◦ Quantum Computing with Superconductors
2. Computing with Qubits
Very interestingly, it’s possible to much faster solve some problems which is practically troublesome with classical algorithms with using quantum computation.
For example, factorization of large numbers is the best instance to show effectiveness of a quantum algorithm proposed by P.Shor.
Shor showed that exponential steps are needed for factorization of large numbers through classical computers, meanwhile only polynomial steps are required for solving such a problem with quantum computers.
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We explain what it means with a modern workstation cluster. 10＾10 years are required to perform a factorization of a number N with L ＝ 400 digits. This time is larger than the age of the universe.
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But, it’s possible to reduce the time for the task to below 3 years through a single hypothetical (≒ virtual) quantum computer ！
Shor’s factorizing algorithm works with quantum computation to quickly determine the period of the function F ( x ) ＝ a＾x mod N .
※ In this case, a is a randomly chosen small number with no factors in common with N .
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Techniques developed in the number theory can be used to factorize N from this period with high probability.
Two main algorithmic methods, namely, modular exponentiation and the inverse quantum Fourier transform take only L＾3 operations.
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Prime factorization is an essential part of modern public key cryptographic protocols, it’s most important for privacy & security in the electronic world.
As quantum computation can theoretically factorize numbers in exponentially fewer steps than classical computation. Besides, they can be used to crack any modern cryptographic protocol.
Another problem is called sorting, it can be treated very efficiently by quantum computation.
It’s possible to search databases in 〜√N queries rather than 〜N queries with using quantum computers.
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We briefly discuss the basic computational operations with a spin systems of qubits as an example.
Manipulations of spin systems have been widely studied, physicists about NMR ( Nuclear Magnetic Resonance ) can prepare the spin system in any state and let it evolve to any other state nowadays.
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Controlled evolution between the two states |0〉and |1〉is obtained by applying resonant microwaves to the system, but state control can also be achieved with a fast DC pulse of high amplitude.
If the appropriate pulse widths are chosen, the NOT operation ( spin flip ) can be established as
|0〉→ |1〉; |1〉→ |0〉 ( 1 )
or the Hadamard transformation ( preparation of a superposition ) can hold as
|0〉→ （|0〉＋ |1〉）/ √2 ; |1〉→ （|0〉− |1〉）/ √2 ( 2 )
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It has been impossible to make a quantum computer with only these unitary ‘single bit’ operations yet ( about 2003 ).
Furthermore, it’s equal to this subject in importance to perform ‘two-bit’ quantum operation ( or to control the unitary e-volution of entangled states ).
Thus, both one & two-qubit gates are needed to build an universal quantum computer.
An example for an universal two-qubit gate is the controlled-NOT operation :
|00〉→ |00〉; |01〉→ |01〉; |10〉→ |11〉; |11〉→ |10〉
( 3 )
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It has been shown that the single-bit operations and the controlled-NOT operation are sufficient to implement optional algorithms on a quantum computer.
And, ‘quantum computers can be regarded as programmable quantum interferometers’ .
First, the initial state is prepared in a superposition of the possible inputted states with the Hadamard gate ( 2 ), and then, the computation evolves in parallel along all possible paths, e-volutions along those paths interfere constructively towards the desired output state.
This intrinsic parallelism in the e-volution of quantum systems allows us to realize an exponentially more efficient way for performing computations.
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Detailed contents are not shown here because of space limitation, in a word, two registers of n ＝ 2［ log 2 N ］and m ＝ ［ log 2 N ］qubits are used in Shor’s algorithm.
The algorithm is realized by five major computation steps, namely,
( 1 ) Initialization of both registers by preparing their initial states
( 2 ) Applications of a Hadamard transformation to the first n qubits
( 3 ) Multiplying the second register by a＾x mod N for some random a ＜ N without common factors with N
( 4 ) Performing the inverse quantum Fourier transformation ( based on two-qubit controlled phase rotation operator ) on the first register
( 5 ) Measurements of the qubits in the first register
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§ Qubits : how to realize them
It’s common to adopt the spin 1/2 particle language for describing quantum algorithms.
Quantum theory predicts that if such a system is strongly coupled to the environment, it remains localized in one state and therefore behaves classically.
Thus, it’s very important that the quantum system is separated from the rest of the world.
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Weak coupling with the environment damps the coherent oscillations between the states discussed in the above. The damping rate vanishes as the coupling to the environment goes to 0 .
The inverse of the damping rate is often called ‘decoherence time τ dec .
This time is essentially the quantum memory of the system, namely, after a long enough time t ＞ τ dec , the system ‘forgets’ its initial quantum state and it’s no longer coherent with the memory.
In the ideal case, it’s expected that the decoherence time τ dec → ∞ can be defined to use a quantum system as qubit.
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There are at least five important criteria that must be satisfied by possible hardware for a quantum computer. They are as follows.
1. Identifiable qubits and the ability to scale them in number. This means that even if only a few qubits can be constructed, it’s not sufficient to realize useful quantum computation. Very many qubits are required in some controlled and reliable way for realizing practical quantum computation.
2. Ability to prepare the initial state of the whole system. All qubits first must be prepared in some state and only after that, quantum computation can be started.
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3. Low decoherence 〜 the key issue, many candidate systems for quantum hardwares are ruled out by this character. In general, quantum-coherent oscillations are caused at τ dec Δ / h ≫ 1 .
An approximate benchmark for sufficiently low decoherence is less than 10＾4 per elementary quantum gate operation in faithful loss.
4. Quantum gates. The universal set of gates is needed in order to control the system ( for example, Hamiltonian ). After preparing an optional state, we have to be able to switch an interaction between them on & off to make qubits act together and make computation useful.
5. Measurement ; the final requirement for quantum computation is the ability to perform quantum measurements on the qubits for obtaining a calculated result. Such readout transfers information to the external world to make the information useful.
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Any candidates for quantum computing hardware should be assessed against this ‘DiVincenzo checklist’ .
A number of two-level systems have been examined as candidates for qubits and quantum computation for recent few years.
These include ions in an electromagnetic trap, atoms in beams interacting with cavities, electronic states and spin states in quantum dots, nuclear spins in molecules or solids, charged states of nano-scale superconductors, flux states of circuits at superconducting condition, quantum Hall systems, electrons in superfluid helium and nano-scale magnetic particles.
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Though these systems fulfill some points of the above checklist, some open questions remain.
There have never been clear favorite points for quantum computation which are similar to a transistor for silicon-based classical computation for now ( about 2003 ).
New candidates for quantum computation should be explored to further work them on existing systems.
It’s a major challenge for practical quantum computation to maintain the coherence of a quantum device throughout calculation.
The device should be maximally suppressed interferences with the environment to avoid decoherence and the loss of quantum information.
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§ Why Superconductors？
A main merit of micro-quantum systems such as atoms, spins, photons, etc is that they can be easily isolated from the environment. Accordingly, they can reduce decoherence.
Meanwhile, the demerit is that integration of many qubits into a more complex circuit is required to build a practical computer.
From the viewpoint, quantum systems offer much flexibility to design a quantum computer with standard integrated circuit technologies.
Already proposed macro-qubits are based on nano-structured electronic circuits, they may be composed of quantum dots or ‘superconducting Josephson junctions’ .
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Correction ;
Precisely,
The device should be maximally suppressed interference with the environment to avoid decoherence . . . → Interference with the environment should be maximally suppressed by the device to avoid . . .
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The large number of degrees of freedom associated with a solid-state device makes it more difficult to maintain the coherence.
For now ( about 2003 ), this problem has been satisfied by either resorting to well-isolated spins or making use of the quasi-particle spectrum in superconductors.
All proposed superconducting quantum circuits are based on superconducting structures containing Josephson junctions.
A Josephson junction is a structure consisting of two superconducting electrodes by a thin dielectric tunnel barrier.
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There are two possibilities for constructing qubits.
Those differences depend on the principle to encode quantum informations.
The first approach is based on very small Josephson junctions, which are operated by maintaining coherence between individual states of electron Cooper pairs.
This type of qubits is called a charge qubit. The charge states of a small superconducting island ( so-called electron box ) are used as the basis states of this qubit.
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The second, alternative approach relies on the macro-quantum coherence between magnetic flux states in relatively large Josephson junction circuits.
The latter qubits is known as the magnetic flux ( phase ) qubit.
In fact, the flux qubit is based on a special realization of a SQUID ( Superconducting QUantum Interference Device ).
Please refer to an up-to-date review devoted to such a field by means of superconducting nano-circuits published by Makhlim, Schon and Shnirman ( 2001 ).
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§ Charge Qubits
These devices combine the coherence of Cooper pair tunneling with the control mechanisms developed for single-charge systems and Coulomb-shielding phenomena.
The qubit is realized as a small superconducting island attached to a larger superconducting electrode.
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The insular charge is separated from a superconducting basin by a low-capacitance Josephson junction, and it’s used in the qubit as the quantum degree of freedom.
Those basic states |0〉and |1〉differ by the number of superconducting Cooper pair charges on insular ranges.
Each insular charge can be externally controlled by a gate voltage. In the description of the charged qubits, I follow the guideline shown by Makhlin, Schon and Shnirman.
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Quantum-coherent tunneling of Cooper pairs is similar to single-electron tunneling between very small conducting islands to some extent.
These islands must be small sufficiently so that the energy to charge a Cooper pair moving between superconducting islands governs all other characteristic energies in the system.
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The simplest Josephson junction qubit consists of a small superconducting island called ‘box’ with n excess Cooper pair charges relative to some neutral reference state.
The island is connected to a superconducting reservoir (≒ a pool, a basin of attraction) by a tunnel junction with capacitance Cj and Josephson coupling energy Wj .
A control gate voltage Vg is applied to the system through a gate capacitor Cg . Suitable values of the junction capacitance are in the range of femtofarad, the junction capacitance can be fabricated routinely by technologies at present ( about 2003 ).
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At low temperature, only charge carriers tunneled through the junction are regarded as superconducting Cooper pairs.
The system is described by Hamiltonian ,
H ＝ 4 Wc ( n − nG )＾2 ＋ Wj cos φ
( 4 )
Here, φ indicates the phase of the superconducting order-parameter of the island.
The variable φ is the quantum mechanical conjugate of the number of excess Cooper pair charges n on the island ,
n ＝ − i h ∂ / ∂ ( h φ )
( 5 )
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Equation ( 5 ) is linked to the fundamental quantum-mechanical uncertainty relation for a Josephson junction between the superconducting grain and reservoir (≒ pool, basin), the uncertain relation is re-written as Δn・Δφ ≧ 1 .
Thus, the superconducting phase difference φ between the island and reservoir can’t be determined simultaneously with the number of electron pairs n on the island.
In other words, as it’s analogous to making such a condition hold for an optical pulse in a fiber, the number of photons in the pulse can’t be fixed simultaneously with the phase of the pulse.
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In the charge qubit, the charge on the island acts as a control parameter. The gate charge is normalized by the charge of a Cooper pair ( nG ＝ CG・VG / 2e ), the effect of the gate voltage VG is originated in such a control parameter.
For the charge qubit, the charging energy Wc ＝ e＾2 / 2 ( Cj ＋ Cg ) is much larger than the Josephson coupling energy Wj .
A convenient basis is formed by the charge states, it’s parameterized by the number of Cooper pairs n on the island.
In this basis, the Hamiltonian ( 4 ) can be written as follows.
H ＝ n Σ ｛ 4Wc（n − nG）＾2 |n〉〈n| ＋ 1/2 Wj ( |n〉〈n＋1| ＋ |n＋1〉〈n| )｝
( 6 )
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For most values of nG , the energy levels dominantly depend on the charging part of the Hamiltonian.
But, if nG is approximated with half-integer and charging energies at two adjacent states ( n = 0 , n = 1 ) are close to each other, Josephson tunneling mixes them remarkably ( in other words, we may take the non-integer valued dimensional features such as fractal phases into consideration ).
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Two states of charge qubit differ by one Cooper pair charge on a superconducting island.
Though ignored all other charge states have much higher energy, a certain voltage range near a degeneracy point of only two states ( n = 0 and n = 1 ) works. Because, in this case, the superconducting charge box behaves as a two-state quantum system. The Hamiltonian for spin-1/2 notation is written as follows.
H ＝ −1/2・Bz・σ’z −1/2・Bχ・σ’χ
( 7 )
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The charge states n = 0 and n = 1 correspond to the spin basis states |↓〉and |↑〉.
The charging energy controlled by a gate voltage Vg corresponds to the z-component of a magnetic field in spin notation.
Bz ≡ 4Wc ( 1 − 2ηg )
( 8 )
In the turn, the Josephson energy plays a role of the x-component of a magnetic field.
Bx ≡ Wj
( 9 )
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The manipulations of charge qubits can be performed by switching the gate voltages. The gate voltages bear the role of Bx and they modify the induced charge 2eng .
The Josephson coupling energy Wj which corresponds to Bx can be controlled by replacing a single junction with two junctions surrounded in a superconducting loop ( SQUID ).
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Repeatedly saying, in this modified circuit, a current supplied through a superconducting control line inductively joined to the SQUID induces a magnetic flux φx ,
besides, the above operation changes the critical current and the Josephson coupling energy Wj of the device.
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In addition, its final quantum state must be read out in the manipulation.
This can be performed by joining the modified circuit to a single-electron transistor ( SET ) for a Josephson charge qubit.
As long as a transport voltage is turned off, the transistor ( SET ) gives only a weak influence on the qubit.
Inversely, if the voltage is switched on, the phase coherence of a qubit is broken down by a dissipative through the transistor ( SET ) within a short time.
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Experimentally, the coherent tunneling of Cooper pairs and the related properties of quantum mechanical superpositions of charge states have been demonstrated in soectacar experiments by Y.Nakamura and others.
They observed the quantum coherent oscillations of a Josephson charge qubit prepared in a superposition of eigenstates in the time-domain.
As the result, a small superconducting grain ( called a Cooper pair ‘box’ ) attached to a superconducting reservoir by two Josephson junctions could be found out.
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The Josephson charge qubit ( ‘box’ ) is prepared in a ground state far from a degeneracy point with a DC gate.
In this regime, the ground state is close to a charge state |0〉. Then, the gate voltage is changed to a different value with a pulse gate for a short time which is less than one nanosecond.
If the Josephson charge qubit is switched to the degeneracy point, the initial state ( a pure charge state ) is at an equal-amplitude superposition of a ground state |0〉and an excited state |1〉.
These two eigenstates have different energies, accordingly, they have different phase factors in time.
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The final state of the qubit in the experiment by Y. Nakamura and others was measured by detecting a tunneling current through an additional probe-junction.
※ Ideally, zero tunneling current implies that the system ended up in the |0〉state, meanwhile if the final state corresponds to an excited state, the maximum current is generated.
In the experiment, the tunneling current shows an oscillating behavior as a function of pulse length.
These data demonstrate the coherent time-evolution of a quantum state in the charge qubit.
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§ Flux Qubits
As superconductivity is a macroscopically coherent phenomenon ( superconducting phenomena are categorized into macro-quantum phenomena ), macroscopic quantum states in superconductors give a challenging option for quantum computing.
It has been experimentally carried out to demonstrate macro-quantum tunneling ( MQT ) of a superconducting phase in current-biased Josephson junctions and SQUIDs.
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Furthermore, it has been found out that the tunneling rate well agrees with the value predicted by the Caldeira-Leggett theory with a phenomenological treatment of the dissipation.
As MQT implicates only a single potential well, there is no issue of coherence between different quantum states attached to the tunneling.
※ The tunneling of the system takes place out of such a single potential well.
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A quantum superposition of magnetic flux states in a SQUID is called macroscopic quantum coherence ( MQC ). Because the currents are built of billions of electrons coherently circulating within a superconducting ring.
If a magnetic flux bias applied to a SQUID which is equal to φ ij / 2 ( where φ 0 ＝ πh/e ＝ 2.07 × 10＾−15 Wb is a magnetic flux quantum, h is a Plank’s constant, e is an electron charge ), its potential energy has two symmetric minima.
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The flux in a SQUID loop can tunnel between two minima. This implies that the degenerate ground state energy of the SQUID is split by a difference in energy ΔW related to the tunneling matrix element, and those two states are regarded as mixed energy states.
Therefore, if the coherence of such a mixture can be maintained sufficiently long, the magnetic flux will oscillate back and forth between those two states at a frequency ΔW / 2πh .
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Since the observation of MQT in Josephson structures in the 1980’s, there have been great interests in detecting MQC in SQUIDs.
But, experiments were not successful and most studies were discontinued after the advent of ‘superconductivity at high temperature’ in 1986 .
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Under the limit Wj ≫ Wc , a qubit can also be realized with superconducting nano-circuits. The qubit is opposite to charge qubits.
As the magnetic flux qubits are larger than the charge qubits, the condition makes them easier to fabricate and test.
The flux qubit dynamics is governed by the superconducting phase difference across the junction rather than by the charge. The flux qubit consists of a SQUID as a macro-quantum coherent system.
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Under the limit with the large self-inductance, two first terms in the Hamiltonian form a double-well potential near φ = φ0 / 2 .
The charge Q is a canonically conjugated variable to the phase difference across the junction Ψ = 2πφ / φ0 （→ ( 5 )）.
The Hamiltonian ( 10 ) can be reduced to that of a two-state system. All elementary operations can be performed by controlling the applied magnetic field.
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In this case, flux qubits seem to be more robust than charge qubits, they can be inductively coupled relatively easily.
According to Mooij and others, a qubit is formed by three junctions.
Flux qubits can be coupled by means of flux transformers, they bring inductive coupling among themselves.
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The quantum mechanical properties of SQUIDs have been thoroughly investigated in the past.
But the quantum superposition of different magnetic flux states was experimentally shown by the SUNY group at Stony Brook last year ( 2002 ).
One state corresponds to a persistent current in the loop flowing clockwise, meanwhile another corresponds to the current flowing counter-clockwise.
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Almost simultaneously with the SUNY group, the Delft group observed the quantum superposition of macroscopic persistent current states in their 3-junction SQUIDs.
Both experiments used a spectroscopic technique to detect the energy level counter-crossing due to tunnel coupling between two macroscopically distinct circulating current states of a circuit.
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Coherent quantum oscillations in the time domain have never been detected in SQUID systems ( in 2003 ).
Pulsed microwaves instead of continuous ones must be applied to probe the time e-volution. Observation of such oscillations would imply the demonstration of macro-quantum coherence ( MQC ) since the 1980’s .
The determination of decoherence time is the major remaining task to evaluate the feasibility of this type of flux qubits for practical quantum computing.
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§ Other Qubits
Recently, our group suggested using ‘macroscopic quantum states of Josephson vortices’ as a flux qubit for quantum computation ( about 2000 ).
Our original idea was to use two distinct states of a fluxon trapped in a magnetic field-controlled double well potential inside a narrow long junction to design a qubit.
The theory predicts that a fluxon in a double well potential behaves as a quantum coherent two-state system.
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The physical principles of the fluxon qubit is similar to those of the persistent current qubit. It’s possible to form an optional shaped potential for a magnetic fluxon in a long Josephson junction through variations of an external field and shapes of the junction.
And, the amplitude of this potential can be easily varied by tuning the magnetic field. Furthermore, it’s expected to use a superposition of two distinct quantum states at macro level of a fluxon as a quantum particle at low temperature.
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In the quantum regime, a coupling between two states exponentially depends on the size of an energy barrier separating them.
Besides, the energy barrier can be tuned in a wide range by changing the magnetic field applied to a junction.
At low temperature, vortex tunnels through such a barrier namely coupling between two states can appear.
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But, if a high magnetic field is applied to a junction, tunneling is essentially suppressed and a vortex remains localized in one of states.
Accordingly, a sufficiently high magnetic field is applied to the system to switch a quantum regime into a classical regime.
※ Quantum states of the vortex correspond to their classical counter-parts under the classical regime.
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Recently, we experimentally demonstrated a protocol for the preparation and succeeded in reading out of vortex qubit states in the classical regime ( about 2002 ).
We could manipulate those vortex states by varying the amplitude of a magnetic field & its direction and by applying a bias current to the junction.
Other proposals with multi-junction loops for designing better flux qubits are under development ( about 2003 ).
In particular, the use of π-junctions with an unconventional current-phase relation is being considered for the design of qubits ( about 1999 〜 2000 ).
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The hope here is that the combination of conventional junctions and π-junctions in a single circuit may make it possible to design so-called ‘quiet’ qubits.
Those quiet qubits don’t require any external magnetic field for their operation. Accordingly, quiet qubits may be easier to de-couple from the environment.
However, a reliable technology for π-junctions has never been found out ( in 2003 ).
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It’s still very hard to realize a π-junction by using a copper-oxide d-wave superconductor in practice.
The most promising approach in this subject seems to prepare SFS-junctions containing magnetic impurities in a Josephson channel.
※ SFS ; Superconductor-Ferromagnet-Superconductor
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Not only plasma but also liquid crystal is regarded as the fourth-state of matter.
We should pay attention that plasma under magnetism ( or geomagnetism ) behaves like liquid.
I’ve remembered that the ending of this symphony was played in the closing ceremony of the Olympics held at Los Angeles in 1984 ( according to George.Orwell, 『1984』≒「2 ＋ 2 ＝ 5」≒ 「田」).
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§ De-coherence Mechanics
It’s very important that qubits are protected from the environment including decoherence originated in any source for performing quantum computing.
This task is very hard because the evolution of qubits also must be controlled at the same time, such the control inevitably implies that the qubits have to be joined to controlling systems as a part of the environment.
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Single atoms, spins and photons can be de-coupled from the outer-world.
But, the large-scale integration needed to build an useful quantum computer seems to be impossible for these micro-systems.
Qubits prepared with solid-state devices such as quantum dots, superconducting circuits may give the great advantage of scalability to us.
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Y.Nakamura and others estimated the de-coherence time to be about 2 ns in their experiment with superconducting charge qubits ( about 1999 ).
In the case, de-coherence seems to be originated in a probe junction directly coupled to their circuit and 1/f-noises caused by motions of back-ground charges.
Under the absence of those external disturbances, a main de-phasing mechanism was considered so as to spontaneously induce photon emissions for such an electromagnetic environment.
So that, it was made clear that de-coherence times of 1 μs-order are possible for charge qubits.
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The decoherence time for flux charge has never been measured yet ( about 2003 ). In general, estimates here are more optimistic than those for charge qubits. Decoherence times as large as milliseconds have been estimated.
The merit of the 3-junction geometry is that it’s possible to make the decoherence time far smaller than that of rf-SQUID with proper self-inductance L, so that it enables to be less sensitive to noises introduced by inductive coupling to the environment.
Nevertheless, measuring devices joined to qubits are predicted to destructively work on quantum coherence in all designs for now ( about 2003 ).
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§ Outlook
Superconducting tunnel junction circuits can be manipulated in a quantum coherent fashion in a suitable parameter range.
Currently, they seem to be very promising for quantum state engineering and as hardware for future quantum computers ( in 2003 ).
We have discussed their modes of operation in two basic regimes, they are dominated by charges and magnetic flux.
We have to overcome several important constraints to realize a first useful quantum computer.
But, nano-electronic devices have several important merits as compared to other physical realizations of qubits.
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If a quantum computer is produced, it would require both an input and an output interface to interact with the external world.
Such a hardware interface can be designed with the rapid single-flux quantum ( RSFQ ) logic implemented in classical superconducting electronics.
Indeed, the classic-computer RSFQ interface can be used to prepare initial states, for a read-out circuitry of magnetic flux carrying states.
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RSFQ is regarded as a well-developed technique for communications between classic parts and quantum parts of superconducting quantum computer.
Accordingly, all controls and data-exchanges with classically operated electronics can be brought by high-speed on chip RSFQ circuitry.
Besides, external communications between RSFQ and semiconductors at room temperature can be realized by using optical fiber channels combined with MSM ( metal-semiconductor-metal ) switches and laser-emitting diodes.
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＞ de-coherence ( experimentally estimated by Y.Nakamura and others ) seems to be originated in a probe junction directly coupled to their circuit and 1/f-noises caused by motions of back-ground changes
This preparation of the condition is interesting even from the viewpoint of cognitive science.
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＞ external communications between RSFQ ( Rapid Single-Flux Quantum ) and semiconductors at room temperature
It was pointed out by Szent-Gyorgyi that specific proteins in a living body behave like semiconductors ( or organic semiconductors ).
From 「Notes on Artificial Medical Materials」,
6.3 Geometrical Customization
6.3.1 Necessity of geometrical customization
In this country ( Japan ？), 23.3 % of the total population is aged people ( in 2013 ), this tendency is getting higher year by year.
A number of patients suffering from osteo-arthritis including kinetic disabilities has increased with such a tendency.
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If the pathological condition of osteo-arthritis gets worse, it’s needed for compensating for a lost body-function to replace the damaged part with an artificial joint.
But, in general, its durable term is about 10 〜 20 years. Accordingly, an implant having longer lifespan has been requested.
In general, an artificial joint at present has a standardized shape on average skeletal shapes, so inevitably, an in-compatible case with a skeletal shape can happen.
It’s valid for avoiding such an undesirable case as much as possible to customize a shape.
These detailed procedures are explained in an other section.
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Meanwhile, geometrical customization can be applied to components for bone-joining.
A supracondylar humerus fracture and a fracture of the stem of an antebrachial bone are often caused in childhood, as it’s hard to apply conservative treatment to remarkable cases in displacement of those fractures, such cases can be often healed at deformed state.
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And, patients suffering from fracture on the distal position of a radial bone as well as osteoporosis as a complication have rather increased due to the aged society getting serious.
Though cases being healed at deformed state have been suppressed recently, especially in conservative treatments, displacement often turns out to be healed at deformed state because of bone-brittleness.
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Murase and others applied computer-simulations to processes to be healed at deformed state after a fracture to develop a new type of correcting osteotomy.
They mainly applied correcting osteotomy to a mirrored image in a healthy side as a target through this system and utilized a plate for bone-joining.
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In case of patients who were healed at deformed state, its skeletal shape also deformed due to re-modeling after a fracture.
Besides, in many cases, even if one position is corrected so as to fit it to a mirrored image in a healthy side through osteotomy, the skeletal shape around the position to which osteotomy is applied remains abnormal.
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Accordingly, as an anatomical plate produced on average skeletal shapes would not fit in the skeletal shape after correcting osteotomy,
consequently bending is needed for a surgery.
It’s difficult to perform it during a surgery.
Because it must be performed under an unstable situation provisionally fixing a reduced position after osteotomy and a limited visual space.
Besides, the strength of a component for bone-joining falls due to bending, so that the component can be broken down after a surgery.
At present, custom-made components for bone-joining to precisely perform a surgery without bending are being developed ( in 2013 ).
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6.3.2 Correcting-osteotomy with computer simulation
It has been possible to simulate a surgery on an osteo-joint at high accuracy owing to recently remarkably developing 3-dimensional imaging technologies instead of pre-surgical planning until now with 2-dimensional images such as simple X-ray.
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Murase and others produced an unique simulation software to give an optimized surgery （ ① ）,
and they developed a surgical method with a custom-made surgiical template ( an apparatus to support a surgery ) designed on a computer and produced through the latest molding technology for an individual patient to perform a surgery according to the simulation ( ② ).
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It’s possible to precisely and practically support a surgery on an osteo-joint by this technology.
For example, we could perform a simulated surgery with a bone taken out of a dead body at error of 1 mm, accuracy of below 1° .
The 3-dimensional computer model of a targeted bone is produced on CT-data, surgical simulations such as osteotomy and a way to put an implant on the position are performed on a computer.
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Then, required conditions such as a position to which osteotomy is applied, a bored position on a bone and a direction to bore a bone are caught, a custom-made surgical template is designed to refer to those caught informations during a surgery.
Such a template has a shape to closely fit with a surface of bone.
Slits and drilled holes made on the template play roles as guides for osteotomy and boring.
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The actual-sized model of a template was produced with a 3-dimensional printer with high accuracy called EDEN 250 RP machine ( manufactured by Objet.com in Israel ) on data for designing by a computer.
This model was sterilized with ethylene oxide to actually use it in a surgery.
Actually, a produced template is fitted to a surface of bone, respective operations such as osteotomy, boring on a bone, putting an implant on a damaged part are performed according to slits and drilled holes made on it.
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〈 Additions 〉
・ First, a model in a pathological side is superposed on a mirrored image in a healthy side at a proximal position, next, a mirrored image in a healthy side is superposed on a model in a pathological side at a distal position.
And, a difference in variation between both conditions is drawn, a deformation axis and a quantity in deformation are drawn on the difference.
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・ A custom-made template is fitted to the surface of a deformed bone, the template is fixed with k-wires as guides for correction, osteotomy is applied to the bone through an additional slit for osteotomy, and the bone is reduced with a guide so as to make k-wires parallel.
・ A correcting osteotomy simulation is applied to a model in a pathological side with referring to a mirrored model in a healthy side, a position on which a distal locking screw is put is determined, and a plate compatible with a skeletal shape after correcting osteotomy simulation is designed.
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6.3.3 Geometric customization of bone-joining implant
There are various parts which are healed at deformed state after fracture.
Murase and others diagnostically, mainly are dealing with bones of upper limbs which are healed at deformed state after fracture.
※ The distal part of a humerus, the stem part of a radial ulna, the distal end of a radial bone
Here, we explain about the geometric customization of a component for the distal end of a radial bone of the bone-joining components applied to upper limbs which are healed at deformed state after correcting osteotomy.
>>87
〈 Production of bone-model and calculation of quantity in deformation 〉
Images are caught through a 3D-CT from both sides, a bone-model is produced on drawn DICOM data.
Then, a model in a pathological side is superposed on a mirrored image in a healthy side at a proximal position and a distal position respectively.
〈 Simulation of correction on deformation 〉
Osteotomy is applied to a proper part of a pathological model near to a center in deformation.
And, a deformed model is corrected so as to overlap it on a healthy mirrored model to produce an osteo-model after correcting.
>>88
〈 Design for a customized implant 〉
A basic concept to put a locking plate on a hand for fracture on the distal end of a radial bone is as follows.
A custom-made component for bone-joining covered with a smooth surface has a locking mechanism, the component is designed so as to fit it to a bone-model after correcting with following procedures.
・ To support a sub-chondral bone by distal locking pins.
・ To put a plate within the watershed line not to give damages on a flexor tendon.
>>89
And, the positional direction into which a screw is put determined on a computer is concretized through a custom-made template.
Next, the custom-made component for bone-joining is put so as to fit it to the actual skeletal shape with locking the screw with the plate.
So that, it’s possible to perform a reduction and a fixation at the same time.
>>90
〈 Conclusion 〉
In many cases of correcting osteotomy with computer simulation developed by us in the past,
it’s needed to apply bending to a plate in fixing after reduction.
But, it’s possible to not only perform a reduction and a fixation at the same time but also go on a surgery smoothly with a customized implant for bone-joining.
>>73
＞ These detailed procedures are explained in an other section
From 「Notes on artificial medical materials」,
3.5.1 Customized Artificial Hip Joint
3.5.1.1 Customized artificial hip-joint
An artificial hip joint is mainly composed of an acetabular component, a femoral component and an acetabular insert & a femoral caput constituting a rubbing interface.
Metallic implants are mainly used for acetabular・femoral components, two methods ※ are mainly adopted to fix an implant on osseous tissues.
※ One is a method with surgical cement, another is a method for fixation without surgical cement.
Age, individual pathological conditions, osteo-characteristic states are taken into consideration to determine an applied method of them.
>>92
At present ( about 2013 ), surgeries with artificial hip joints are tending to be performed with cementless artificial hip joints.
But, if a fixation of an implant on osseous tissues fails, such a failure gives bad influences on stability over a long period.
Therefore, a fixation of an implant on osseous tissues is very important.
一
>>93
Factors which affect an initial fixation of an artificial hip joint and its stability over a long period are roughly classified into ( 1 ) the side of implant and ( 2 ) the side of living body as follows.
( 1 ) the surfacial condition of an implant, designs for implant, rubbing surface ( generations of abrasive powders ), etc.
( 2 ) sex, age, physical constitution including weight & body mass index, osteo-quality, extent of activity, etc.
с
>>94
Furthermore, designs for cementless artificial femoral component were classified as follows by Khanuja and others.
① single wedge
② double wedge
③ tapered
④ cylindrical fully coated
⑤ modular
⑥ anatomical
A most fitting part for the shape of the applied femoral medullary cavity is usually chosen from various ready-made implants in size to use a femoral component.
>>95
Especially, Japanese women suffering from hip joint disease tend to experience secondary osteo-arthritis of hip following acetabular dysplasias.
Besides, we must take remarkable individual differences in shape of thigh-bone into consideration.
а
>>96
Accordingly, to acquire an ideal fitting & filling condition, we need to optionally prepare a femoral component as a modular system interlocking the proximal part of a thigh-bone with its distal part and a customized stem fitting for each individual shape of thigh-bone.
In particular, as a customized stem is designed with bearing the optimal fitting for a femoral medullary cavity in mind, it’s regarded as the ultimate anatomical component.
>>97
3.5.1.2 Clinical results in customized artificial hip-joint
First, customized stems suitable to individual pathological conditions in a femoral side had been developed.
But, as mismatches between surfacial conditions of used customized stems and individual cases appeared in many cases at that time, only poor clinical results were obtained in customized artificial hip-joint.
一
>>98
An implant made of titanic alloy produced by molding a shape of a femoral medullary cavity during a surgery was introduced to the clinical field in 1989 .
As this implant as an anatomical stem had a 3-dimensional curve, it fitted to a femoral medullary cavity, good clinical results were obtained in fitting and filling.
But, such an implant often failed in initial fixation due to its smooth surfacial condition, so that a non-infectious loosening was caused within a short term after a surgery in many cases.
с
>>99
And, an other type customized stem has been produced on CT-imaging data through CAD and CAM .
Lateral sides of this stem were curved, titanic wire mesh pads were put on the frontal side and the back side of the proximal position of the stem and in the inside of it.
But, in this case, as those pads were not all-circumferential, dissociation between pads and a stem after formation of osseous tissues on pads was often reported as a serious problem.
Consequently, non-infectious loosenings were frequently caused in such cases too.
а
>>100
There were few reports of customized stem in the first half of the 1990’s .
Meanwhile, in the latter half of the 1990’s , customized stems having various surfacial conditions such as blasting, a coating on the proximal position of a stem with plasma-spraying, a coating with hydroxyapatite, etc were introduced into clinical fields,
comparatively good clinical results over a short and a middle term also were reported.
>>101
Furthermore, a length of stem was remarkably shortened to be to a higher order position of a lesser trochanter for keeping osseous tissues.
So that, partial good results over a middle term also were reported.
But, even if a length of stem was remarkably shortened, bone-atrophy caused around the proximal position of a thigh-bone due to stress-shielding has never been completely overcome ( in 2013 ).
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>>102
3.5.1-3 Ways to produce a customized stem
〈 Determination of a gesign for an implant 〉
Usually, each sectional figure of an implant for each axial section is determined on data of a thigh-bone drawn through helical CT , the 3D figure is designed with CAD / CAM -system.
Though stems produced on X-ray images rather than CT also have been reported, it’s insufficient to 3-dimensionally produce an implant with such ways.
Next, we check whether the produced implant can be just put in the femoral medullary cavity or not through simulations on a computer.
And finally, the design for the implant is determined.
>>103
〈 Parameters to design a customized stem 〉
Following respective factors are taken into consideration to prepare an implant suitable to each individual pathological condition.
・ stem-length
・ offset
・ neck-shaft angle
・ neck-cut angle
・ bowing around a lateral side
・ a range of proximal coating
Then, we need to sufficiently check the risks of breakdown of stem through stress analysis.
>>104
〈 Production of a customized stem 〉
Here, we pay attention to a layering molding method with powdered Ti-6Al-4V alloys through electron-beams of some ways to produce this component.
First, powdered alloys are melted by applying an electron-beam to them,
next, those melted alloys are solidified through cooling.
And, a stem is produced through such an alternate repetition of melting and solidification according to a drawn 3D CAD model.
According to many reports, we also heard that most of the hopeless alcoholics and the chaps habitually presenting e×treme erotic advertisements and vulgar ones would fight against the world as their enemies from now.
Indeed, we also heard that the people habitually and intentionally making annoying and noisy sounds with vehicles in Japan also would fight against the world as their enemies.
а
We also heard that the people habitually presenting undesirable advertisements such as unreliable ones dealing with defective products and fakes like in this site would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable ones dealing with defective products & fakes on the net also would be conveyed to purgatories owing to the judgment by the king of Enma (閻魔).
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and advertisements of unreliable products on the net also would fight against the world as their enemies.
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
Besides, according to many reliable informations, it’s highly probable that the people habitually presenting undesirable advertisements on the net would be transferred to purgatories owing to the judgment by the king of Enma (閻魔).
>>110 〜 >>144
We also heard that the people habitually presenting undesirable contents such as e×tremely erotic & vulgar contents and unreliable advertisements dealing with fakes on the net and intentionally making various harassments including auditory harassments would fight against the world as their enemies, and they would be transferred to ‘purgatories’ due to the judgment by the king of Enma (閻魔).
