Faster quantum chemistry simulation on fault-tolerant quantum computers

Jones, N. Cody; Whitfield, James D.; McMahon, Peter L.; Yung, Man Hong; Meter, Rodney Van; Aspuru‐Guzik, Alán; Yamamoto, Yoshihisa

doi:10.1088/1367-2630/14/11/115023

Cited by 110 publications

(64 citation statements)

References 69 publications

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“…Other operations in a quantum algorithm like routing of qubits for long-range interactions may become important. The resource savings factor for the entire algorithm will always be less than that for the individual Toffoli gates; still, most quantum algorithms like factoring [6,7,33] and simulation [34,35] benefit substantially from a more efficient Toffoli construction.…”

Section: Discussionmentioning

confidence: 99%

“…We propose the term quantum logic synthesis for methods of synthesizing arbitrary-size, fault-tolerant quantum logic networks in a hierarchical arrangement of preparation and teleportation. The possible techniques go far beyond "sequential" decompositions [6][7][8]35], where a quantum algorithm is decomposed into a long sequence of fundamental gates from a small set. For each fundamental gate, faulttolerant constructions are known, but the cost of each is high because every operation must have very low error rate.…”

Section: Discussionmentioning

confidence: 99%

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Composite Toffoli gate with two-round error detection

Jones

2013

Phys. Rev. A

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We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for quantum computers by more than an order of magnitude. The procedure uses Clifford operations and 64 copies of the non-Clifford gate $T = \exp[i \pi (I - \sigma^z) /8]$. Quantum codes detect errors in the circuit. When the dominant source of error is $T$-gate failure with probability $p$, then the composite Toffoli circuit has postselected failure rate of $3072p^4$ to lowest order.Comment: 8 pages, 8 figure

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Composite Toffoli gate with two-round error detection

Jones

2013

Phys. Rev. A

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“…In faster quantum chemistry on fault tolerant quantum computers by Jones et al [32], the authors investigate how quantum simulations addressing quantum chemistry could be implemented within a device that already incorporates quantum error correction and therefore provides fault-tolerance, that is, already requires the main ingredients for universal quantum computation. They examine how to improve the efficiency in general and analyse, as a specific example, the ground-state energy calculation for lithium hydride.…”

Section: Relativistic Physicsmentioning

confidence: 99%

Focus on quantum simulation

Schaetz

Monroe

Esslinger³

2013

New J. Phys.

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The endeavour to control increasingly larger systems of particles at the quantum level is a natural goal, and will be a driving force for the physical sciences in the coming decades. The control of a many-body system at the highest level possible can indeed be regarded as the ultimate form of engineering. Within this general research avenue, building quantum simulators and performing experimental quantum simulations will play a key role. A quantum simulator is a promising candidate to become the first application of quantum information science reaching beyond classical limitations [1], since the requirements on the number of quantum particles and fidelities of operations are predicted to be substantially relaxed compared to that envisioned for a universal quantum computer. This issue forms an extensive open-access resource spanning the various areas of experimental quantum simulation, from its relation to quantum information processing to its potential use for different applications.

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“…The details necessary for the simulation can be found elsewhere 18 including the desiderata for faulttolerant quantum simulations. 25 As a second example to illustrate the Wigner projections, consider cyclopropenyl cation, C 3 H + 3 , with D 3h symmetry in the second quantized representation. We restrict attention to the C 3 subgroup which has only one dimensional IRs.…”

Section: Examplesmentioning

confidence: 99%

Communication: Spin-free quantum computational simulations and symmetry adapted states

Whitfield

2013

The Journal of Chemical Physics

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The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. The methods here are the first to explicitly deal with preparing N-body symmetry-adapted states and open the door for future investigations into group theory, chemistry, and quantum simulation. © 2013 AIP Publishing LLC.

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Faster quantum chemistry simulation on fault-tolerant quantum computers

Cited by 110 publications

References 69 publications

Composite Toffoli gate with two-round error detection

Composite Toffoli gate with two-round error detection

Focus on quantum simulation

Communication: Spin-free quantum computational simulations and symmetry adapted states

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