Silent phase qubit tuning for logic operations

Reduced control Hamiltonian of the silent phase qubit has been found and dependence of the Hamiltonian matrix elements on applied magnetic field has been analyzed. The obtained results yield in concept of qubit logic operations accomplished by means of magnetic field application. One can propose a set of the qubits, each designed for specific logic operation. The qubit logic specialization may be fixed by both the junction current-phase relation and the characteristic Josephson-to-Coulomb energy ratio s. As current-phase relation is assigned, the qubit specialization can be tuned by the ratio s which varies with Josephson junction area. Examples of some logic operations are considered. Estimation of both the decoherence time and the quality factor Q has been obtained for such a qubit based on high-T c superconductors, which could provide the required current-phase relation.Reduced control Hamiltonian of the silent phase qubit has been found and dependence of the Hamiltonian matrix elements on applied magnetic field has been analyzed. The obtained results yield in concept of qubit logic operations accomplished by means of magnetic field application. One can propose a set of the qubits, each designed for specific logic operation. The qubit logic specialization may be fixed by both the junction current-phase relation and the characteristic Josephson-to-Coulomb energy ratio s. As current-phase relation is assigned, the qubit specialization can be tuned by the ratio s which varies with Josephson junction area. Examples of some logic operations are considered. Estimation of both the decoherence time and the quality factor Q has been obtained for such a qubit based on high-T c superconductors, which could provide the required current-phase relation.

Journal of Physics Conference SeriesFeb 1, 200817 citations

Dynamic Qubit Coupling

ScienceMay 3, 20070 citations

What determines the ultimate precision of a quantum computer

Xavier Waintal

A quantum error correction (QEC) code uses ${N}_{\mathrm{c}}$ quantum bits to construct one ``logical'' quantum bit of better quality than the original ``physical'' ones. QEC theory predicts that the failure probability ${p}_{L}$ of logical qubits decreases exponentially with ${N}_{\mathrm{c}}$ provided the failure probability $p$ of the physical qubit is below a certain threshold $p<{p}_{\mathrm{th}}$ . In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing ${N}_{c}$ . In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ${\ensuremath{\eta}}_{\mathrm{L}}$ to the precision of the logical qubits (irrespectively of ${N}_{c}$ ). ${\ensuremath{\eta}}_{\mathrm{L}}$ directly controls the maximum number of operations $\ensuremath{\propto}1/{\ensuremath{\eta}}_{\mathrm{L}}^{2}$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error---silent stabilizer failure---as a mechanism responsible for finite ${\ensuremath{\eta}}_{\mathrm{L}}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of ${N}_{c}$ .A quantum error correction (QEC) code uses ${N}_{\mathrm{c}}$ quantum bits to construct one ``logical'' quantum bit of better quality than the original ``physical'' ones. QEC theory predicts that the failure probability ${p}_{L}$ of logical qubits decreases exponentially with ${N}_{\mathrm{c}}$ provided the failure probability $p$ of the physical qubit is below a certain threshold $p<{p}_{\mathrm{th}}$. In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing ${N}_{c}$. In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ${\ensuremath{\eta}}_{\mathrm{L}}$ to the precision of the logical qubits (irrespectively of ${N}_{c}$). ${\ensuremath{\eta}}_{\mathrm{L}}$ directly controls the maximum number of operations $\ensuremath{\propto}1/{\ensuremath{\eta}}_{\mathrm{L}}^{2}$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error---silent stabilizer failure---as a mechanism responsible for finite ${\ensuremath{\eta}}_{\mathrm{L}}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of ${N}_{c}$.

arXiv:1702.07688Physical Review AApr 10, 20199 citations

Coherence control for qubits

K. M. Fonseca-Romero, Sigmund Kohler, Peter Hänggi A

arXiv:quant-ph/0307236Chemical PhysicsOct 17, 200340 citations

An Improved Josephson Phase Qubit

Raymond W. Simmonds

APSMar 1, 20040 citations

A loophole in quantum error correction

Xavier Waintal

A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one quantum bits of better quality than the original ones. QEC theory predicts that the failure probability $p_L$ of logical qubits decreases exponentially with $N_{\rm c}$ provided the failure probability $p$ of the physical qubit is below a certain threshold $p<p_{\rm th}$ . In particular QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing $N_{\rm c}$ . In this letter, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit $\eta_{\rm L}$ to the precision of the logical qubits (irrespectively of $N_{\rm c}$ ). $\eta_{\rm L}$ directly controls the maximum number of operations $\propto 1/\eta_{\rm L}^2$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error - silent stabilizer failure - as a mechanism responsible for finite $\eta_{\rm L}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of $N_c$ .A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one quantum bits of better quality than the original ones. QEC theory predicts that the failure probability $p_L$ of logical qubits decreases exponentially with $N_{\rm c}$ provided the failure probability $p$ of the physical qubit is below a certain threshold $p<p_{\rm th}$. In particular QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing $N_{\rm c}$. In this letter, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit $\eta_{\rm L}$ to the precision of the logical qubits (irrespectively of $N_{\rm c}$). $\eta_{\rm L}$ directly controls the maximum number of operations $\propto 1/\eta_{\rm L}^2$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error - silent stabilizer failure - as a mechanism responsible for finite $\eta_{\rm L}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of $N_c$.

Feb 24, 20170 citations

A quantum error correction (QEC) code uses

{N}_{\mathrm{c}}

quantum bits to construct one ``logical'' quantum bit of better quality than the original ``physical'' ones. QEC theory predicts that the failure probability

{p}_{L}

of logical qubits decreases exponentially with

{N}_{\mathrm{c}}

provided the failure probability

p

of the physical qubit is below a certain threshold

p<{p}_{\mathrm{th}}

. In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing

{N}_{c}

. In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ${\ensuremath{\eta}}_{\mathrm{L}}$ to the precision of the logical qubits (irrespectively of

{N}_{c}

). ${\ensuremath{\eta}}_{\mathrm{L}}$ directly controls the maximum number of operations $\ensuremath{\propto}1/{\ensuremath{\eta}}_{\mathrm{L}}^{2}$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error---silent stabilizer failure---as a mechanism responsible for finite ${\ensuremath{\eta}}_{\mathrm{L}}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of

{N}_{c}

A quantum error correction (QEC) code uses

N_{\rm c}

quantum bits to construct one quantum bits of better quality than the original ones. QEC theory predicts that the failure probability

p_L

of logical qubits decreases exponentially with

N_{\rm c}

provided the failure probability

p

of the physical qubit is below a certain threshold

p<p_{\rm th}

. In particular QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing

N_{\rm c}

. In this letter, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit

\eta_{\rm L}

to the precision of the logical qubits (irrespectively of

N_{\rm c}

\eta_{\rm L}

directly controls the maximum number of operations

\propto 1/\eta_{\rm L}^2

that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error - silent stabilizer failure - as a mechanism responsible for finite

\eta_{\rm L}

and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of

N_c