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ConstantDepth Quantum Circuits with Gates for Addition
"... Abstract. We investigate a class QNC 0 (ADD) that is QNC 0 with gates for addition of two binary numbers, where QNC 0 is a class consisting of quantum operations computed by constantdepth quantum ..."
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Abstract. We investigate a class QNC 0 (ADD) that is QNC 0 with gates for addition of two binary numbers, where QNC 0 is a class consisting of quantum operations computed by constantdepth quantum
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 ..."
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Cited by 19 (1 self)
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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
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2004
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1 ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. 1
Adaptive Quantum Computation, Constant Depth Quantum Circuits and ArthurMerlin Games
, 2003
"... We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. We show that if an efficient ‘cou ..."
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We present evidence that there exist quantum computations that can be carried out in constant depth, using 2qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. We show that if an efficient
A New Lower Bound Technique for Quantum Circuits without Ancillæ
"... We present a technique to derive depth lower bounds for quantum circuits. The technique is based on the observation that in circuits without ancillæ, only a few input states can set all the control qubits of a Toffoli gate to 1. This can be used to selectively remove large Toffoli gates from a quant ..."
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quantum circuit while keeping the cumulative error low. We use the technique to give another proof that parity cannot be computed by constant depth quantum circuits without ancillæ. 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
NonIdentity Check Remains QMAComplete for Short Circuits
, 2008
"... The NonIdentity Check problem asks whether a given a quantum circuit is far away from the identity or not. It is well known that this problem is QMAComplete [14]. In this note, it is shown that the NonIdentity Check problem remains QMAComplete for circuits of short depth. Specifically, we prove ..."
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Cited by 4 (0 self)
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that for constant depth quantum circuit in which each gate is given to at least Ω(log n) bits of precision, the NonIdentity Check problem is QMAComplete. It also follows that the hardness of the problem remains for polylogarithmic depth circuit consisting of only gates from any universal gate set
Results 1  10
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2,332