Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

Superconducting tetrahedral quantum bits: Emulation of a noise-resistant spin- 12 system

M. V. Feigel’man, L. B. Ioffe, V. B. Geshkenbeǐn, P. Dayal, G. Blatter

Published Dec 30, 2004• 11 citations
Publisher

Abstract

We propose a design for a quantum bit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux quantum per loop and one-half Cooper pair per island. This structure emulates a noise-resistant spin-$1∕2$ system in a vanishing magnetic field. The tetrahedral quantum bit combines a number of advances such as a doubly degenerate ground state minimizing decoherence via phonon radiation, a weak quadratic sensitivity to electric and magnetic noise, relieved constraints on the junction fabrication, a large freedom in manipulation, and attractive measurement schemes. The simultaneous appearance of a degenerate ground state and a weak noise sensitivity are consequences of the tetrahedral symmetry, while enhanced quantum fluctuations derive from the special magnetic frustration. We determine the spectral properties of the tetrahedral structure within a semiclassical analysis and confirm the results numerically. We show how proper tuning of the charge frustration selects a doubly degenerate ground state and discuss the qubit's manipulation through capacitive and inductive coupling to external bias sources. The complete readout of the spin components ${\ensuremath{\sigma}}_{i}$, $i=x,y,z$, is achieved through coupling of the internal qubit currents to external junctions driven close to criticality during the measurement.

DOI
10.1103/physrevb.70.224524

Related papers

Superconducting Tetrahedral Quantum Bits

M. V. Feigel’man, L. B. Ioffe, V. B. Geshkenbeǐn +2 more

We propose a design for a qubit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux quantum per loop and one-half Cooper pair per island. This structure emulates a noise-resistant spin-1/2 system in a vanishing magnetic field. The flux frustration boosts quantum fluctuations and relieves the constraints on junction fabrication. Variability of manipulation and optimized readout are additional benefits of this design.

arXiv:cond-mat/0407663•Physical Review Letters•Mar 3, 2004•21 citations

Protected quantum bits and Josephson junction arrays

R. A. Usmanov

In this thesis we consider a Josephson junction device whose symmetry is described by the point group Td. It can be visualized as a tetrahedron that contains two Josephson junctions on each edge. We find the conditions under which the ground state of the system is degenerate or almost degenerate. In this case, the low-energy degrees of freedom can be mapped to the Hilbert space of a quantum spin 1/2. We evaluate effects of different physical perturbations on the degenerate ground state and find that they are small for most perturbations. We argue that this system can be considered as a very promising candidate for a protected quantum bit with built-in error correction. We propose and discuss an experimental method that allows to test validity of some of the theoretical results obtained for the tetrahedral Josephson junction array and other similar symmetric circuits. We have chosen a simpler pyramidal array to demonstrate the main ideas of our method. Even though the noise resistance and theoretical decoherence time of the pyramidal array are worse than those of the more complex tetrahedral systems, it is much easier to realize the pyramid experimentally. The proposed design can be used with any symmetric Josephson junction circuit. We explore a natural generalization of the tetrahedral quantum bit and consider devices whose symmetry can be described by one of the higher-order permutation groups Sn. We study the level structure and the associated built-in protection of some conceptually simple circuits and show that these circuits have many interesting properties. In particular, their ground state can be highly degenerate and stable with respect to perturbations violating the symmetry. Unfortunately, these highly symmetric systems consist of a large number of identical Josephson junctions. This makes them too complicated for experimental realization.

•Jan 1, 2010•0 citations

Design aspects of superconducting-phase quantum bits

G. Blatter, V. B. Geshkenbeǐn, L. B. Ioffe

A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called $\ensuremath{\pi}$ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such $\ensuremath{\pi}$ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one $\ensuremath{\pi}$ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and $\ensuremath{\pi}$ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].

Physical review. B, Condensed matter•Apr 11, 2001•181 citations

Theoretical investigation of a protected quantum bit in a small Josephson junction array with tetrahedral symmetry

R. A. Usmanov, L. B. Ioffe

We consider a Josephson junction device which has a symmetry of a tetrahedron; it can be visualized as a tetrahedron that contains two Josephson junctions at each edge. We find the conditions for which the ground state of the system is degenerate or almost degenerate; in this case, the low-energy degrees of freedom can be mapped on a quantum spin $1∕2$. We evaluate the effect of the physical perturbations and imperfections on the level splitting in this system and find that they are small for most perturbations. We argue that this system can provide a possible physical implementation of a protected quantum bit with a built-in error correction. We propose a way of manipulating the effective quantum spin by means of electrical potentials and an experimental scheme to read the information that it contains.

Physical Review B•Jun 21, 2004•5 citations

Superconducting qubits : survey and theoretical investigations for solid state quantum computing

Santosh Kumar Gupta

Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.

•Jan 1, 2010•0 citations

Superconducting Qubits and Environmental Noise

Elias J. Griffith

We examine the energy level structure of a Josephson charge qubit (Cooper pair box) coupled to its environment, utilising a backreaction technique originally proposed for characterising persistent current qubits. The system consists of a model charge qubit coupled to three electromagnetic modes: a low frequency bias field, a higher frequency microwave to excite the qubit into higher states, and a lossy reservoir representing the cavity containing the qubit and control fields. Specifically, the qubit is a small superconducting island connected to a bulk superconductor via a weak Josephson junction, allowing Cooper pairs to tunnel on and off the island coherently. The classical bias field experiences a backreaction from the qubit and the noise power increases when the qubit is operating near a transition.

AIP conference proceedings•Jan 1, 2004•1 citation
We propose a design for a quantum bit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux quantum per loop and one-half Cooper pair per island. This structure emulates a noise-resistant spin-1∕21∕21∕2 system in a vanishing magnetic field. The tetrahedral quantum bit combines a number of advances such as a doubly degenerate ground state minimizing decoherence via phonon radiation, a weak quadratic sensitivity to electric and magnetic noise, relieved constraints on the junction fabrication, a large freedom in manipulation, and attractive measurement schemes. The simultaneous appearance of a degenerate ground state and a weak noise sensitivity are consequences of the tetrahedral symmetry, while enhanced quantum fluctuations derive from the special magnetic frustration. We determine the spectral properties of the tetrahedral structure within a semiclassical analysis and confirm the results numerically. We show how proper tuning of the charge frustration selects a doubly degenerate ground state and discuss the qubit's manipulation through capacitive and inductive coupling to external bias sources. The complete readout of the spin components \ensuremathσi{\ensuremath{\sigma}}_{i}\ensuremathσi​, i=x,y,zi=x,y,zi=x,y,z, is achieved through coupling of the internal qubit currents to external junctions driven close to criticality during the measurement.
In this thesis we consider a Josephson junction device whose symmetry is described by the point group Td. It can be visualized as a tetrahedron that contains two Josephson junctions on each edge. We find the conditions under which the ground state of the system is degenerate or almost degenerate. In this case, the low-energy degrees of freedom can be mapped to the Hilbert space of a quantum spin 1/2. We evaluate effects of different physical perturbations on the degenerate ground state and find that they are small for most perturbations. We argue that this system can be considered as a very promising candidate for a protected quantum bit with built-in error correction. We propose and discuss an experimental method that allows to test validity of some of the theoretical results obtained for the tetrahedral Josephson junction array and other similar symmetric circuits. We have chosen a simpler pyramidal array to demonstrate the main ideas of our method. Even though the noise resistance and theoretical decoherence time of the pyramidal array are worse than those of the more complex tetrahedral systems, it is much easier to realize the pyramid experimentally. The proposed design can be used with any symmetric Josephson junction circuit. We explore a natural generalization of the tetrahedral quantum bit and consider devices whose symmetry can be described by one of the higher-order permutation groups Sn. We study the level structure and the associated built-in protection of some conceptually simple circuits and show that these circuits have many interesting properties. In particular, their ground state can be highly degenerate and stable with respect to perturbations violating the symmetry. Unfortunately, these highly symmetric systems consist of a large number of identical Josephson junctions. This makes them too complicated for experimental realization.
A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called $\ensuremath{\pi}$ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such $\ensuremath{\pi}$ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one $\ensuremath{\pi}$ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and $\ensuremath{\pi}$ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].
We consider a Josephson junction device which has a symmetry of a tetrahedron; it can be visualized as a tetrahedron that contains two Josephson junctions at each edge. We find the conditions for which the ground state of the system is degenerate or almost degenerate; in this case, the low-energy degrees of freedom can be mapped on a quantum spin 1∕21∕21∕2. We evaluate the effect of the physical perturbations and imperfections on the level splitting in this system and find that they are small for most perturbations. We argue that this system can provide a possible physical implementation of a protected quantum bit with a built-in error correction. We propose a way of manipulating the effective quantum spin by means of electrical potentials and an experimental scheme to read the information that it contains.
Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.
We examine the energy level structure of a Josephson charge qubit (Cooper pair box) coupled to its environment, utilising a backreaction technique originally proposed for characterising persistent current qubits. The system consists of a model charge qubit coupled to three electromagnetic modes: a low frequency bias field, a higher frequency microwave to excite the qubit into higher states, and a lossy reservoir representing the cavity containing the qubit and control fields. Specifically, the qubit is a small superconducting island connected to a bulk superconductor via a weak Josephson junction, allowing Cooper pairs to tunnel on and off the island coherently. The classical bias field experiences a backreaction from the qubit and the noise power increases when the qubit is operating near a transition.