Resource requirements for fault-tolerant quantum simulation: The ground state of the transverse Ising model

Clark, Craig Robert; Metodi, Tzvetan S.; Gasster, Samuel D.; Brown, Kenneth R.

doi:10.1103/physreva.79.062314

Cited by 51 publications

(85 citation statements)

References 41 publications

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“…Recently, the resource requirements (total number of physical qubits and computation time) for computing the ground state energy of the one-dimensional quantum transverse Ising model with N spin-1/2 particles, as functions of the system size and the numerical precision, were investigated in (Clark et al, 2009a). The quantum circuit was decomposed into fault-tolerant operations, and the total number of qubits and the total number of steps were estimated as functions of the desired precision.…”

Section: Resource Estimation and Fault Tolerance A Resource Estimmentioning

confidence: 99%

Quantum simulation

2014

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Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

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Section: Resource Estimation and Fault Tolerance A Resource Estimmentioning

confidence: 99%

Quantum simulation

2014

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“…These operations will lower the initial error and in the end limit the resources required for quantum error correction. This will ultimately determine the feasibility of performing large quantum chemistry calculations on a quantum computer [91,92].…”

Section: Discussionmentioning

confidence: 99%

Progress in Compensating Pulse Sequences for Quantum Computation

Merrill

Brown

2014

Advances in Chemical Physics

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The control of qubit states is often impeded by systematic control errors. Compensating pulse sequences have emerged as a resource efficient method for quantum error reduction. In this review, we discuss compensating composite pulse methods, and introduce a unifying control-theoretic framework using a dynamic interaction picture. This admits a novel geometric picture where sequences are interpreted as vector paths on the dynamical Lie algebra. Sequences for single-qubit and multi-qubit operations are described with this method.

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“…A scalable architecture has been proposed based on shuttling ions between traps [11] and work is ongoing to implement this architecture experimentally [12][13][14][15][16][17][18][19][20]. This framework has been the basis for a number of studies on the resource requirements for implementing large quantum algorithms [21][22][23] and has also been considered as the elementary logical unit of hybrid schemes using photonic interconnects [24].…”

Section: Introductionmentioning

confidence: 99%

Comparison of ancilla preparation and measurement procedures for the Steane [[7,1,3]] code on a model ion-trap quantum computer

et al. 2013

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We schedule the Steane [[7,1,3]] error correction on a model ion trap architecture with ballistic transport. We compare the level one error rates for syndrome extraction using the Shor method of ancilla prepared in verified cat states to the DiVincenzo-Aliferis method without verification. The study examines how the quantum error correction circuit latency and error vary with the number of available ancilla and the choice of protocol for ancilla preparation and measurement. We find that with few exceptions the DiVincenzo-Aliferis method without cat state verification outperforms the standard Shor method. We also find that additional ancilla always reduces the latency but does not significantly change the error due to the high memory fidelity.

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Resource requirements for fault-tolerant quantum simulation: The ground state of the transverse Ising model

Cited by 51 publications

References 41 publications

Quantum simulation

Quantum simulation

Progress in Compensating Pulse Sequences for Quantum Computation

Comparison of ancilla preparation and measurement procedures for the Steane [[7,1,3]] code on a model ion-trap quantum computer

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