scholarly journals Surface code quantum computing with error rates over 1%

2011 ◽  
Vol 83 (2) ◽  
Author(s):  
David S. Wang ◽  
Austin G. Fowler ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Quantum Computing ◽  
Error Rates ◽  
Surface Code

scholarly journals Removing leakage-induced correlated errors in superconducting quantum error correction

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. McEwen ◽  
D. Kafri ◽  
Z. Chen ◽  
J. Atalaya ◽  
K. J. Satzinger ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Error Correction ◽  
Energy Levels ◽  
System Size ◽  
High Energy ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Correlated Errors ◽  
Surface Code ◽  
Quantum Error

AbstractQuantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.

scholarly journals A silicon-based surface code quantum computer

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Device Fabrication ◽  
Impurity Atoms ◽  
Dipole Interactions ◽  
Total Phase ◽  
Surface Code ◽  
Silicon Based

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

scholarly journals Optimization of the surface code design for Majorana-based qubits

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 352
Author(s):  
Rui Chao ◽  
Michael E. Beverland ◽  
Nicolas Delfosse ◽  
Jeongwan Haah
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
Nearest Neighbor ◽  
Error Correcting Code ◽  
Error Rates ◽  
Code Design ◽  
Trade Offs ◽  
Planar Grid ◽  
Connectivity Degree ◽  
Surface Code

The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.Here, we present surface code error-correction schemes using only Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds.Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.

scholarly journals A multi-commodity network model for optimal quantum reversible circuit synthesis

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0253140
Author(s):  
Jihye Jung ◽  
In-Chan Choi
Keyword(s):  
Quantum Computing ◽  
Network Flow ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Error Rates ◽  
Quantum Circuits ◽  
Circuit Synthesis ◽  
Multiple Control ◽  
Proposed Model ◽  
Implementation Costs

Quantum computing is a newly emerging computing environment that has recently attracted intense research interest in improving the output fidelity, fully utilizing its high computing power from both hardware and software perspectives. In particular, several attempts have been made to reduce the errors in quantum computing algorithms through the efficient synthesis of quantum circuits. In this study, we present an application of an optimization model for synthesizing quantum circuits with minimum implementation costs to lower the error rates by forming a simpler circuit. Our model has a unique structure that combines the arc-subset selection problem with a conventional multi-commodity network flow model. The model targets the circuit synthesis with multiple control Toffoli gates to implement Boolean reversible functions that are often used as a key component in many quantum algorithms. Compared to previous studies, the proposed model has a unifying yet straightforward structure for exploiting the operational characteristics of quantum gates. Our computational experiment shows the potential of the proposed model, obtaining quantum circuits with significantly lower quantum costs compared to prior studies. The proposed model is also applicable to various other fields where reversible logic is utilized, such as low-power computing, fault-tolerant designs, and DNA computing. In addition, our model can be applied to network-based problems, such as logistics distribution and time-stage network problems.

scholarly journals Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 296 ◽  
Author(s):  
Ian D. Kivlichan ◽  
Craig Gidney ◽  
Dominic W. Berry ◽  
Nathan Wiebe ◽  
Jarrod McClean ◽  
...  
Keyword(s):  
Condensed Phase ◽  
Fault Tolerant ◽  
Error Rates ◽  
Correlated Electrons ◽  
Quantum Simulations ◽  
Correlated Electron ◽  
Split Operator ◽  
Electron Models ◽  
Surface Code ◽  
The Cost

Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with N<105 fermionic modes can be performed with roughly O(1) and O(N2) T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.

Polyestimate: a library for near-instantaneous surface code analysis

2015 ◽  
Vol 15 (1&2) ◽  
pp. 1034-1444
Author(s):  
Austin G. Fowler
Keyword(s):  
Quantum Computation ◽  
Error Rate ◽  
Nearest Neighbor ◽  
Careful Analysis ◽  
Error Rates ◽  
Code Analysis ◽  
Logical Error ◽  
Surface Code ◽  
User Friendly ◽  
Library User

The surface code is highly practical, enabling arbitrarily reliable quantum computation given a 2-D nearest-neighbor coupled array of qubits with gate error rates below approximately 1\%. We describe an open source library, Polyestimate, enabling a user with no knowledge of the surface code to specify realistic physical quantum gate error models and obtain logical error rate estimates. Functions allowing the user to specify simple depolarizing error rates for each gate have also been included. Every effort has been made to make this library user-friendly. Polyestimate provides data essentially instantaneously that previously required hundreds to thousands of hours of simulation, statements which we discuss and make precise. This advance has been made possible through careful analysis of the error structure of the surface code and extensive pre-simulation.

Graphical algorithms and threshold error rates for the 2d color code

2010 ◽  
Vol 10 (9&10) ◽  
pp. 780-802
Author(s):  
David S. Wang ◽  
Austin G. Fowler ◽  
Charles D. Hill ◽  
Lloyd C.L. Hollenberg
Keyword(s):  
Quantum Computation ◽  
Error Rate ◽  
Graph Matching ◽  
Fault Tolerant ◽  
Error Rates ◽  
Color Code ◽  
Clifford Group ◽  
Universal Quantum ◽  
Surface Code ◽  
Topological Error

Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1\%. However, the 2d surface code requires the use of a complex state distillation procedure to achieve universal quantum computation. The color code of is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the color code and its error correcting methodology, discussing one approximate technique based on graph matching. We derive an analytic lower bound to the threshold error rate of 6.25\% under error-free syndrome extraction, while numerical simulations indicate it may be as high as 13.3\%. Inclusion of faulty syndrome extraction circuits drops the threshold to approximately 0.10 \pm 0.01\%.

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