The ‘threat’ from cleaner water and air

Capus, Joseph

doi:10.1016/0026-0657(94)91518-0

Cited by 3 publications

(3 citation statements)

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“…While alternative fault-tolerance methods such as completely transversal Clifford + T scheme [12] and anyonic quantum computing [13] are also being explored, minimization of the number of T gates in quantum circuits remain an important and widely studied goal. With recent advances in quantum information processing technologies [14][15][16][17] and fault-tolerant thresholds [7,18,19], as scalable quantum computation is appearing more and more viable [20] we need efficient automated design tools targeting fault-tolerant quantum computers.…”

Section: Introductionmentioning

confidence: 99%

A polynomial time and space heuristic algorithm for T-count

Mosca¹,

Mukhopadhyay²

2021

Quantum Sci. Technol.

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An important part of reaping computational advantage from a quantum computer is to reduce the quantum resources needed to implement a desired quantum algorithm. Quantum algorithms that are too large to be practical on noisy intermediate scale quantum devices will require fault-tolerant error correction. This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set. More specifically, in this paper we consider the group of unitaries that can be exactly implemented by a quantum circuit consisting of the Clifford + T gate set. The Clifford + T gate set is a universal gate set and in this group, using state-of-the-art surface codes, the T gate is by far the most expensive component to implement fault-tolerantly. So it is important to minimize the number of T gates necessary for a fault-tolerant implementation. Our primary interest is to compute a circuit for a given n-qubit unitary U, using the minimum possible number of T gates (called the T-count of unitary U). We consider the problem COUNT-T, the optimization version of which aims to find the T-count of U. In its decision version the goal is to decide if the T-count is at most some positive integer m. Given an oracle for COUNT-T, we can compute a T-count-optimal circuit in time polynomial in the T-count and dimension of U. We give a provable classical algorithm that solves COUNT-T (decision) in time O N 2(c−1) m c poly(m, N) and space O N 2 m c poly(m, N) , where N = 2 n and c 2. This gives a space-time trade-off for solving this problem with variants of meet-in-the-middle techniques. We also introduce an asymptotically faster multiplication method that shaves a factor of N 0.7457 off of the overall complexity. Lastly, beyond our improvements to the rigorous algorithm, we give a heuristic algorithm that outputs a T-count-optimal circuit and has space and time complexity poly(m, N), under some assumptions. In our heuristic algorithm we developed a novel way of pruning the search space. While our heuristic method still scales exponentially with the number of qubits (though with a lower exponent), there is a large improvement by going from exponential to polynomial scaling with m. We implemented our heuristic algorithm with up to 4 qubit unitaries and obtained a significant improvement in time. For all benchmark and random unitaries we studied, the T-count returned by our algorithm is at most the T-count of their circuits shown in previous papers. iπ 4 P.Roughly speaking, each R(P) can be implemented with a circuit consisting of only one T gate. More detail has been given in section 2.2. Operator P is an n-qubit non-identity Pauli operator (defined in section A.1). We developed a fast algorithm in section 3 that computes W in time O(N 4 ). Currently the fastest algorithm

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Section: Introductionmentioning

confidence: 99%

A polynomial time and space heuristic algorithm for T-count

Mosca¹,

Mukhopadhyay²

2021

Quantum Sci. Technol.

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“…Production of powders consisting of carbon and metallic nano-and micro-particles excites considerable interest because their broad use in microelectronics, metallurgy, surface modification, catalysis and biological labeling [1][2][3]. Recently a technique based on an arc discharge with carbon and metal (e.g.…”

Section: Introductionmentioning

confidence: 99%

Ni–C powder synthesis by a submerged pulsed arc in breakdown mode

Parkansky

Frenkel

Alterkop

et al. 2008

Journal of Alloys and Compounds

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“…In recent years, the study of nano-sized materials such as nanocomposites has attracted considerable interest due to their usefulness in microelectronic devices, metallurgy, surface modification, catalysis, biological labeling, photonics and information storage [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Nanomaterials and Nanocomposites with Complex Shapes through Arc Discharge in Foam

Kim

Nishikawa

Sano

2009

e-J. Surf. Sci. Nanotechnol.

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Several types of carbon nanomaterial were produced using a simple method involving arc discharge in foam, and Fe-C composite materials were produced using this technique in foam containing Fe particles. In TEM observation, it was observed that the surfaces of the Fe particles were covered with a 20-50 carbon layer. Spherical objects with complex shapes were also observed on the nanomaterials, and varied from 200 nm to above 600 nm in size. It was found that these spherical objects formed a twisted graphite sheet.

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The ‘threat’ from cleaner water and air

Cited by 3 publications

References 0 publications

A polynomial time and space heuristic algorithm for T-count

A polynomial time and space heuristic algorithm for T-count

Ni–C powder synthesis by a submerged pulsed arc in breakdown mode

Synthesis of Nanomaterials and Nanocomposites with Complex Shapes through Arc Discharge in Foam

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