# Strengths and Weaknesses of Quantum Computing

@article{Bennett1997StrengthsAW, title={Strengths and Weaknesses of Quantum Computing}, author={C. H. Bennett and Ethan Bernstein and G. Brassard and U. Vazirani}, journal={SIAM J. Comput.}, year={1997}, volume={26}, pages={1510-1523} }

Recently a great deal of attention has been focused on quantum computation following a sequence of results [Bernstein and Vazirani, in Proc. 25th Annual ACM Symposium Theory Comput., 1993, pp. 11--20, SIAM J. Comput., 26 (1997), pp. 1277--1339], [Simon, in Proc. 35th Annual IEEE Symposium Foundations Comput. Sci., 1994, pp. 116--123, SIAM J. Comput., 26 (1997), pp. 1340--1349], [Shor, in Proc. 35th Annual IEEE Symposium Foundations Comput. Sci., 1994, pp. 124--134] suggesting that quantumâ€¦Â Expand

#### Topics from this paper

#### Paper Mentions

#### 1,171 Citations

Quantum Computability

- Computer Science, Mathematics
- SIAM J. Comput.
- 1997

It is shown that when quantum Turing machines are restricted to have transition amplitudes which are algebraic numbers, BQP, EQP, and nondeterministic quantum polynomial time (NQP) are all contained in PP, hence in P and PSPACE. Expand

Fourier Transforms and Quantum Computation

- Computer Science
- Theoretical Aspects of Computer Science
- 2000

This survey paper focusses on presenting the essential ideas in a simple way, rather than getting the best results. Expand

Quantum and classical tradeoffs

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2004

This paper presents two results on the study of quantifying the quantumness of a quantum circuit by the number of gates that do not preserve the computational basis, as a means to understand the nature of quantum algorithmic speedups. Expand

Evolutionary Algorithms for Quantum Computers

- Computer Science
- Algorithmica
- 2013

It turns out that the advantage of the respective quantum search heuristic over its classical counterpart varies with the problem structure and ranges from no speedup at all for the problem Discrepancy to exponential speedup for the problems TinyTrap. Expand

On quantum computation theory

- Computer Science
- 2002

The content of the Chapters 3 through 7 of this Ph.D. thesis corresponds with the following articles written by the author. Chapter 3: Quantum Oracle Interrogation â€¢ â€œQuantum Oracle Interrogation:â€¦ Expand

Quantum Complexity Theory

- Computer Science
- SIAM J. Comput.
- 1997

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation. Expand

Quantum Computation

- Physics
- 1998

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, ifâ€¦ Expand

Quantum algorithms and learning theory

- Computer Science
- 2018

A quantum algorithm to solve a search space of N elements using essentially sqrt{N} queries and other operations, improving over the gate count of Grover's algorithm is described. Expand

The complexity of the consistency and N-representability problems for quantum states - eScholarship

- Mathematics, Physics
- 2007

Quantum mechanics has important consequences for machines that store and manipulate information. In particular, quantum computers might be more powerful than classical computers; examples of thisâ€¦ Expand

Quantum computing : pro and con BY JOHN PRESKILL

- 1997

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and considerâ€¦ Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

Quantum Complexity Theory

- Computer Science
- SIAM J. Comput.
- 1997

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation. Expand

A fast quantum mechanical algorithm for database search

- Computer Science, Physics
- STOC '96
- 1996

In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . Expand

The quantum challenge to structural complexity theory

- Computer Science
- [1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference
- 1992

There are cryptographic tasks that are demonstrably impossible to implement with unlimited computing power probabilistic interactive turning machines, yet they can be implemented even in practice by quantum mechanical apparatus. Expand

Quantum theory, the Churchâ€“Turing principle and the universal quantum computer

- Mathematics
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1985

It is argued that underlying the Churchâ€“Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: â€˜every finitely realizibleâ€¦ Expand

Algorithms for quantum computation: discrete logarithms and factoring

- Mathematics, Computer Science
- Proceedings 35th Annual Symposium on Foundations of Computer Science
- 1994

Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given. Expand

Tight bounds on quantum searching

- Computer Science, Physics
- 1996

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

Quantum Circuit Complexity

- Mathematics, Computer Science
- FOCS
- 1993

It is shown that any function computable in polynomial time by a quantum Turing machine has aPolynomial-size quantum circuit, and this result enables us to construct a universal quantum computer which can simulate a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them. Expand

Oracle Quantum Computing

- Computer Science
- 1994

Oracles are constructed relative to which there is a decision problem that can be solved with certainty in worst-case polynomial time on the quantum computer, yet it cannot be solved classically in probabilistic expected polynometric time if errors are not tolerated. Expand

Learning DNF over the uniform distribution using a quantum example oracle

- Computer Science, Mathematics
- COLT '95
- 1995

It is shown that DNF is efficiently learnable with respect to the uniform distribution by a quantum algorithm using a quantum example oracle, and the notion of classification noise to the quantum setting is generalized and shows that the quantum DNF algorithm learns even in the presence of such noise. Expand

Reversibility and stability of information processing systems

- Physics
- 1984

Classical and quantum models of dynamically reversible computers are considered. Instabilities in the evolution of the classical ''billiard ball computer'' are analyzed and shown to result in aâ€¦ Expand