Parity meter for charge qubits: an efficient quantum entangler

A.N. Jordan; B. Trauzettel; C.W.J. Beenakker; M. Buttiker

REVIEW

Parity meter for charge qubits: an efficient quantum entangler

B. Trauzettel, A.N. Jordan, C.W.J. Beenakker, M. Buttiker

Mesoscale and Nanoscale Physics · Submitted 22 Feb 2006 · 20 references

Pith's verdict: A clever and clean proposal for a charge parity meter that gets quadratic coupling from geometric symmetry rather than an inflection point; the physics is sound if the left–right symmetry is maintained, but the paper never quantifies how good that symmetry must be.

T0 · AI review

How this review was made: An AI referee (deepseek-v4-flash) read the paper on August 28, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDcond-mat/0602514 (version 2)

Pith IDSEZKLJ7D, Pith's permanent record of this paper and its review

CitationA.N. Jordan, B. Trauzettel, C.W.J. Beenakker, M. Buttiker. "Parity meter for charge qubits: an efficient quantum entangler." arXiv:cond-mat/0602514 (2006). https://pith.science/paper/SEZKLJ7D

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The real contribution here is the move from tuning to an inflection point (Mao et al.) to using spatial symmetry: a QPC placed symmetrically between two DQDs gives t ∝ σ_z^(1)σ_z^(2) for arbitrary transmission. The capacitive derivation in Eqs. (9)–(15) is plausible and self-contained, and it is honest that the CNOT protocol is taken from their own earlier work. The Bell-test and CNOT applications are sensible extensions, not the main advance.

Where the paper is soft: the symmetry assumption after Eq. (10) is load-bearing. The claim that both odd configurations produce no QPC dipole requires equal capacitances and equal densities of states on both sides, D_L = D_R. The paper states this but never quantifies the tolerance. A small asymmetry δ gives the odd states a residual dipole, and with a finite bias the current splitting scales as V_bias·δ, so the detector can distinguish |↑↓⟩ from |↓↑⟩ and the Bell-state pointer is lost. The remark that asymmetries can be tuned with top gates is too vague; a referee should ask for the required precision or a fidelity estimate versus asymmetry.

Two smaller issues. Equation (10) is printed with the same expression for Q5 and Q6, which is internally inconsistent; the second line should involve U6, U2, U4. And the master-equation verification of the state-preparation algorithm is mentioned but never shown. Given that the entangler claim depends on it, that is a missing support, not a stylistic complaint.

The title's 'efficient' is also optimistic. Their own numbers give T_M ~ µs for GaAs against coherence times of ns, so efficiency depends on unproven nanotube or nanowire coherence. That tempers the claim but does not break the physics.

Overall, if the symmetry can be maintained or tolerances given, the central mechanism holds. I would send this to a serious referee, with the symmetry quantification and the missing master-equation details as conditions. I would cite it for the geometry-derived quadratic coupling.

Referee report

Significance

If the mechanism works as claimed, the device would provide a simple and experimentally accessible way to entangle charge qubits by measuring a DC current alone, without relying on direct qubit-qubit interactions or on noise measurements. The paper gives an explicit capacitance model with concrete parameter dependences, connects the setup to the general quadratic-detector framework of Mao et al., and uses standard QPC transmission theory. The two proposed applications, a Bell-inequality test and a CNOT gate, are relevant and clearly described. The main weaknesses are that the central parity property depends on an unquantified left-right symmetry of the device, and that the entangler claim is supported by a verbal algorithm and a reference to an unpublished master-equation calculation rather than by a displayed derivation.

Major objections (3)

[Sec. II, Eq. (10)] As printed, Eq. (10) is internally inconsistent: the two lines have identical right-hand sides, Q5 = Cp(U5−U6)+C(U5−U1)+C(U5−U3) = Qd and Q6 = Cp(U5−U6)+C(U5−U1)+C(U5−U3) = −Qd, which would imply Qd = −Qd. The second line should have the opposite sign structure, e.g., Q6 = Cp(U6−U5)+C(U6−U2)+C(U6−U4) = −Qd. Because Eqs. (11)–(15) are derived by solving this linear system, the corrected equations and their solution should be stated explicitly.
[Sec. II, after Eq. (10); Sec. III] The parity property — that the detector cannot distinguish |↑↓⟩ from |↓↑⟩ — relies on the exact cancellation of the QPC dipole in the odd subspace, which requires equal left/right capacitances and densities of states (D_L = D_R). The manuscript states this assumption and remarks that asymmetries "can be slightly tuned with top gates", but it gives no quantitative tolerance. If a small asymmetry δ remains, the two odd states acquire different saddle-point shifts, producing a current difference δI ∝ V_bias δ; the measurement then acquires which-qubit information and the pointer states are no longer the Bell states. Please estimate the allowed asymmetry δC/C and δD/D set by the condition δI √(S_I T_M) < 1 over the measurement time of Eq. (19), and assess the resulting Bell-state fidelity.
[Sec. III, Eqs. (21)–(25)] The central claim that a current measurement alone prepares |Ψ_B1⟩ or |Ψ_B2⟩ is supported only by a verbal algorithm and by the statement that a master-equation calculation agrees; no master equation is displayed. The three-outcome classification after Eq. (25) is also imprecise: a single parity measurement cannot distinguish |Ψ_B1⟩ from |Ψ_B3⟩ because both are odd-parity states, so the outcome Iodd alone does not identify the prepared state. Please provide the Lindblad/master equation (or a more formal argument) showing how the time-resolved measurement record projects the state onto the Bell states, and clarify the role of the measurement time T_M.

Minor objections (5)

[Sec. II, Eq. (15)] The denominator in Eq. (15) should be 2mω_x^2 d^2, not 2mω_x d^2, to be consistent with Eq. (8); as printed the formula is dimensionally inconsistent.
[Sec. II, Eqs. (10)–(12)] The symbol U is used both for (U5−U6)/2 and for U5 in Eq. (12); the solution refers to the half-difference, so the notation should be clarified.
[Sec. II, Eq. (14)] The formula is ambiguous as printed ("C4sum" and missing parentheses); please rewrite it in a clear form, for example ΔE_c = [4 C^2 (C_p(2C_i+C)+2C_i C)]/[C_2sum^2 (2C_i+C)] Q_L Q_R.
[Sec. III, after Eq. (25)] The sentence "with Iodd < Imix < Ieven" after defining Imix ≡ (Iodd+Ieven)/2 is tautological; it would be clearer to say that a mixed measurement record yields an average current between the two values.
[Sec. II, end] The statement "all three situations are distinguishable in principle" could be misread; the even configurations with dipole up/down are distinguishable from each other by the dipole direction but not by the QPC current, which is the point of the parity meter. Please rephrase for clarity.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Two charge qubits can be entangled by reading a single DC current through one point contact.

The reading

Two charge qubits in double quantum dots can be entangled by nothing more than reading the DC current through a single quantum point contact placed between them. The paper shows that this geometry makes the point contact a parity meter: its transmission amplitude depends on the product of the two qubit charge operators, so the current reveals only whether the two qubits have even or odd combined parity, never which state within each parity class. At the symmetry point of the two-qubit Hamiltonian, the two parity classes coincide with two of the four Bell states, so a current measurement projects the pair into a Bell state, and a string of identical outcomes confirms the preparation. The same device can be pinched off to switch off the qubit–qubit coupling, and it supplies the core element for a solid-state Bell-inequality test and a controlled-NOT gate.

What carries the argument

The central object is the parity meter: one quantum point contact placed symmetrically between two double quantum dots, so that its transmission amplitude through the saddle point is proportional to the product $\sigma_z^{(1)} \sigma_z^{(2)}$ of the two qubits' charge pseudospins. The mechanism is a symmetry-enforced quadratic coupling: in odd-parity configurations the two dot charges cancel at the point contact, leaving no dipole; in even-parity configurations a dipole shifts the saddle-point potential upward by an amount proportional to $(Q_L+Q_R)^2$, independent of the dipole's sign. This quadratic coupling is a consequence of geometric symmetry rather than a transmission inflection point, so it works for arbitrary QPC transmission. The result is that the QPC current has only two values, $I_{\rm odd}$ and $I_{\rm even}$, which is exactly the parity readout needed for the entangling measurement.

Extended reading notes

Core claim

The paper's central claim is that a single quantum point contact (QPC) placed symmetrically between two double quantum dots (DQDs) is a physical realization of a quadratic quantum measurement detector, with transmission amplitude $t \propto \sigma_z^{(1)} \sigma_z^{(2)}$. In the odd-parity configurations $|\uparrow\downarrow\rangle$ and $|\downarrow\uparrow\rangle$ the two dot charges cancel at the QPC, leaving no dipole and a saddle-point potential $V_0$; in the even-parity configurations $|\uparrow\uparrow\rangle$ and $|\downarrow\downarrow\rangle$ a dipole is induced and the saddle-point potential rises to $V_1>V_0$, with the same rise for both states. Hence the detector current takes only two values, $I_{\rm odd}$ and $I_{\rm even}$, and performs a parity measurement. When the DQDs are tuned to the symmetry point ($\epsilon_1=\epsilon_2=0$, $\Delta_1=\Delta_2=\Delta$), the two Bell states $|\Psi_{B1}\rangle=(|\uparrow\downarrow\rangle-|\downarrow\uparrow\rangle)/\sqrt{2}$ and $|\Psi_{B2}\rangle=(|\uparrow\uparrow\rangle-|\downarrow\downarrow\rangle)/\sqrt{2}$ are eigenstates of the qubit Hamiltonian with opposite parity, so the measurement drives the system into one of them; starting from a product state, the success probability for a given Bell state is $1/2$. Repeated identical parity outcomes give a statistically confident preparation, and the paper uses this to design a Bell-inequality test and a deterministic CNOT gate.

Load-bearing premise

The load-bearing premise is that the point contact sits exactly symmetrically between the two double dots, with equal capacitances and equal densities of states on both sides, so that the two odd-parity charge arrangements produce no net electric field at the point contact and therefore the same detector current.

Editorial extensions

If this is right

Starting from the easily prepared product state $|\uparrow\downarrow\rangle$, an odd-parity current measurement prepares $|\Psi_{B1}\rangle$ with probability $1/2$; from $|\uparrow\uparrow\rangle$, an even-parity measurement prepares $|\Psi_{B2}\rangle$ with probability $1/2$.
Once a Bell state is confirmed, setting the QPC bias to zero and pinching off the point contact turns off the effective qubit–qubit coupling, so the prepared entanglement can be held for later operations.
The parity meter plus two outer single-electron-transistor detectors and single-qubit rotations gives a complete CHSH Bell-inequality test in a solid-state system, with rotations applied to the qubits rather than the detectors.
Two parity meters and one ancilla qubit, with Hadamard gates realized by pulsing each double dot to $\epsilon_\alpha=\Delta_\alpha$ for time $\pi/(\sqrt{2}\Delta)$, implement a deterministic CNOT gate followed by single-qubit post-processing.
The parity measurement time in GaAs double quantum dots is a few microseconds, much longer than the few-nanosecond coherence times, so the practical experimental target is carbon-nanotube, nanowire, or isolated silicon double-dot charge qubits with longer coherence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Extension: the geometric-symmetry argument should transfer to any charge-based qubit pair coupled symmetrically to a central conductor with an inversion-symmetric saddle point, so the parity meter could be ported to superconducting or spin-based platforms.
Extension: because gate voltages can force the four classical charge configurations, the same device doubles as an in-situ diagnostic of coupling asymmetry, allowing the symmetry requirement to be checked and tuned rather than assumed.
Extension: viewed as a syndrome-like parity check, the stable-outcome branch of the protocol resembles measurement-based error correction; extending the scheme to more qubits would test whether repeated parity measurements alone can produce larger entangled states.

Original abstract

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,635 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.58 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact.	contribution 0.96	0.62	0.12	asserted 0.74
s1	Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)].	background 0.98	0.05	0.05	asserted 1.00
s2	Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter.	contribution 0.65	0.80	0.48	asserted 0.99
s3	Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.	contribution 0.83	0.55	0.19	asserted 0.92

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from argument 0.72.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (20)

[1]

Fix the desired initial state in the measurement ba- sis. It can be randomly chosen, or can be ﬁxed as a state that is experimentally simple to prepare

View on Pith
[2]

Apply a unitary transformation to change to the Bell basis, where Hamiltonian evolution is simple. More explicitly, if we represent an arbitrary state as |Ψ ⟩ = a| ↓↓⟩ + b| ↓↑⟩ + c| ↑↓⟩ + d| ↑↑⟩, (26) a simple basis transformation enables us to write the same state as |Ψ ⟩ = α|Ψ B1⟩ + β|Ψ B2⟩ + γ|Ψ B3⟩ + δ|Ψ B4⟩. Then, the time evolution in the Bell basis...

View on Pith
[3]

Apply Hamiltonian evolution with a randomly cho- sen time

View on Pith
[4]

Transform back to the measurement basis

View on Pith
[5]

Do a parity measurement: • Find the probability of getting the result even (E), or odd ( O) from the state. • Use these probabilities to choose a random outcome, E or O. • Based on the result, update the state

View on Pith
[6]

Transform back to the Bell basis

View on Pith
[7]

Repeat the algorithm from step 2. As mentioned before, this algorithm gives three possible outcomes: (i) the parity meter measures O all the time → state |Ψ B1⟩ has been prepared, (ii) the parity meter measures E all the time → state |Ψ B2⟩ has been prepared, and (iii) the parity meter measures a string of a mixture of O and E results → a dynamical superp...

View on Pith
[8]

Preparation step. During the preparation step, the two DQD’s have to be held at the symmetry point, i.e. ǫ1 = ǫ2 = 0 and ∆ 1 = ∆ 2 = ∆, where the Hamiltonian HSP describes the two-qubit system. A measurement of the parity meter, i.e. the center QPC, is done. If the measurement is either Iodd or Ieven, then we know that either state |Ψ B1⟩ or state |Ψ B2⟩,...

View on Pith
[9]

Decoupling step. Once we know that the system is in one of the two Bell states |Ψ B1⟩ or |Ψ B2⟩, we would like to turn the coupling between the two qubits oﬀ. In our setup, the coupling between the two DQD’s can be minimized by setting Vbias = 0 and by pinching oﬀ the QPC. 6 FIG. 3: Bell inequality setup. In order to be able to do a measurement of a viola...

View on Pith
[10]

Single qubit rotation step. In order to do a mea- surement of a violation of a Bell inequality in the Clauser-Horne-Shimony-Holt (CHSH) form, 18 we have to rotate each qubit and afterwards measure qubit-qubit correlators in diﬀerent bases. The sin- gle qubit rotation can be done by pulsing ∆ 1(t) and ∆ 2(t) independently of each other. Thus, during this s...

View on Pith
[11]

Measurement step. Immediately after the single qubit rotation step , we should be able to do a strong (projective) measurement in the σz basis of the qubit using high-ﬁdelity single shot detectors. This can, for instance, be accomplished by single elec- tron transistors as illustrated in Fig. 3. The time delay between the two projective measurements is an...

View on Pith
[12]

It should be rather easy to prepare the desired state of the ancilla qubit because it is the ground state of the DQD system when the tun- nel coupling is ﬁnite. 22 Under the constraint ∆ top ≪ 1, mentioned above, the outcome of the parity measure- ment can just take two values, corresponding to Iodd or Ieven of Sec. III. Then, a measurement of Iodd shows ...

View on Pith
[13]

A Hadamard gate acting on qubit α can be realized by tuning the corresponding single qubit Hamiltonian Hα = − 1 2 ( ǫα σ(α ) z + ∆ α σ(α ) x ) (34) to the special symmetry point ǫα = ∆ α and letting it act for a time tH = π/ √ 2∆. For this single qubit rotation, we need to raise ∆ and ǫ temporarily. The operation scheme of the CNOT gate goes as fol- lows:

View on Pith
[14]

Preparation of the ancilla qubit. This can be ei- ther done by acting with H2 on state |0⟩ of qubit 2 or by ground state preparation of a tunnel-coupled double dot

View on Pith
[15]

Parity measurement with QPC 1. The outcome of that measurement p1 has to be stored. p1 = 0 corresponds to the odd parity class, whereas p1 = 1 corresponds to the even parity class. The same holds, of course, for p2, i.e. the outcome of the parity measurement 2 below. Afterwards, we need to decouple the control and the ancilla qubit

View on Pith
[16]

Hadamard step 1. Acting with H2 on the ancilla qubit and with H3 on the target qubit, which means in practice to wait for an appropriate time tH after tuning the single qubit Hamiltonians

View on Pith
[17]

Parity measurement with QPC 2. The outcome of that measurement p2 has to be stored. After- wards, we need to decouple the ancilla and the tar- get qubit

View on Pith
[18]

Hadamard step 2. Once more, acting with H2 on the ancilla qubit and with H3 on the target qubit

View on Pith
[19]

Measurement of ancilla qubit. This measurement has to be done in a projective way

View on Pith
[20]

Post-processing step. Depending on the outcome of the measured state of the ancilla qubit as well as p1 and p2, we ﬁnally have to apply single qubit op- erations to the control and the target qubit, which we call σc and σt. For the control qubit, σc = σz if p2 = 0, while no post-processing of the control qubit is needed if p2 = 1. For the target qubit, σt...

View on Pith Pith review arXiv 2004

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

Fix the desired initial state in the measurement ba- sis. It can be randomly chosen, or can be ﬁxed as a state that is experimentally simple to prepare

View on Pith

[2] [2]

Apply a unitary transformation to change to the Bell basis, where Hamiltonian evolution is simple. More explicitly, if we represent an arbitrary state as |Ψ ⟩ = a| ↓↓⟩ + b| ↓↑⟩ + c| ↑↓⟩ + d| ↑↑⟩, (26) a simple basis transformation enables us to write the same state as |Ψ ⟩ = α|Ψ B1⟩ + β|Ψ B2⟩ + γ|Ψ B3⟩ + δ|Ψ B4⟩. Then, the time evolution in the Bell basis...

View on Pith

[3] [3]

Apply Hamiltonian evolution with a randomly cho- sen time

View on Pith

[4] [4]

Transform back to the measurement basis

View on Pith

[5] [5]

Do a parity measurement: • Find the probability of getting the result even (E), or odd ( O) from the state. • Use these probabilities to choose a random outcome, E or O. • Based on the result, update the state

View on Pith

[6] [6]

Transform back to the Bell basis

View on Pith

[7] [7]

Repeat the algorithm from step 2. As mentioned before, this algorithm gives three possible outcomes: (i) the parity meter measures O all the time → state |Ψ B1⟩ has been prepared, (ii) the parity meter measures E all the time → state |Ψ B2⟩ has been prepared, and (iii) the parity meter measures a string of a mixture of O and E results → a dynamical superp...

View on Pith

[8] [8]

Preparation step. During the preparation step, the two DQD’s have to be held at the symmetry point, i.e. ǫ1 = ǫ2 = 0 and ∆ 1 = ∆ 2 = ∆, where the Hamiltonian HSP describes the two-qubit system. A measurement of the parity meter, i.e. the center QPC, is done. If the measurement is either Iodd or Ieven, then we know that either state |Ψ B1⟩ or state |Ψ B2⟩,...

View on Pith

[9] [9]

Decoupling step. Once we know that the system is in one of the two Bell states |Ψ B1⟩ or |Ψ B2⟩, we would like to turn the coupling between the two qubits oﬀ. In our setup, the coupling between the two DQD’s can be minimized by setting Vbias = 0 and by pinching oﬀ the QPC. 6 FIG. 3: Bell inequality setup. In order to be able to do a measurement of a viola...

View on Pith

[10] [10]

Single qubit rotation step. In order to do a mea- surement of a violation of a Bell inequality in the Clauser-Horne-Shimony-Holt (CHSH) form, 18 we have to rotate each qubit and afterwards measure qubit-qubit correlators in diﬀerent bases. The sin- gle qubit rotation can be done by pulsing ∆ 1(t) and ∆ 2(t) independently of each other. Thus, during this s...

View on Pith

[11] [11]

Measurement step. Immediately after the single qubit rotation step , we should be able to do a strong (projective) measurement in the σz basis of the qubit using high-ﬁdelity single shot detectors. This can, for instance, be accomplished by single elec- tron transistors as illustrated in Fig. 3. The time delay between the two projective measurements is an...

View on Pith

[12] [12]

It should be rather easy to prepare the desired state of the ancilla qubit because it is the ground state of the DQD system when the tun- nel coupling is ﬁnite. 22 Under the constraint ∆ top ≪ 1, mentioned above, the outcome of the parity measure- ment can just take two values, corresponding to Iodd or Ieven of Sec. III. Then, a measurement of Iodd shows ...

View on Pith

[13] [13]

A Hadamard gate acting on qubit α can be realized by tuning the corresponding single qubit Hamiltonian Hα = − 1 2 ( ǫα σ(α ) z + ∆ α σ(α ) x ) (34) to the special symmetry point ǫα = ∆ α and letting it act for a time tH = π/ √ 2∆. For this single qubit rotation, we need to raise ∆ and ǫ temporarily. The operation scheme of the CNOT gate goes as fol- lows:

View on Pith

[14] [14]

Preparation of the ancilla qubit. This can be ei- ther done by acting with H2 on state |0⟩ of qubit 2 or by ground state preparation of a tunnel-coupled double dot

View on Pith

[15] [15]

Parity measurement with QPC 1. The outcome of that measurement p1 has to be stored. p1 = 0 corresponds to the odd parity class, whereas p1 = 1 corresponds to the even parity class. The same holds, of course, for p2, i.e. the outcome of the parity measurement 2 below. Afterwards, we need to decouple the control and the ancilla qubit

View on Pith

[16] [16]

Hadamard step 1. Acting with H2 on the ancilla qubit and with H3 on the target qubit, which means in practice to wait for an appropriate time tH after tuning the single qubit Hamiltonians

View on Pith

[17] [17]

Parity measurement with QPC 2. The outcome of that measurement p2 has to be stored. After- wards, we need to decouple the ancilla and the tar- get qubit

View on Pith

[18] [18]

Hadamard step 2. Once more, acting with H2 on the ancilla qubit and with H3 on the target qubit

View on Pith

[19] [19]

Measurement of ancilla qubit. This measurement has to be done in a projective way

View on Pith

[20] [20]

Post-processing step. Depending on the outcome of the measured state of the ancilla qubit as well as p1 and p2, we ﬁnally have to apply single qubit op- erations to the control and the target qubit, which we call σc and σt. For the control qubit, σc = σz if p2 = 0, while no post-processing of the control qubit is needed if p2 = 1. For the target qubit, σt...

View on Pith Pith review arXiv 2004