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2,547
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 ..."
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Cited by 18 (2 self)
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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
Quantum fanout is powerful
 Theory of Computing
"... 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, thr ..."
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Cited by 9 (0 self)
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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
Quantum Fanout is Powerful
, 2004
"... 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 QNC0 f) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, major ..."
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, and the quantum Fourier transform with arbitrary moduli can also be approximated in constant depth. ACM Classification: F.2.1, F.2.2 AMS Classification: 68Q15, 81P68 Key words and phrases: quantum computing, quantum circuits, fanout, quantum Fourier transform, constant depth circuits, threshold circuits 1
Quantum Lower Bounds for Fanout
, 2003
"... We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Tooli gates, and when they use only constantly many ancill. Under this constraint, t ..."
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Cited by 9 (3 self)
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We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Tooli gates, and when they use only constantly many ancill. Under this constraint
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 ..."
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Cited by 17 (1 self)
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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
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 ..."
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Cited by 19 (1 self)
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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
On the Complexity of Quantum ACC
 in Fifteenth Annual Conference on Computational Complexity Theory, IEEE Computer
, 2000
"... For any q> 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t> 1, MODq is equivalent to MODt (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC (0) , ACC[q], and ACC, denoted ..."
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Cited by 6 (1 self)
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For any q> 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t> 1, MODq is equivalent to MODt (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC (0) , ACC[q], and ACC, denoted
On the Complexity of Quantum ACC
 in Fifteenth Annual Conference on Computational Complexity Theory, IEEE Computer
, 2000
"... For any q?1, let MOD q be a quantum gate that determines if the number of 1's in the input is divisible by q.Weshow that for any q# t ? 1, MOD q is equivalent to MOD t (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC ,ACC[q], and ACC, denoted ..."
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For any q?1, let MOD q be a quantum gate that determines if the number of 1's in the input is divisible by q.Weshow that for any q# t ? 1, MOD q is equivalent to MOD t (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC ,ACC[q], and ACC
Elementary Gates for Quantum Computation
, 1995
"... We show that a set of gates that consists of all onebit quantum gates (U(2)) and the twobit exclusiveor gate (that maps Boolean values (x,y) to (x,x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We in ..."
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Cited by 276 (11 self)
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We show that a set of gates that consists of all onebit quantum gates (U(2)) and the twobit exclusiveor gate (that maps Boolean values (x,y) to (x,x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We
Results 1  10
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2,547