Results 1  10
of
38
Improved simulation of stabilizer circuits
 Phys. Rev. Lett
"... The GottesmanKnill theorem says that a stabilizer circuit—that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates—can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. • By removing the need for Gaussian elimination, we ..."
Abstract

Cited by 65 (6 self)
 Add to MetaCart
The GottesmanKnill theorem says that a stabilizer circuit—that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates—can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. • By removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freelyavailable program called CHP (CNOTHadamardPhase), which can handle thousands of qubits easily. • We show that the problem of simulating stabilizer circuits is complete for the classical complexity class ⊕L, which means that stabilizer circuits are probably not even universal for classical computation. • We give efficient algorithms for computing the inner product between two stabilizer states, putting any nqubit stabilizer circuit into a “canonical form ” that requires at most O ( n 2 /log n) gates, and other useful tasks. • We extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of nonstabilizer gates, and circuits acting on general tensorproduct initial states but containing only a limited number of measurements. 1
Architectural implications of quantum computing technologies
 ACM Journal on Emerging Technologies in Computing Systems (JETC
, 2006
"... In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, ..."
Abstract

Cited by 27 (4 self)
 Add to MetaCart
In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss clusterstate quantum computation.
Circuit for Shor’s algorithm using 2n+3 qubits
 54
, 2002
"... We try to minimize the number of qubits needed to factor an integer of n bits using Shor’s algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n 3 lg(n)) elementary quantum gates in a depth of O(n 3) to implement the factorization algorithm. The circuit is computable ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
We try to minimize the number of qubits needed to factor an integer of n bits using Shor’s algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n 3 lg(n)) elementary quantum gates in a depth of O(n 3) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored. 1
Quantum Circuits with Unbounded Fanout
 20th STACS Conference, 2003, LNCS 2607
, 2003
"... Abstract. We demonstrate that the unbounded fanout gate is very powerful. Constantdepth polynomialsize quantum circuits with bounded fanin and unbounded fanout over a fixed basis (denoted by QNC 0 f) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, maj ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We demonstrate that the unbounded fanout gate is very powerful. Constantdepth polynomialsize quantum circuits with bounded fanin and unbounded fanout over a fixed basis (denoted by QNC 0 f) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and counting. Classically, we need logarithmic depth even if we can use unbounded fanin gates. If we allow arbitrary onequbit gates instead of a fixed basis, then these circuits can also be made exact in logstar depth. Sorting, arithmetical operations, phase estimation, and the quantum Fourier transform can also be approximated in constant depth. 1
Bounds on the power of constantdepth quantum circuits. Preprint: quantph/0312209
 In Proc. 15th International Symposium on on Fundamentals of Computation Theory (FCT 2005), volume 3623 of Lecture Notes in Computer Science
, 2004
"... We show that if a language is recognized within certain error bounds by constantdepth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ɛ ≤ δ ≤ 1, we define BQNC 0 ɛ,δ to be the class of languages recognized by constant d ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
We show that if a language is recognized within certain error bounds by constantdepth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ɛ ≤ δ ≤ 1, we define BQNC 0 ɛ,δ to be the class of languages recognized by constant depth, polynomialsize quantum circuits with acceptance probability either < ɛ (for rejection) or ≥ δ (for acceptance). We show that BQNC 0 ɛ,δ ⊆ P, provided that 1 − δ ≤ 2 −2d (1 − ɛ), where d is the circuit depth. On the other hand, we adapt and extend ideas of Terhal & DiVincenzo [TD04] to show that, for any family F of quantum gates including Hadamard and CNOT gates, computing the acceptance probabilities of depthfive circuits over F is just as hard as computing these probabilities for arbitrary quantum circuits over F. In particular, this implies that NQNC 0 = NQACC = NQP = coC=P, where NQNC 0 is the constantdepth analog of the class NQP. This essentially refutes a conjecture of Green et al. that NQACC ⊆ TC 0 [GHMP02]. 1
Counting, Fanout, And The Complexity Of Quantum Acc
, 2002
"... q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upp ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
(Show Context)
q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We dene classes of languages closely related to QACC[2] and show that restricted versions of them can be simulated by polynomialsize circuits. With further restrictions, language classes related to QACC[2] operators can be simulated by classical threshold circuits of polynomial size and constant depth. Keywords: quantum computation, quantum & circuit complexity, threshold circuit Communicated by : R Cleve & J Watrous 1. Introduction Advances in quantum computation
Quantum Circuits: Fanout, Parity, and Counting
 In Los Alamos Preprint archives
, 1999
"... Abstract. We propose definitions of QAC 0, the quantum analog of the classical class AC 0 of constantdepth circuits with AND and OR gates of arbitrary fanin, and QACC 0 [q], where nary MODq gates are also allowed. We show that it is possible to make a ‘cat ’ state on n qubits in constant depth if ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We propose definitions of QAC 0, the quantum analog of the classical class AC 0 of constantdepth circuits with AND and OR gates of arbitrary fanin, and QACC 0 [q], where nary MODq gates are also allowed. We show that it is possible to make a ‘cat ’ state on n qubits in constant depth if and only if we can construct a parity or MOD2 gate in constant depth; therefore, any circuit class that can fan out a qubit to n copies in constant depth also includes QACC 0 [2]. In addition, we prove the somewhat surprising result that parity or fanout allows us to construct MODq gates in constant depth for any q, so QACC 0 [2] = QACC 0. Since ACC 0 [p] ̸ = ACC 0 [q] whenever p and q are mutually prime, QACC 0 [2] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. 1