. Expand
State preparation based on quantum phase estimation
TLDR
This work decomposes the diagonal unitary operators included in the phase estimation algorithms into the basic gates in a deterministic and a probabilistic state preparation algorithm to discuss the gate complexity in these algorithms. Expand
Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms
In this review article, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware.Expand
Fast black-box quantum state preparation based on linear combination of unitaries
TLDR
This work proposes to perform black-box state preparation using the technique of linear combination of unitaries (LCU) with improved results by reducing the required additional qubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision n. Expand
Efficient Quantum Algorithms for GHZ and W States, and Implementation on the IBM Quantum Computer
TLDR
Efficient algorithms with logarithmic step complexities for the generation of entangled GHZ and W states useful for quantum networks are proposed and an implementation on the IBM quantum computer up to N=16 is demonstrated. Expand
Preparation of many-body states for quantum simulation.
TLDR
The present algorithm is able to prepare general pure and mixed many-particle states of any number of particles and operates in time that is polynomial in all the essential descriptors of the system, the number ofarticles, the resolution of the lattice, and the inverse of the maximum final error. Expand
Parallel quantum trajectories via forking for sampling without redundancy
TLDR
A framework based on quantum forking is presented that bypasses this fundamental issue and expedites a family of tasks that require sampling from independent quantum processes and is demonstrated via applications to implementing non-unitary quantum channels, studying entanglement and benchmarking quantum control. Expand
Fast Black-Box Quantum State Preparation
TLDR
This work reduces the required qubit overhead from g to $\log_2(g)$ in the bit precision, and shows how various sets of coefficients can be loaded significantly faster than in $O(\sqrt N)$ rounds of amplitude amplification by bootstrapping the procedure with an optimised initial state. Expand
Quantum Algorithm Design: Techniques and Applications
TLDR
An overview of the development of quantum algorithms, then five important techniques are investigated: Quantum phase estimation, linear combination of unitaries, quantum linear solver, Grover search, and quantum walk, together with their applications in quantum state preparation, quantum machine learning, and Quantum search. Expand
Using Quantum Computers for Quantum Simulation
TLDR
The theoretical and experimental development of quantum simulation using quantum computers is surveyed, from the first ideas to the intense research efforts currently underway. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 41 REFERENCES
EFFICIENT ALGORITHM FOR INITIALIZING AMPLITUDE DISTRIBUTION OF A QUANTUM REGISTER
TLDR
An efficient algorithm which requires a polynomial number of elementary operations for initializing the amplitude distribution of a quantum register is presented. Expand
Efficient scheme for initializing a quantum register with an arbitrary superposed state
Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as \i(1)i(2)...i(n)> withExpand
State preparation based on Grover’s algorithm in the presence of global information about the state
TLDR
The alternative algorithm is considerably simpler than the one described previously, on the assumption that a sufficient amount of knowledge about the distribution of the absolute values of the complex amplitudes is available. Expand
Efficient State Preparation via Ion Trap Quantum Computing and Quantum Searching Algorithm
We present a scheme to-prepare a quantum state in an ion trap with probability approaching to one by means of ion trap quantum computing and Grover's quantum search algorithm acting on trapped ions.
Simulating quantum systems on a quantum computer
  • Christof Zalka
  • Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
We show that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer. The time needed for such aExpand
Quantum algorithms revisited
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantumExpand
Quantum Simulations on a Quantum Computer
We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonicExpand
Grover's quantum search algorithm for an arbitrary initial amplitude distribution
Grover’s algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First-order linear difference equations are found for the time evolution of theExpand
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Quantum mechanics can speed up a range of search applications over unsorted data. For example, imagine a phone directory containing $N$ names arranged in completely random order. To find someone'sExpand
Tight bounds on quantum searching
TLDR
A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table. Expand
...
1
2
3
4
5
...