# Quantum Circuit Complexity

@inproceedings{Yao1993QuantumCC, title={Quantum Circuit Complexity}, author={Andrew Chi-Chih Yao}, booktitle={FOCS}, year={1993} }

We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by… Expand

#### 705 Citations

Quantum computers that can be simulated classically in polynomial time

- Computer Science
- STOC '01
- 2001

It is shown that two-bit operations characterized by 4 \times 4 matrices in which the sixteen entries obey a set of five polynomial relations can be composed according to certain rules to yield a class of circuits that can be simulated classically in polynometric time. Expand

On the Complexity of Quantum Languages

- Physics, Mathematics
- 2005

The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of {0, 1} � . However, a quantum machine can also… Expand

Quantum complexity theory

- Computer Science
- STOC '93
- 1993

This dissertation proves that relative to an oracle chosen uniformly at random, the class NP cannot be solved on a quantum Turing machine in time $o(2\sp{n/2}).$ and gives evidence suggesting that quantum Turing Machines cannot efficiently solve all of NP. 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 Turing Machines Computations and Measurements

- Computer Science
- ArXiv
- 2017

A new formulation of Quantum Turing Ma- chines is proposed, as an extension of those proposed by Bernstein and Vazirani, to define a class of quantum computable functions - any such a function is a mapping from a general quantum state to a distribution of probability of natural numbers. Expand

Quantum computing and quantum complexity theory

- Computer Science
- 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353)
- 2000

This paper will describe two formal models for quantum computers: quantum circuits and quantum Turing Machines, introduced by Deutsch [1985]. Expand

A SCHEMATIC DEFINITION OF QUANTUM POLYNOMIAL TIME COMPUTABILITY

- Computer Science, Mathematics
- The Journal of Symbolic Logic
- 2020

A new, schematic definition of quantum functions mapping finite-dimensional Hilbert spaces to themselves, which avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Expand

An Introduction to Quantum Complexity Theory

- Physics
- 1999

In 1985, D. Deutsch introduced quantum Turing machines (QTMs for short) as Turing machines which can perform so called quantum parallel computations. Then, in 1994, P. Shor showed that QTM can factor… Expand

Quantum branching programs and space-bounded nonuniform quantum complexity

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2005

It is shown that non-uniform quantum Turing machines with algebraic amplitudes and QBPs with a suitable analogous set of amplitudes are equivalent in computational power if both models work with bounded or unbounded error. Expand

On the Power of Quantum Computation

- Computer Science
- SIAM J. Comput.
- 1997

This work presents a problem of distinguishing between two fairly natural classes of functions, which can provably be solved exponentially faster in the quantum model than in the classical probabilistic one, when the function is given as an oracle drawn equiprobably from the uniform distribution on either class. Expand

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