EP1183778A2 - Procede optique de calcul quantique - Google Patents

Procede optique de calcul quantique

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Publication number
EP1183778A2
EP1183778A2 EP99918827A EP99918827A EP1183778A2 EP 1183778 A2 EP1183778 A2 EP 1183778A2 EP 99918827 A EP99918827 A EP 99918827A EP 99918827 A EP99918827 A EP 99918827A EP 1183778 A2 EP1183778 A2 EP 1183778A2
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Prior art keywords
photons
photon
atoms
phase shift
quantum
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EP99918827A
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German (de)
English (en)
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James D. Franson
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Johns Hopkins University
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Johns Hopkins University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena

Definitions

  • the invention relates to quantum computing and, more specifically, is a novel optical method for constructing a quantum computer.
  • quantum-mechanical computers could use nonclassical logic operations to provide efficient solutions to certain problems of that kind, including the factoring of large numbers.
  • a nonclassical logic function consider the conventional NOT operation, which simply flips a single bit from 0 to 1 or from 1 to 0.
  • a quantum computer could also implement a new type of logic operation known as the square root of NOT. When this operation is applied twice (squared), it produces the usual NOT, but if it is applied only once, it gives a logic operation with no classical interpretation.
  • quantum computers In addition to performing nonclassical logic operations, quantum computers will be able to perform a large number of different calculations simultaneously on a single processor, which is clearly not possible for a conventional computer. This quantum parallelism is responsible for much of the increased performance of a quantum computer.
  • Quantum computers will use a binary representation of numbers, just as conventional computers do.
  • An individual quantum bit often called a qubit, will be physically represented by the state of a quantum system. For example, the ground state of an atom could be taken to represent the value 0, while an excited state of the same atom could represent the value 1.
  • a 0 is represented by a single photon in a given path. The same photon in a different path represents a 1.
  • Quantum-mechanical superpositions of this kind are fundamentally different from classical probabilities in that the system cannot be considered to be in only one of the states at any given time. For example, consider a single photon passing through an interferometer, as illustrated in Fig. 1, with phase shifts ⁇ and ⁇ inserted in the two paths. A beam splitter gives a 50% probability that the photon will travel in the upper or the lower path. If a measurement is made to determine where the photon is located, it will be found in only one of the two paths. But if no such measurement is made, a single photon can somehow measure both phase shifts ⁇ and l simultaneously, since the observed interference pattern depends on the difference of the two phases.
  • a quantum computer can provide results that depend on having performed a large number of calculations, even though a measurement to determine exactly what the computer was doing would show that it was programmed to perform only one specific calculation.
  • N input bits N input bits
  • the result can be described by N output bits, as illustrated in Fig. 2.
  • input bits 2 ⁇ * different combinations of input bits, each of which corresponds to a specific input state denoted by
  • output k The equal number of specific combinations of output bits.
  • output k Each input state can produce a superposition of possible output states
  • the input state can be a superposition of all of the possible inputs to the computer:
  • the probability of getting a particular output depends on all of the coefficients ⁇ , which represent the results of all possible calculations on the computer.
  • the result also depends on interference between all of the possible inputs, in the sense that Pj ⁇ will be large if all of the input states contribute in phase with each other. Conversely, Pfc will be small if the contributions from all of the initial states cancel out.
  • the goal of quantum computing is to program the computer in such a way that the desired result occurs with high probability while all incorrect results occur with negligible probability.
  • ⁇ j is a highly nonlinear function of / ' .
  • the quantity Q corresponds to a weighted average of the function/Over all possible inputs to the computer, which is a Fourier transform of sorts. Calculations of this kind could be implemented on a quantum computer by programming the computer itself to calculate ⁇ j) and then creating a superposition of input states corresponding to the desired weighted average.
  • quantum computers could be used to efficiently factor large numbers, which is responsible for much of the current interest in quantum computing.
  • the algorithm involved uses interference effects to ensure that, with high probability, the output of the computer will correspond to one of the desired factors.
  • any practical implementation of a quantum computer will probably require a modular approach in which many separate logic gates can be connected with some equivalent of the wiring in a conventional computer.
  • the ability to correct for the growth of errors in the quantum states is also essential.
  • Individual quantum gates have been demonstrated using the nuclear spins of ions in a trap. This approach is not modular, however, and the transfer of information from one ion to another is a very complex process.
  • optical interferometers are widely used in many current applications because their phase is relatively stable and can be controlled using feedback techniques. Interferometers based on charged particles, such as electrons, do exist but are very sensitive to stray electromagnetic fields. In addition, optical fibers or waveguides could readily be used to connect optical quantum gates as needed to perform the desired logic operations. For these and other reasons, the most practical approach to the construction of quantum computers will likely be based on the use of optical devices.
  • a controlled-NOT gate can be implemented using the optical arrangement illustrated in Fig. 4.
  • bit A has the value 1 if a single photon is in the path indicated by the dashed line, whereas it has the value 0 if that photon is in the path indicated by the solid line.
  • Input B is represented in a similar way by a second photon; the two photons have different frequencies ⁇ 1 and ⁇ 2 . which allow them to be distinguished.
  • the two paths for photon B are combined by a beam splitter to form an interferometer with one arm passing through a nonlinear medium.
  • the phase shift experienced by photon B depends on the index of refraction of the medium, which in turn depends on the strength of the electric field at that location (Kerr effect). If photon A passes through the medium at the same time, its electric field will introduce an additional % phase shift, which changes the output path that photon B must take. The net result is that photon A can control the path of photon B.
  • the approach of the invention is based on a new physical effect that should greatly enhance these kinds of nonlinear phase shifts.
  • Earlier nonlinear mechanisms involved the interaction of two photons with individual atoms, which gives a phase shift proportional to the number NA of atoms in the medium.
  • the new mechanism involves the interaction of two photons with pairs of atoms, which gives a phase shift proportional to NA . since that is the number of pairs of atoms in the medium.
  • the proposed mechanism consists of the absorption of photon 1 and the emission of photon 2 by atom A, followed by the absorption of photon 2 and the emission of photon 1 by atom B.
  • this new mechanism should produce much larger phase shifts at the two-photon level. This in turn will allow other design requirements to be relaxed, such as the need for high-quality mirrors or atomic beams. As a result, this approach is eventually expected to allow the construction of large numbers of quantum gates on a single substrate, with optical waveguides to provide the necessary logical connections.
  • the method of the invention is expected to provide a practical means of scaling-up to a full-size computer.
  • the method disclosed herein can be applied to conventional optical data processing, i.e., the optical approach described above can be used to build a standard computer to increase speed and reduce heat generated by the components.
  • Fig. 1 illustrates a single photon passing through an interferometer. Such a photon can simultaneously measure the phase shifts in both paths, even though it will always be found in only one path.
  • Fig. 2 illustrates a general purpose quantum computer with N input bits and N output bits. Superpositions of different input and output states allow the computer to effectively perform many different calculations simultaneously.
  • Fig. 3 illustrates a controlled-NOT (XOR) gate, which can form the basic logic element of a quantum computer.
  • Bit B is inverted if and only if bit A is 1.
  • Fig. 4 illustrates optical implementation of a controlled-NOT gate based on a nonlinear index of refraction in one arm of an interferometer.
  • Fig. 5 illustrates predicted mechanism for the enhancement of nonlinear phase shifts at the two-photon level.
  • An exchange interaction in which atom A absorbs photon 1 while making a transition from its ground state to its excited state, after which it re-emits photon 2.
  • Atom B absorbs and re-emits the photons in the opposite order. This interchange of the two photons produces a nonlinear phase shift.
  • a mechanism of this kind is expected to be relatively strong at single-photon intensities because the two photons are not required to interact with the same atom.
  • Fig. 6 illustrates a conventional mechanism for the production of nonlinear phase shifts (Kerr effect), in which virtual transitions between atomic levels
  • a photon at frequency ⁇ i is present to produce a virtual transition from level
  • Mechanisms of this kind require both photons to interact with the same atom, which is unlikely to occur at single-photon levels.
  • the nonlinear phase shift is equal to the difference in the phases in the two cases, which can be strongly affected by exchange interactions.
  • Fig. 8 illustrates a virtual state in which atoms A and B are both excited and which may have been produced in two ways: Photon 1 may have excited atom A while photon 2 excited atom B, or photon 1 may have excited atom B while photon 2 excited atom A. Constructive interference between these two probability amplitudes can produce a factor of 2 enhancement in the probability of there being two excited atoms.
  • Fig. 9 consisting of Figs. 9(a) and 9(b), illustrates, respectively, an atomic medium whose density p is a slowly- varying function of position z and sufficiently thin that ⁇ k ⁇ z « ⁇ /2, where ⁇ z is the thickness and a periodic medium satisfying the condition ⁇ k ⁇ z «2p ⁇ , where ⁇ z is the periodicity and p is an integer. In either case, there is constructive interference between the probability amplitudes of Fig. 8.
  • Fig. 10 illustrates the application of a laser pulse that is detuned from the transition between levels 2 and 3, which can be used to produce a Stark shift in the energy of level 2 and a corresponding phase shift in that state.
  • Fig. 11 illustrates a laser-induced transition, in which photon 1 or 2 is off-resonance from level 3, but the application of a laser pulse allows a resonant transition into level 2.
  • Fig. 12 illustrates a five-pulse sequence producing a nonlinear phase shift of ⁇ .
  • Pulse 1 produces a transition from the initial state
  • Pulse 2 has no net effect when the photons are in two different media but produces a superposition of states
  • Pulse 3 produces a phase shift in the state
  • the last pulse returns the system to its initial state aside from a relative phase shift of ⁇ .
  • Fig. 13 consisting of Figs. 13(a) and 13(b), illustrates plots of the real part R of the probability amplitude of state
  • Fig. 13(a) illustrates effects of pulse 2, which produces a superposition of states
  • Fig. 13(b) illustrates effects of pulse 4, which reverses the effects of pulse 2 and returns the system to state
  • Fig. 14 illustrates real and imaginery parts of the probability amplitude of state
  • the radius of the dashed circle represents the magnitude of the probability amplitude of state
  • Vector b represents the contribution from the initial probability amplitude of state
  • the phase and detuning of the pulse can be adjusted to make the resultant vector lie anywhere on the dashed circle, which gives an arbitrary phase shift.
  • Fig. 15, consisting of Figs. 15(a) and 15(b), illustrates, respectively, two classical systems, S ( and S 2 , that are connected by a sequence of physical interactions that may involve one or more auxiliary systems labeled A and two classical systems that are not connected by a sequence of physical interactions. There is no path for the flow of information in the latter case and a classical control process cannot occur.
  • Fig. 16 illustrates an implementation of a controlled-NOT gate giving the conventional phase shifts.
  • Fig. 17 illustrates the interaction of two photons in optical fibers by means of their overlapping evanescent fields in a thin crystal. This mechanism could be used to produce the nonlinear phase shifts required to operate quantum logic gates.
  • Fig. 18 illustrates a Controlled-NOT gate acting on two photons A and B with the same frequency. A scratch qubit at a different frequency is used but returned to its initial state of 0.
  • Fig. 19 illustrates a two-bit adder circuit.
  • Fig. 20 illustrates a memory storage device consisting of two loops of optical fiber with electro-optical switches.
  • Fig. 21 illustrates the use of feedback to minimize the effects of phase errors.
  • a medium such as an atomic vapor cell
  • the medium will typically be very small. For example, if the medium contains 10 10 atoms and the
  • the frequency of photon 2 is relatively close to the transition frequency
  • atom A absorbs photon 1 and re-emits photon 2
  • atom B absorbs photon 2 and re-
  • each photon has a probability on the order of unity of being absorbed by an atom
  • ⁇ k is the difference in the k vectors of the two photons and ⁇ r is the difference in the positions of the two atoms. This is the same condition that is required for the observation of the
  • atoms A and B are viewed as two "detectors" placed in front of a well-collimated source.
  • the factor of 2 difference in P can be exploited by applying a laser pulse to produce a
  • the laser pulse will depend on the population of the excited atomic states and a different phase
  • suitable sequence of such laser pulses can give a nonlinear phase shift of ⁇ , which can then be
  • interaction with the laser pulses can then be determined by solving a six-dimensional eigenvalue
  • optical medium will be assumed to be an atomic vapor cell for simplicity, although
  • Equation (1) can be satisfied
  • photons is much less than their average frequency and they propagate in the same direction.
  • ⁇ - ⁇ 2 may be on the order of a few GHz in a typical experiment, which would allow
  • the thickness of the vapor cell to be on the order of 1 cm.
  • N of atoms in the medium will be assumed to be large ( ⁇ 10 10 ).
  • the thickness of the atomic medium can be substantially increased while still satisfying
  • Equation (1) by using a periodic density of atoms as illustrated in Figure (9b), where it is
  • a laser beam is used to couple the second atomic level to a third atomic state that is of no
  • the incident photons are assumed to propagate along the z direction and are represented
  • multi-mode Fock states (not merely weak coherent states) corresponding to gaussian wave
  • the temporal width ⁇ of the wave packets is assumed to be much longer than the
  • the incident photons can be represented by two single-photon creation operators, a f and a f ,
  • packets have the same amplitude and width but different values for their central k-vectors, k and
  • Equation (3) involves only the
  • G (z)and G (z) is a slowly varying function of z and the exact shape of the wave packets is not
  • e is the energy of the excited state (level 2) of an atom
  • ⁇ is one of the Pauli spin matrices in a two-dimensional Hubert space consisting of the ground and excited states of atom i. (This does not imply any spin
  • E(R ) is the second-quantized electric field
  • ⁇ is the permittivity of free space
  • V is the volume used for periodic boundary conditions
  • the photon wave packets are not eigenstates of H o and they will propagate at the speed
  • H'(t) exp[/H 0 (/-r o ) h] H exp[- H 0 (/-f 0 )/fc]as usual. H'(t) will be found to be a slowly-
  • the eigenvectors can be computed numerically or analytically, but in either
  • the postulates of quantum mechanics allow us to choose any set of orthonormal basis
  • c is a normalization constant and the last two terms provide the desired orthogonality.
  • Equation (2) Making use of Equations (2), (5), and (11) allows to be written as
  • Equation (15) then reduces to
  • the matrix elements involving the modified plane-wave states can be evaluated in the
  • the photons are linearly polarized along the x direction, for example, then the atomic
  • atoms will be denoted by c( ⁇ , ⁇ ) and c( ⁇ , ⁇ ) .
  • Equation (20) is simplified by introducing a new
  • Equation (24) An inspection of Equation (24) reveals that it is equivalent to Schrodinger's equation for a six-dimensional vector whose components are taken to be
  • Equation (26) The exponential factors in Equation (26) are rapidly varying functions of time. This time
  • Equations (30) and (31) determine the time evolution of the system for the case in which both
  • c '(y ) is the total probability amplitude that photon 1 remains with no excited atoms
  • the photon wave packets have been assumed to be far from the medium at the initial time
  • two-photon dressed state may be nothing more than the tensor product of two single-photon
  • eigenvector in each case will be the one whose energy is nearest the initial value of zero.
  • Table (1) were calculated numerically to an accuracy to 40 significant digits but only the first 20
  • Equation (41) Equation (41)
  • E the energy of the two-photon dressed state that occurs when both photons propagate
  • Equations (41) and (43) directly.
  • the factor of 2 can be easily derived for the case of equal
  • photon wave packets are centered on it.
  • the electric field of the laser pulse will produce a
  • ⁇ E(t) is the change in the energy of the excited states that is produced by the application
  • the intensity and duration of the laser pulse can be adjusted to give any desired
  • the second and third components of the state vector correspond to a single excited atom and are
  • ⁇ > can be conveniently expressed as a linear combination of the
  • Equation (48) Expanding the left-hand-side of Equation (48) to
  • Equation (50) applies to the case in which both photons are propagating in the same medium
  • Equation (53) shows that the nonlinear phase shift is directly proportional to the
  • phase shift is thus expected to be proportional to N 2 in the weak coupling limit, which makes it
  • the nonlinearity depends on the fact that the two-excited-atom states undergo a phase shift of ⁇ ,
  • Equation (47) orthogonal state
  • the system will be excited into a virtual state in which the atom is in
  • Equation (45) which generalizes Equation (45).
  • ⁇ , ⁇ , and ⁇ 0 are the phase shifts in the states
  • ⁇ > , and 10> , and the value of ⁇ depends on the amplitude of the laser pulses (all the pulses
  • pulses can then be tuned to produce resonant transitions into level 2, where one frequency will
  • the frequency and amplitude of the first laser pulse are chosen to produce a resonant
  • the frequency of the second pulse is then chosen to be on resonance for photon 1
  • the frequency of pulse 3 is chosen to be slightly off-resonance from a photon 1 transition
  • labeled b represents the contribution from the probability amplitude of state 10> before the pulse
  • pulse 2 except for a phase shift.
  • the amplitude and frequency of pulse 4 are therefore chosen to
  • this pulse can be adjusted to eliminate the
  • electromagnetic field are those generated by a and a ⁇ . It is expected that this condition can be
  • Figure 15(a) provides a path for the flow of information from one system to the
  • phase shift is proportional to ⁇ E, this gives a nonlinear phase shift proportional to N, not N 2 ,
  • Equation (57) shows that the nonlinear phase shift cannot be due to a local polarization of
  • phase shift is the phase shift
  • quantum mechanics and classical determinism is not limited to random events; a quantum control
  • a Controlled-NOT gate can be implemented using the interferometer arrangement
  • Input bit A is represented by a single photon located in one of two paths, and is assigned the values 0 or 1 depending on the location of the photon as shown. For the time being, these paths can be considered to be two optical fibers.
  • Input B is similarly represented by another photon located in one of two other paths. Photon B enters an interfer- ometer, with one arm of the interferometer passing through a medium. This produces a phase shift if and only if photon 1 is located on the path that represents the bit 0, which also passes through the medium. The magnitude of the phase shift can be adjusted by varying the density of the atoms in the medium and constant phase shifts can be added to either path as required. Photon B will then either emerge in the same path it entered or in the opposite path, depending on the phase shift established by photon A. The net result is that bit B will be reversed if and only if bit A had the value 1.
  • the interferometer of Fig. 4 causes the photons to exit the gate in the desired paths, but the relative phases of the various output states do not correspond to those of the Controlled-NOT gate as conventionally defined.
  • the desired phases can be imposed using the circuit of Fig. 16.
  • a square box located in a single path represents a conventional single-photon phase shift of the kind that could be produced by a piece of glass, while a square box connected to two paths represents a nonlinear phase shift that only occurs if a photon is present in each of those paths.
  • the desired magnitude of the nonlinear phase shifts can be achieved by varying the density of the atoms in the medium or other parameters, such as an external magnetic field.
  • Another way, in addition to laser pulse(s), of increasing exchange interactions is to add a buffer gas, such as Argon, which increases the rate of collisions.
  • Fig. 16 can be modified to implement a Controlled square-root of NOT gate instead, which is convenient for some applications.
  • the physical implementation of the nonlinear phase shifts depends on the nature of the photon paths. Basic path options include free-space propagation in beams, propagation in optical fibers, and propagation in waveguides on the surface of a substrate. The basic implementation is the same in all cases. For optical fiber paths, the nonlinear phase shifts can be implemented as shown in Fig.
  • Fig. 17 can now be viewed as replacing the nonlinear phase-shift boxes in circuit diagrams like Figs. 4 and 16, while the interferometers would consist of conventional fiber-optic interferometers. Fig. 17 can also be implemented using one fiber and one crystal by having both photons travel in the same fiber.
  • the physical implementation for photon beams in free space would replace beam splitters with etalons tuned in such a way that photons with frequency ⁇ > ⁇ are transmitted while photons with frequency ⁇ 2 are reflected. This would allow the two photons to be merged into a common path through an atomic vapor cell without the 50% losses associated with ordinary (frequency- independent) beam splitters. The two photons would then be separated into two different paths using their transmission or reflection from a second etalon.
  • Fig. 17 The phase shift-implementation of Fig. 17 can be inco ⁇ orated into the circuit diagram of Fig. 16 to provide a specific description of a Controlled-NOT logic gate.
  • the nonlinear phase shift mechanism discussed above requires that the two photons have different frequencies.
  • the circuit shown in Fig. 18 performs a Controlled-NOT operation on two photons of frequency coi by making use of a scratch bit at frequency ⁇ 2 -
  • the scratch bit is initially in the state corresponding to 0 and is returned to the state 0 at the end of the calculation, so that "garbage" bits are not accumulated.
  • Controlled-NOT gate and the nonlinear phase shifts of Fig. 17 can be used to implement a Controlled-Controlled-NOT gate, which can then be used in the two-bit adder circuit shown in Fig. 19.
  • the Controlled-NOT circuit can be used to determine whether or not there is a photon in the "0" input path (the solid line of Fig. 4) for bit A without changing the number of photons in that path, which constitutes a quantum non-demolition measurement. This can be accomplished by injecting a series of photons into one of the paths of input B and checking to see if any come out in the opposite path. By repeating the measurement with a set of different nonlinear phase shifts, one can ensure that one and only one photon A is present with an exponentially small error.
  • the proposed light source would be initialized with a weak coherent-state pulse in each of a large number of optical fibers, with the mean number of photons in each fiber equal to one; such a state can easily be produced from a single laser pulse and a set of directional couplers.
  • the number of photons in each of the fibers can then be measured without changing the number of photons.
  • Those fibers containing one and only one photon would then be switched into the input ports of the quantum computer using conventional fiber-optic switches.
  • Such a process should be much more efficient than the use of spontaneous parametric down-conversion, for example, which gives an exponentially small probability of producing N photons at the same time.
  • Additional advantages include the simplicity of the design, which does not require any switches or separate memory devices. Connections between different fibers can be minimized or eliminated, since the logic gates can be formed by bringing the fibers close together and letting them interact via their evanescent field, as shown in Fig. 17. This may also be an important advantage, since the losses associated with connectors is expected to be a major source of technical decoherence.
  • the operation of a quantum computer, as well as most other applications of quantum information technology will require the use of suitable quantum memory devices.
  • Quantum memory devices must be capable of storing the value of a quantum bit (qubit) of information while avoiding the effects of decoherence over relatively long periods of time.
  • pulse one can be used to absorb either photon and store its information (presence or absence of the photon, or the polarization of the photon) in a supe ⁇ osition of excited atomic states in a suitable solid-state material, such as various crystals.
  • the information will be stored in the crystal until another pulse is applied; this is equivalent to the fifth pulse shown in Fig. 12, which has the effect of causing the crystal to re- radiate the photon in the same direction and with the same frequency that it had originally.
  • a quantum memory device of this kind only two pulses would be used, one to store the information and the other to reproduce the original qubit on demand.
  • Coherent memory storage times that are long enough to perform roughly one million quantum logic operations should be achievable in this way. That is sufficiently long to allow the use of quantum error correction methods to extend the coherent storage time indefinitely.
  • Useful calculations on a quantum computer may require up to 10 12 operations. It does not appear feasible to perform that number of operations without the use of memory devices, even taking into account a large degree of parallelism. Nevertheless, parallel processing of this kind may still be applied to perform relatively complex mathematical operations within the computer as a whole.
  • the nonlinear phase-shift device shown in Fig. 17 has a length of 1 cm, for example, then the amount of time ⁇ t op required to perform a logic operation would be on the order of 33 picoseconds, the transit time at the speed of light.
  • the minimum attenuation factor for commercial fibers is 0.16 dB/km, which means that a photon can travel roughly 20 km before it has a 50% probability of being absorbed.
  • Quantum cryptography experiments in optical fibers, as well as two-photon interferometer experiments have shown that the quantum-mechanical coherence of qubits can be maintained over these distances, which correspond to a propagation time of approximately 130 microseconds. Based on these numbers, a photon can be stored in an optical fiber loop long enough to perform roughly 4 x 10 6 logic operations.
  • Error-correction techniques using redundant bits can then be used to "protect" the information against any single decohering event. Provided that the bits are monitored at sufficiently short intervals, the effective storage time can be greatly increased.
  • the quantum non-demolition measurements mentioned earlier can be put to good use here, since it is possible to check for the most common error source (abso ⁇ tion) without disturbing the value of the qubit; one can measure the total number of photons in the two loops without determining which loop the photon is in. This allows frequent checks to ensure that no more than one error has occurred, at which time the error-correction techniques can be used to restore the correct qubit. This suggests that the effective storage time of these devices is limited only by the performance of the basic quantum gates.
  • synchronization devices included in both loops of Fig. 20. These are (classical) nonlinear devices that are switched on at well-defined times in the computer clock cycle.
  • Each sync device consists of an electro-optic material whose index of refraction is turned on by the trigger and has a spatially- varying index of refraction. The index of refraction is higher on the left side of the device, so that photons that are ahead of their nominal position are slowed down. The index of refraction is lower on the right side of the device, so that photons that are behind their nominal position will be sped up.
  • Linear abso ⁇ tion corresponds to the usual attenuation of a photon beam passing through the medium in the absence of any other photos. Since the energy absorbed by the atoms is usually re-emitted in the form of another photon, most of this "abso ⁇ tion" corresponds to scattering of the photons. It is well known that scattering of this kind can be reduced to a negligible level by detuning the photons far from the resonant frequency of the atoms, where the real part of the index of refraction becomes much larger than the imaginary part. This is the reason that a piece of glass is transparent, and the same effect should hold true for the logic gates of the invention.
  • Nonlinear abso ⁇ tion is the additional scattering that occurs when two or more photons are present in the medium at the same time, as discussed above. This form of scattering also becomes negligible for large detuning, and the situation is analogous to the transparency of commonly-used nonlinear crystals, such as lithium iodate.
  • Atomic density fluctuations produce variations in the nonlinear phase shift produced by the medium. These fluctuations also become negligible as the number of atoms in the medium is increased. For the above reasons, all of the known sources of intrinsic decoherence are expected to become negligible compared to the technical decoherence of sufficiently large detunings and for sufficiently large numbers of atoms. If the technical decoherence is assumed to be on the order of 10 ⁇ 3 per logic operation, then, according to the theory, this would require that the detuning be greater than 10 3 line widths and that the number of atoms be greater than 10 6 . Both of these conditions appear to be feasible.
  • the abso ⁇ tion due to scattering in commercially-available fibers limits the intrinsic storage time of the photon qubits to roughly 4xl0 6 logic operations, which corresponds to a memory error rate of 10 "6 per operation. This is lower than that of other expected technical decoherence sources, and it is expected that error-correction techniques could compensate for it.
  • Losses in the fiber-optic switches are primarily due to phase errors in these fiber-optic interferometers. Visibilities of better than 99% are routinely achieved in fiber-optic interfer- ometers, and it seems plausible that phase errors of this kind could be reduced to less than 10 "3 using the feedback techniques to be described below. Once again, losses in waveguide structures may be prohibitive and it may be necessary to use all-fiber devices similar to that shown in Fig.
  • Dispersion is potentially a serious problem and will require some form of compensation.
  • Several mechanisms have been identified for this pu ⁇ ose, as discussed above, but none have been analyzed in detail. In principle, there is no reason that dispersion cannot be reduced to an insignificant level, but detailed calculations and experiments are required in order to provide a quantitative estimate of the likely errors due to dispersion.
  • the magnitude of the nonlinear phase shift applied in any given quantum logic gate will be affected by such factors as variations in the geometry of the device, magnitude of the detuning, and atomic density in the medium. Errors of this kind could be reduced to a very small level using feedback techniques that have been employed in systems for quantum cryptography, which is sensitive to similar phase errors. As illustrated in Fig. 21 test photons that are not part of the actual calculation would periodically be sent through the logic gates and the results measured. An appropriate correction to the phase shift can then be applied by varying an external magnetic field, for example. Based on past experience, this approach should be able to reduce such systematic errors to the 10 "3 level. It is expected that feedback of this kind would be a necessary part of each gate.
  • each of the quantum logic gates is physically separate from all the others, unlike the situation for an ion trap. If one quantum logic gate can be built that works well, then as many as is desired can be built, aside from the cost.
  • the other major advantage of the approach of the invention is that it does not require complicated structures, such as extremely high-Q cavities, atomic beams, atomic traps, etc. As a result, quantum logic gates based on the structure shown in Fig. 17 may eventually be mass fabricated at a sufficiently low cost that an actual computer could be made.
  • Quantum computing is a promising new technique that may eventually provide the ability to perform numerical calculations not possible with conventional computers. These enhanced capabilities result from the use of nonclassical logic elements and the ability of a quantum computer to perform many calculations in parallel on a single processor. The advent of quantum computers would revolutionize computer science and information theory.
  • the invention's optical approach to quantum computing has a number of advantages over other potential methods including the ability to construct independent logic gates that can be connected with optical fibers or waveguides, the ability to minimize decoherence by using large detunings, and the lack of any requirement for high-Q cavities, atomic beams, or traps.

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Abstract

L'invention concerne un procédé optique qui permet le calcul quantique et qui utilise les effets non locaux pour construire les portes quantiques elles-mêmes. Une interaction non locale, dans laquelle les paires d'atomes échangent deux photons, produit un déphasage non linéaire important. Ces déphasages non linéaires sont utilisés pour construire des portes logiques quantiques, telles qu'un NON commandé.
EP99918827A 1998-04-24 1999-04-26 Procede optique de calcul quantique Withdrawn EP1183778A2 (fr)

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JP3520334B2 (ja) 2000-12-27 2004-04-19 独立行政法人通信総合研究所 原子ビーム制御装置および制御方法
US7133173B2 (en) * 2004-07-26 2006-11-07 Hewlett-Packard Development Company, L.P. Nonlinear electromagnetic quantum information processing
GB0516565D0 (en) * 2005-08-12 2005-09-21 Hewlett Packard Development Co A quantum repeater
WO2009072693A1 (fr) * 2007-12-06 2009-06-11 Inha-Industry Partnership Institute Grilles logiques optiques retardées
KR100915171B1 (ko) * 2007-12-06 2009-09-03 인하대학교 산학협력단 시간 지연 광 논리 게이트 및 그 구동 방법
US9379303B2 (en) 2011-06-14 2016-06-28 Glocbalfoundries Inc. Modular array of fixed-coupling quantum systems for quantum information processing
CN103699352A (zh) * 2012-09-27 2014-04-02 陈志波 量子数码
EP3380996A4 (fr) * 2015-11-27 2018-11-14 Qoherence Instruments Corp. Systèmes, dispositifs et procédés d'interaction avec des informations quantiques stockées dans des spins
GB2553848B (en) 2016-09-19 2022-06-22 Royal Holloway & Bedford New College Quantum power sensor
US10176432B2 (en) * 2017-03-07 2019-01-08 International Business Machines Corporation Weakly tunable qubit based on two coupled disparate transmons
EP3777012B1 (fr) * 2018-03-28 2023-08-09 The Research Foundation for The State University of New York Dispositifs, systèmes et méthodes facilitant la mise en mémoire tampon, le stockage et la communication de l'information quantique à température ambiante
CN109004989B (zh) * 2018-08-06 2019-10-15 合肥本源量子计算科技有限责任公司 一种量子比特逻辑信号的生成系统和方法
CN112910454B (zh) * 2021-01-15 2022-03-29 宁波大学 一种可异步置数的可逆单边沿jk触发器
CN112865756B (zh) * 2021-01-15 2022-03-29 宁波大学 一种可异步置数的可逆双边沿d触发器
CN113642279B (zh) * 2021-10-18 2022-02-18 阿里巴巴达摩院(杭州)科技有限公司 量子比特处理方法、装置及计算机设备
CN114446401A (zh) * 2022-02-07 2022-05-06 上海图灵智算量子科技有限公司 量子线路生成晶体原子坐标的方法、装置、产品及介质
CN114627971B (zh) * 2022-03-18 2023-10-31 北京有竹居网络技术有限公司 用于固体系统的数据处理方法和装置

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KR20010085237A (ko) 2001-09-07
CN1163788C (zh) 2004-08-25
CN1419660A (zh) 2003-05-21
CA2326187A1 (fr) 1999-11-04
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WO1999056392A2 (fr) 1999-11-04

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