Abstract:
A capacitive operation method for quantum computing is disclosed where providing a sequence of write pulses above a threshold voltage induces a single charge population, forming a quantum dot (Q-dot). Determining if the single charge population was induced in the Q-dot occurs by monitoring capacitance changes while the writing is performed. Q-bits (Q-dot pairs) are formed without requiring a separate transistor for each Q-dot by multiplexing the calibration. A device which is able to perform the above method is also disclosed. The device utilizes the ability of cryogenic capacitance bridge circuits to measure the capacitance change caused by the introduction of a single charge population to a Q-dot. The device also permits swapping of Q-dot and Q-bit pairs utilizing a signal multiplexed with the voltage pulses that write (e.g. change the charge population) to the Q-dots.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit to U.S. provisional application 60/855,634 filed on Oct. 30, 2006, for “A Capacitive Arrangement for Qubit Operations” by Jeong-Sun Moon, the disclosure of which is incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure relates to quantum computing. In particular, it relates to capacitive calibration/read/write methods and devices for qubit operations. 
     BACKGROUND 
     The importance of charge detection in quantum computing (QC) is recently emphasized in numerous publications, including the paper “Charge Detection Enables Free-Electron Quantum Computation” by C. W. J. Beenakker, D. P. DiVincenzo, C. Emary and M. Kindermann, Physical Review Letters, Vol. 93, July 2004. Beenakker et al. propose in their theoretical paper that the electrometer scheme will enable “free-electron quantum computation” and parity check. 
     For scalable and practical QC, numerous physical limitations are expected. QC requires nanoscale fabrication of qubits because the individual qubits must each consist of only a single electron cell. In addition, the tight control of lithographic dimensions of qubits is required, which poses significant challenges in processing of qubits. Furthermore, each qubit must necessarily be addressed through interconnects externally, unlike with conventional Boolean logic based computing in Si CMOS technology. Although the state-of-the-art lithographic tools are utilized for the fabrication of arrays of qubits, some degree of size fluctuations will be present, which leads to a fluctuation in the number of electrons in the qubits. If more than one electron is in a qubit, then this can inhibit proper operation of a QC algorithm. Therefore, prior to an operation of QC algorithm, accurate calibration of each qubit is required to detect if any of the qubits contain more than one electron which would cause computing errors. 
     Capacitance in quantum dots (q-dots) depends strongly on the discrete density of states (DOS) or charge variation divided by the chemical potential. Thus, a capacitance measurement can, in principle, probe the discrete single electron charging events in q-dots. However, there is significant technical challenge because the capacitance signal is extremely small (10&#39;s of aF, i.e. attofarads, 10 −18  Farads) and influenced by parasitic capacitance. Most of the current research has been using a lateral electron transport, which relies on multiple gates and interconnects, for the calibration of individual qubits. However, to develop scalable QC, the lateral transport scheme would not be practical due to its use of high density interconnects in a very limited space as well as peripheral requirements. 
     Cryogenic capacitance bridge circuits have been utilized to detect a single electron charging event, in which the off-null signal at the balance point is phase-sensitively detected by a cryogenic high electron mobility transistor (HEMT) immersed in LHe3 (an isotope of Helium in liquid state) and dual-channel phase-loop-locked amplifiers outside of the cryostat (i.e. the apparatus needed to maintain the low cryogenic temperature necessary). The total power dissipation of the HEMT transistors used in these measurements is 15 μW at 280 mK (0.28 Kelvin, or about −272.72 degrees Celsius). In the referenced measurements, the input voltage noise is 3 nV/√Hz, yielding charge noise of 0.002 e/√Hz in the case of a 0.1 pF shunt capacitance. 
     A cryogenic bridge geometry can be used to measure single-electron charging events under air-bridged post gates. The chemical potential change due to the AC excitation amplitude is kept below 200 μeV. The typical excitation frequency (KHz MHz) is determined by the RC charging time in the cryogenic set-up. The speed of the measurement depends on the bandwidth for better signal-to-noise ratio. 
     SUMMARY 
     The capacitive read/write scheme in accordance with the present disclosure offers calibration capability compatible with QC architecture, by monitoring local capacitance changes (electrometer) of qubit gates during a write cycle with single electron sensitivity. The qubit “write/read” method and architecture simplify electrical wiring or interconnect schemes since no additional peripheral electron transport measurements are required. 
     One embodiment of the present disclosure provides a capacitive calibration method for quantum computing, comprising: providing quantum dots comprising post gates; writing to said quantum dots by providing a sequence of write pulses to said quantum dots to induce a single charge population within at least one of said quantum dots, wherein said write pulses are above a threshold value; and reading said quantum dots by measuring the capacitance changes across said quantum dots, wherein the measuring is performed using a cryogenic capacitance bridge circuit. 
     A further embodiment of the present disclosure provides a capacitive calibrating device comprising: a cryogenic bridge circuit to detect single electron charging events within each of a plurality of quantum dots, wherein designated neighboring pairs of quantum dots form qubits; a first plurality of gates to access said plurality of quantum dots; a second plurality of gates between two quantum dots within a qubit to allow access to perform a swap operation on said two quantum dots; and a third plurality of gates between neighboring qubits to allow access to perform a swap operation on said neighboring qubits. 
     Another embodiment provides a calibration circuit essentially as depicted in  FIGS. 5 and 6 . 
     Further embodiments of the present disclosure are present in the specification, drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  shows a schematic cross sectional view of the apparatus in accordance with the present disclosure. 
         FIG. 2  is a schematic diagram useful for the understanding of the principle of operation of the device of  FIG. 1 . 
         FIG. 3  is a time vs. capacitance diagram showing variation of capacitance on the capacitor arrangements of  FIGS. 1 and 2 . 
         FIG. 4  is a gate voltage vs. capacitance diagram showing approximate measured capacitance changes due to a charge onset. 
         FIG. 5  is an electrical diagram showing a calibration circuit. 
         FIG. 6  is a table of example values for the calibration circuit components of  FIG. 5 . 
     
    
    
     DETAILED DESCRIPTION 
     The present writing discloses a capacitive calibration (read-while-writing) scheme with a single charge sensitive electrometer which can be compatible with a solid-state quantum computing architecture. The disclosed electrometer measures a capacitance change induced by a single charge population and depopulation in q-dots. The sequence of “write” pulses to q-dots above the threshold voltage will induce a single charge population sequentially, which will be read by the capacitance changes. This forms a read/write scheme for quantum computing not limited by the high-density interconnects. The disclosed scheme can be implemented in any semiconductor technologies including Si/SiGe, Si CMOS, and III-V compound semiconductors. 
       FIG. 1  shows an embodiment of electrical gate pulse lines  100 ,  102 ,  104  connected to the qubit structure to perform QC. A q-dot charging WRITE pulse on the Read/Write line  100  places a single electron in a gate to form individual q-dots DOT in the induced charge areas  107 ,  109 ,  111 ,  113 . A SWAP pulse on the Dot-Swap line  102  between  114 ,  116  two q-dots  107 ,  109  or  111 ,  113  swap the q-dots DOT within each qubit BIT. A swap gate  118  is connected to the Qubit-Swap line  104 . A SWAP pulse on the Qubit-Swap line  104  swap the qubits  107 + 109 ,  111 + 113 . The various q-gates  106 ,  108 ,  110 ,  112  are on top of spacer layer  180 , which is a spacer between the q-gates and the second quantum layer  190 . Also included is a substrate  130  and a first quantum layer  140 . The first quantum layer  140  is fabricated from a narrow band gap semiconducting material and is a 2DEG electron reservoir, which supplies electrons to second quantum layer  190  during the write cycle. The tunnel barrier layer  150  is fabricated from a wide bandgap semiconducting material. There is an ohmic contact  160  to the layers, which is typically connected to a power source. 
     During the write cycle, when a charging pulse is applied to the Read/Write line  100 , an induced charge area  107 ,  109 ,  111 ,  113  is formed under one or more of the q-dot gates  106 ,  108 ,  110 ,  112 . Furthermore, the writing process is carried out by adjusting two specific capacitance parameters, the amplitude of the pulse and the duration of the pulse interval. Since many specific combinations of settings for these two parameters will induce the formation of the induced charge area  107 ,  109 ,  111 ,  113  these two parameters are calibrated to determine the combination settings for these two parameters that will induce the formation of the induced charge area  107 ,  109 ,  111 ,  113 . The two q-dots DOT of any given qubit BIT can be swapped by a pulse delivered on the Dot-Swap line  102 . Two adjoining qubits BIT can be swapped by a pulse delivered on the Qubit-Swap line  104 . The pulses described above can be delivered to the appropriate gates by providing a multiplexed signal down each line  100 ,  102 ,  104 , then de-multiplexing via de-multiplexing circuitry  170  corresponding to each gate. 
       FIG. 2  shows a capacitance change before  200  and after  202  the single electron charging in a q-dot. The transition indicates a successful “write” operation. There is a capacitance C 1  between the gate  210  and the q-dot  220 . There is also a capacitance C 2  between the q-dot  220  and the 2DEG reservoir  140 . The total capacitance is a function of those two capacitances, which changes depending on whether or not there is an electron in the q-dot induced charge area  220 , as shown below. An integrated calibration circuit on the CMOS interface circuitry can be designed to automatically calibrate the charge state of each q-dot in a given array by multiplexing through each of the q-dots sequentially. An example of such calibration circuit is shown in  FIG. 5 . This alleviates the space requirement of having to provide a separate transistor for each q-dot. 
       FIG. 3  is a graph showing the amplitude of the capacitance pulse vs. the capacitance pulse interval duration. These two variables are adjusted during a write/read operation. When the capacitance increases, as shown by the pulse wave  302 , the read operation occurs. The duration of the pulse corresponds to the length of the calibration cycle. The baseline capacitance  300  (no electron in the induced charge area) is 
               C   ⁢           ⁢     1   ·   C     ⁢           ⁢   2         C   ⁢           ⁢   1     +     C   ⁢           ⁢   2             
whereas the q-dot capacitance  302  (indicating an electron in the induced charge area) is C 1 .
 
     A multiplexing technique can be used to access each q-dot within a given array allowing full calibration of the arrays prior to each quantum computing operation. For instance, during the calibration steps, capacitance of q-dots can be monitored locally and in-situ while DC biases are applied to form dots beneath the qubit gates. Due to the energy level of q-dots quantized in Darwin-Fock-like spectra, the capacitance versus DC bias will show peaks when the q-dot is charged by a single electron for the 2DEG reservoir. This provides an elegant way to perform qubit “Write/Read” action substantially simultaneously and thus calibrating the q-dot. 
       FIG. 4  shows the relationship between the Capacitance (pF) and the Gate Voltage (V) for the q-bit being measured. In  FIG. 4 , the two curves shown are  8401 , which depicts the onset of capacitance and S 402 , which depicts a reference sample. The peak in capacitance  401  depicted by S 401  corresponds to the peak in capacitance  302  shown in  FIG. 3 . The implementation of the invention depicted in  FIG. 4  produces the output similar to what is shown as S 401 . Further, if second quantum layer  150  ( FIG. 1 ) is not present in the implementation of the invention, then a curve similar to  8402  is produced with a different peak capacitance  402 . 
       FIG. 5  is an example of a circuit diagram for an embodiment of a cryogenic capacitance bridge circuit adapted for q-bit calibration (here shown as a six-port dual inline package, or DIP-6) with a charge noise of approximately 0.02 e/√Hz when in cryogenic state. The circuit consists of five current sources, two AC V 501 , V 502  and three DC V 503 , V 504 , V 505 , three capacitors C 501 , C 503 , C 504 , four resistors R 501 , R 502 , R 503 , R 504 , one Alumina Transmission line ATL 501 , and a I-1519 1×25 μm HEMT FET 501 . C 502  is the device to be calibrated (which can be represented by its capacitance). The circuit elements are connected as shown in the diagram, including the DIP output port P 501 . The characteristics of the circuit elements are given in the table of  FIG. 6 . The “capacitor” C 502  is actually the q-dot (or arrangement of q-dots/q-bits as shown in  FIG. 1 ) to be calibrated—the line  100  connecting C 502  to the rest of the circuit is the “write” line of the q-dot device. The capacitor C 501  is the reference capacitor for the measurement. The DIP-6 can be immersed in LHe3 for cryogenic operation. The output P 501  can be amplified by a dual-channel phase-loop-locked amplifier PLLA outside of the LHe3. 
       FIG. 6  is a table depicting an example of values for the elements of  FIG. 5 . Since element C 502  is the q-bit device to be measured, the capacitance value is “to be determined” (TBD). One skilled in the art could devise other values to use for the elements based on the arrangement and values provided in this disclosure. 
     The qubit method according to this disclosure simplifies electrical writing or interconnect schemes since additional peripheral electron transport measurements are not required. The maximum AC excitation amplitude will be limited by energy spacing between singlet and triplet separation in a given magnetic field. For a small number of dots (e.g. 100), the multiplexed calibration procedure can be accomplished in milliseconds. A separate calibration circuit can be integrated with each of the qubit cells, enabling each cell calibrated independently and automatically. 
     While several illustrative embodiments of the invention have been shown and described in the above description, numerous variations and alternative embodiments will occur to those skilled in the art. Such variations and alternative embodiments are contemplated, and can be made without departing from the scope of the invention as defined in the appended claims.