Quantum control for high-fidelity multi-qubit gates
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| Anzahl der Teile | 31 | |
| Autor | 0000-0002-3513-6237 (ORCID) 0000-0001-7402-5460 (ORCID) 0000-0002-8326-8912 (ORCID) | |
| Lizenz | CC-Namensnennung 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. | |
| Identifikatoren | 10.5446/38872 (DOI) | |
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Inhaltliche Metadaten
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| Genre | ||
| Abstract |
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00:00
ElementarteilchenphysikGleitlager
00:03
FeldquantSchmidt-KameraVideotechnikGate <Elektronik>Hi-FiReglerBlatt <Papier>
00:22
WarmumformenComputeranimation
00:32
QuantencomputerSensorHi-FiFehlprägungToleranzanalyseElektronisches BauelementHi-FiSensorElektronisches BauelementDrehmeißelFehlprägungGate <Elektronik>Angeregter ZustandComputeranimation
01:09
Angeregter ZustandSchlauchkupplungOberschwingungKapazitätEnergieniveauSchlauchkupplungSupraleiterMonatFeldstärke
01:41
Matrize <Umformen>XerographieThermoelektrischer GeneratorLeistungssteuerung
01:52
Angeregter ZustandGreiffingerVorlesung/Konferenz
01:58
GreiffingerMatrize <Umformen>Hi-FiWooferHi-FiLeistungssteuerungGate <Elektronik>EisenbahnbetriebAngeregter ZustandMatrize <Umformen>Verdrillung <Elektrotechnik>Target
02:18
IntervallFaraday-EffektHi-FiGate <Elektronik>Elektronisches BauelementErwärmung <Meteorologie>
02:37
Gate <Elektronik>ZwangsbedingungSonnenenergieErwärmung <Meteorologie>Lichtstreuung
03:02
Hi-FiGate <Elektronik>Computeranimation
03:15
Hi-FiGate <Elektronik>Computeranimation
03:22
Hi-FiHi-FiGate <Elektronik>WarmumformenFeldquantReglerErdefunkstelleSatz <Drucktechnik>
03:55
ReglerHi-FiGate <Elektronik>Blatt <Papier>ArmbanduhrComputeranimation
Transkript: English(automatisch erzeugt)
00:04
Hi, I'm Raymond Spiteri. I'm a professor in the Department of Computer Science at the University of Saskatchewan. Welcome to the video version of the abstract associated with the paper, Quantum Control for High-Fidelity Multicubic Gates by me, Marina Schmidt, Joy Dipkash, Ehsan Zaha Dinijad, and Barry Sanders.
00:23
This work was supported by Alberta Innovates, the Natural Sciences and Engineering Research Council of Canada, the National Science Foundation, and the Office of Naval Research. Quantum computing holds the promise of converting certain computational problems that are currently deemed intractable into tractable ones by replacing the binary digits or bits with which we now compute with quantum bits or qubits.
00:46
The bad news is that reliable detection of the qubit state still eludes us, and this leads to errors, also known as faults, in computation. The good news is that it is possible to correct for these errors if fault-tolerant components can be built that have sufficiently high fidelity.
01:03
Our approach to achieve this is through the design of multicubic gates that are single-shot and have high fidelity. In general, we consider n-coupled superconducting transmons. Each transmon has j energy states and is located at location k, where k is an integer from 1 to n. We will be taking j equals 3 and denote n harmonicities of the second and third energy levels by parameters
01:26
eta, which we will take to be 200 MHz, and eta prime, which we take to be approximately 3 eta. We also assume only nearest-neighbour capacitive coupling between transmons. We denote this coupling strength by g and give it the value of 30 MHz.
01:42
The Hamiltonian for our system of n-capacitively coupled transmons is the j to the power n dimensional block diagonal matrix given by the rather involved expression shown. Now we take this Hamiltonian and reduce it through projections to consider only n excitations. We now evolve the Hamiltonian over the gate time theta to obtain the unitary operator u of theta.
02:02
We now project the unitary operator u of theta into a computational subspace of at most j equals 3 excitations. Finally, the fidelity is the absolute value of the trace of the complex conjugate transpose of the target matrix for the gate times u sub cs divided by 2 to the power n. The feasibility problem for the design of a single-shot high-fidelity n-cubic gate with gate time theta is a
02:24
function epsilon of t that is defined on the interval 0 theta that has n components, each restricted to the range minus 2.5 GHz to plus 2.5 GHz, such that the fidelity of the system is at least 99.99%. The formulation allows us to solve the feasibility problem using the global search solver from MATLAB's global optimization toolbox.
02:44
The optimization is performed subject to the feasibility constraint equation that f must be at least 99.99%. The algorithm we use is known as scatter search. Although we are interested in solutions for the smallest possible gate times theta, in practice we fix theta to a reasonable value and try to find a feasible solution.
03:03
Here we have what the piecewise constant pulses look like for the single-shot high-fidelity 3-cubic Toffoli gate. Each dot represents the constant value of the pulse on a given subinterval of 1 nanosecond. Here we visualize the piecewise constant pulses for the single-shot high-fidelity 4-cubic CCCZ gate.
03:22
To wrap up, we have shown how to formulate the problem of designing multi-cubic gates as a feasibility problem. We have found a single-shot high-fidelity 3-cubic Toffoli gate with a duration time of 23 nanoseconds. We have also found a single-shot high-fidelity 4-cubic CCCZ gate with a duration time of 70 nanoseconds.
03:43
This is the first published single-shot high-fidelity 4-cubic gate of this type. Our work on this problem continues on single-shot high-fidelity 5 -cubic gates, as well as translating this largely theoretical work into practical protocols. We hope you enjoyed our video abstract for the paper, Quantum Control for High-Fidelity Multi-Cubic Gates.
04:01
Thanks for watching.