prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How many brother does Njoroge have?

Read the following text and answer briefly.

Context 1: Weep Not, Child is a 1964 novel by Kenyan author Ngũgĩ wa Thiong'o  It was his first novel, published in 1964 under the name James Ngugi  It was among the African Writers Series  It was the first English language|English novel to be published by an East African  Thiong'o's works deal with the relationship between Africans and white settlers in colonial Kenya, and are heavily critical of colonial rule  Specifically, Weep Not, Child deals with the Mau Mau Uprising, and "the bewildering dispossession of an entire people from their ancestral land " Ngũgĩ wrote the novel while he was a student at Makerere University 

The book is divided into two parts and eighteen chapters  Part one deals mostly with the education of Njoroge, while part two deals with the rising Mau Mau movement 

Plot summary

Njoroge, a little boy, is urged to attend school by his mother  He is the first one of his family able to go to school  His family lives on the land of Jacobo, an African made rich by his dealings with white settlers, namely Mr  Howlands, the most powerful land owner in the area  Njoroge's brother Kamau works as an apprentice to a carpenter, while Boro, the eldest living son, is troubled by his experiences while in forced service during World War II, including witnessing the death of his elder brother  Ngotho, Njoroge's father and a respected man in the surrounding area, tends Mr  Howlands' crops, but is motivated by his passion to preserve his ancestral land, rather than for any compensation or loyalty 

One day, black workers call for a strike to obtain higher wages  Ngotho is ambivalent about participating in the strike because he fears he will lose his job  However, he decides to go to the gathering, even though his two wives do not agree  At the demonstration, there are calls for higher wages  Suddenly, the white police inspector brings Jacobo to the gathering to pacify the native people  Jacobo tries to put an end to the strike  Ngotho attacks Jacobo, and the result is a riot where two people are killed  Jacobo survives and swears revenge  Ngotho loses his job and Njoroge’s family is forced to move  Njoroge’s brothers fund his education and seem to lose respect for their father 

Mwihaki, Jacobo's daughter and Njoroge's best friend, enters a girls' only boarding school, leaving Njoroge relatively alone  He reflects upon her leaving, and realizes that he was embarrassed by his father's actions towards Jacobo  For this reason, Njoroge is not upset by her exit and their separation  Njoroge switches to another school 

For a time, everyone's attention is focused on the upcoming trial of Jomo Kenyatta – a revered leader of the movement  Many blacks think that he is going to bring forth Kenya’s independence  But Jomo loses the trial and is imprisoned  This results in further protests and greater suppression of the black population 

Jacobo and a white landowner, Mr  Howlands, fight against the rising activities of the Mau Mau, an organization striving for Kenyan economic, political, and cultural independence  Jacobo accuses Ngotho of being the leader of the Mau Mau and tries to imprison the whole family  Meanwhile, the situation in the country is deteriorating  Six black men are taken out of their houses and executed in the woods 

One day Njoroge meets Mwihaki again, who has returned from boarding school  Although Njoroge had planned to avoid her due to the conflict between their fathers, their friendship is unaffected  Njoroge passes an important exam that allows him to advance to High School  His village is proud of him, and collects money to pay Njoroge's High School tuition 

Several months later, Jacobo is murdered in his office by a member of the Mau Mau  Mr  Howlands has Njoroge removed from school for questioning  Both father and son are brutally beaten before release and Ngotho is left barely alive  Although there doesn't seem to be a connection between Njoroge's family and the murder, it is eventually revealed that Njoroge's brothers are behind the assassination, and that Boro is the real leader of the Mau Mau  Ngotho soon dies from his injuries and Njoroge finds out that his father was protecting his brothers  Kamau has been imprisoned for life  Only Njoroge and his two mothers remain free, and Njoroge is left as the sole provider of his two mothers  Njoroge fears that he cannot make ends meet; he gives up hope of continuing in school and loses faith in God 

Njoroge asks Mwihaki's for support, but she is angry because of her father’s death  When he finally pledges his love to her, she refuses to leave with him, realizing her obligation to Kenya and her mother  Njoroge decides to leave town and makes an attempt at suicide; however, he fails when his mothers find him before he is able to hang himself  The novel closes with Njoroge feeling hopeless, and ashamed of cowardice 

Characters in Weep Not, Child
 Njoroge: the main character of the book whose main goal throughout the book is to become as educated as possible 
 Ngotho: Njoroge's father  He works for Mr Howlands and is respected by him until he attacks Jacobo at a workers strike  He is fired and the family is forced to move to another section of the country  Over the course of the book his position as the central power of the family weakened, to the point where his self-realization that he has spent his whole life waiting for the prophecy (that proclaims the blacks will be returned their land) to come true rather than fighting for Kenyan independence, leads to his depression 
 Nyokabi and Njeri: the two wives of Ngotho  Njeri is Ngotho's first wife, and mother of Boro, Kamau, and Kori  Nyokabi is his second wife, and the mother of Njoroge and Mwangi 
 Njoroge has four brothers: Boro, Kamau, Kori and Mwangi (who is Njoroge's only full brother, who died in World War II) 
 Boro: Son of Njeri who fights for the Allies in World War II  Upon returning his anger against the colonial government is compounded by their confiscation of the his land  Boro's anger and position as eldest son leads him to question and ridicule Ngotho, which eventually defeats their father's will (upon realizing his life was wasted waiting and not acting)  It is eventually revealed that Boro is the leader of the Mau Mau (earlier alluded to as "entering politics") and murders Mr Howlands  He is caught by police immediately after and is scheduled to be executed by the book's end  It is highly likely that it is also Boro who kills Jacobo 
 Mwihaki: Njoroge's best friend (and later develops into his love interest)  Daughter of Jacobo  When it is revealed that his family killed Jacobo (most likely Boro), Mwihaki distances herself from Njoroge, asking for time to mourn her father and care for her mother 
 Jacobo: Mwihaki's father and an important landowner  Chief of the village 
 Mr  Howlands: A white settler who emigrated to colonial Kenya and now owns a farm made up of land that originally belonged to Ngotho's ancestors  Has three children: Peter who died in World War II before the book's beginning, a daughter who becomes a missionary, and Stephen who met Njoroge while the two were in high school 

Themes and motifs
Weep Not, Child integrates Gikuyu mythology and the ideology of nationalism that serves as catalyst for much of the novel's action  The novel explores the negative aspects of colonial rule over Kenya  Njoroge's aspiration to attend university is frustrated by both the violence of the Mau Mau rebels and the violent response of the colonial government  This disappointment leads to his alienation from his family and ultimately his suicide attempt 

The novel also ponders the role of saviours and salvation  The author notes in his The River Between: "Salvation shall come from the hills  From the blood that flows in me, I say from the same tree, a son shall rise  And his duty shall be to lead and save the people " Jomo Kenyatta, the first prime minister of Kenya, is immortalised in Weep Not, Child  The author says, "Jomo had been his (Ngotho's) hope  Ngotho had come to think that it was Jomo who would drive away the white man  To him, Jomo stood for custom and traditions purified by grace of learning and much travel " Njoroge comes to view Jomo as a messiah who will win the struggle against the colonial government 
Context 2: Paper Info

Title: Compressed quantum error mitigation
Publish Date: 10 May 2023
Author List: Maurits Tepaske (from Physikalisches Institut, Universität Bonn), David Luitz (from Physikalisches Institut, Universität Bonn)

Figure

FIG 3 The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and time t, for the infinite temperature initial state, for a denoised second-order Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 We consider evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise with p = 0 01 
FIG  4  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 0046 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is evident that the denoiser recovers all the noiseless eigenvalues from the noisy circuit 
FIG  2  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 036 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is clear that the denoiser recovers with high accuracy the noiseless eigenvalues from the noisy circuit 
FIG  3  The half-chain channel entanglement entropy S at different two-qubit depolarizing noise strengths p, for a secondorder Trotter supercircuit with Mtrot = 16 and t = 2, for a M = 4 denoiser The Trotter circuit is for a Heisenberg model with PBC of size L = 6 The different curves correspond to the different supercircuits, i e  the noisy supercircuit, the denoiser, the corresponding denoised supercircuit, and the noiseless variant 
FIG  4  The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and stacked time t, for the infinite temperature initial state, for a denoised secondorder Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 It is optimized at t = 2 and stacked up to ten times The calculations are for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarization with p = 0 01 The denoiser is affected by the same noise 
FIG 6 The distribution of the ZZ angle α of M = 2 denoisers (top panels) and M = 8 denoisers (bottom panels), with the lightest color corresponding to the denoiser for the Trotter supercircuit with t = 0 5, and the darkest color with t = 5 As usual, we consider the Heisenberg model on a periodic chain, and second-order Trotter supercircuits with depths Mtrot = 8, 16, 32, 64, which together with the denoiser is affected by a two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG  7  The sampling overhead γ of the optimized denoisers from Fig  2 of the main text, with denoiser depths M = 1, 2, 4, 6, 8 and Trotter depths Mtrot = 8, 16, 32, 64 at times t = 0 5, 1,    , 5, for the Heisenberg model on a chain with PBC affected by two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG 8 The domain wall magnetization Z dw after evolving a periodic density wall |dw |dw * with the denoised second-order Trotter supercircuits D C from Fig 2of the main text These supercircuits have various Trotter depths Mtrot = 8, 16, 32, 64, denoiser depths M = 1, 2, 4, 6, 8, and evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise of strength p = 0 01 The denoiser is affected by the same noise The non-denoised results are labelled with M = 0 and the noiseless results with p = 0 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively We see that the denoiser allows us to recover the noiseless behavior 

abstract

We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit  Our approach is based on applying an optimal "denoiser" after the action of a noisy circuit and can be performed with an arbitrary number of extra gates 
The denoiser is given by an ensemble of circuits distributed with a quasiprobability distribution  For a simple noise model, we show that efficient, local denoisers can be found, and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains  Introduction 
-Quantum information processing has been theoretically shown to hold great promises, and quantum algorithms were developed which can in principle achieve an exponential speed-up over their classical counterparts, both for general purpose computing and quantum simulation   However, present day quantum computing prototypes still suffer from significant noise processes which hinder the execution of many potentially groundbreaking quantum algorithms  
Nontrivial quantum algorithms typically require large sequences of quantum gates, each of which introduces dissipation and hence an overall loss of coherence, eventually rendering the results useless  Until quantum error correction becomes practical, quantum error mitigation seems to be more feasible to increase the accuracy of expectation values 
Here the goal is to induce the (partial) cancellation of errors that stem from noisy quantum gates by extending the circuit corresponding to the desired algorithm with an ensemble of gates , sampled from a quasiprobability distribution  The traditional way to accomplish this is with the gatewise method from , where noise is mitigated by inverting the noise channel of each gate separately, i e  the cancellation of errors is performed for each gate on its own 
Here the local noise channel is approximated in a way such that it can be easily inverted analytically, e g  using Pauli twirling   Gates are then sampled from the inverted noise channel by interpreting it as a quasiprobability distribution  Because in this gate-wise approach every noisy gate has to be modified separately, the sign problem is exponentially large in the number of gates, limiting the practicality of the mitigation 
The success of the gate-wise approach resulted in a large body of work concerning these methods , including extensions for simultaneous mitigation of multiple gates by Pauli-twirling entire layers or variationally constructing a mitigating matrix product operator   In principle, errors during the execution of a circuit can propagate and accumulate 
These propagated errors * david luitz@uni-bonn de ≈ C

C

FIG  1  An example of the quantum error mitigation procedure used in this work for the time evolution of the wave function of a spin chain  The ideal second-order Trotter supercircuit C of depth Mtrot = 1 (light blue) is approximated by applying a denoiser D of depth M = 1 (red) to the noisy Trotter supercircuit C (dark blue) 
Because the denoiser is applied after fully executing the noisy Trotter supercircuit, it represents an approximate inverse of the global noise channel with a precision tunable by the depth of the denoiser  can potentially blow up and lead to large errors for the circuit as a whole   Here we introduce a mitigation technique that takes into account the propagation of errors, can be performed with a tunable number of extra gates, and works for non-Clifford local noise channels since the inversion of the accumulated global noise channel is implicit 
We first execute the targeted noisy circuit completely, letting the noise propagate and accumulate, and only afterwards we apply an extra random circuit sampled from a quasiprobability distribution  We call the corresponding ensemble of random circuits a denoiser, and we construct it such that upon averaging the accumulated errors cancel 
Essentially, the denoiser inverts a global noise channel  Since we will construct it as a local brickwall circuit, following the classical preprocessing approach from , we call this compressed quantum error mitigation  Method  -Due to the inevitable coupling of a quantum processor to its environment, every qubit operation is affected by noise 
Therefore, the simplest technique to minimize the impact of the resulting noise is to minimize the number of operations when performing a quantum algorithm  In we showed that many-body time evolution operators can be efficiently compressed into brick-wall circuits with high fidelity per gate  In this Letter, we consider the noise explicitly by treating quantum operations as (generally non-unitary) quantum channels, corresponding to completely positive and trace preserving (CPTP) maps  
For example, instead of a noiseless two-qubit gate G, which acts on a quantum state |ρ in superoperator form as G|ρ = G⊗G * |ρ , we get the noisy channel G = N G, where the noise channel N implements the two-qubit noise   These channels are used to construct a "supercircuit" C = N G i=1 Gi , consisting of N G channels, which is affected by multi-qubit accumulated noise 
This supercircuit encodes an ensemble of circuits   For simplicity, we assume that the noisy channels Gi in each half brickwall layer are lattice inversion and translation invariant, such that we can construct a denoiser with these properties, limiting the number of variational parameters  The purpose of quantum error mitigation is to modify the ensemble of circuits described by C in a way that we can use it to obtain the noiseless expectation values 
In superoperator language, we do this by following the supercircuit C with a denoiser supercircuit D, such that D C is as close to the noiseless supercircuit C = C ⊗ C * as possible  Here C is the target unitary circuit  Because the noise channel N is non-unitary, hence making the supercircuit C non-unitary, we need to use a non-unitary denoiser to retrieve the unitary C 
We illustrate the mitigation procedure in Fig  , where a denoiser with one layer is used to mitigate errors for a second-order Trotter supercircuit with one layer  This circuit architecture is commonly used to simulate the time evolution of a quantum many-body system, until some time t, with controllable precision , and we will use it to benchmark the denoiser 
In practice, we cannot directly implement a supercircuit, and so we have to utilize its interpretation as an ensemble of circuits  Essentially, after executing a shot of the noisy circuit we sample the denoiser and apply it  The goal is to construct the denoiser in a way that averaging over many of its samples cancels the accumulated errors and gives us a good approximation of the noiseless expectation values 
It should be noted that our approach requires more gate applications on the quantum processor than with the gate-wise scheme, since there each sample from the mitigation quasiprobability distribution can be absorbed into the original circuit, whereas our approach increases the circuit depth  We take this into account by imposing the same noise on the denoiser 
Furthermore, within our scheme, the dimensionality of the quasiprobabilistic mitigating ensemble can be controlled, in contrast to the gate-wise approach where it is equal to the gate count  To facilitate the stochastic interpretation we parameterize each two-qubit denoiser channel G i as a sum of CPTP maps, such that we can sample the terms in this sum and execute the sampled gate on the quantum processor 
Concretely, we use a trace preserv-ing sum of a unitary and a non-unitary channel  For the unitary part we take a two-qubit unitary channel U( φ i ) = U ( φ i ) ⊗ U * ( φ i ), with U ( φ i ) a two-qubit unitary gate parameterized by φ i   For this we take the two-qubit ZZ rotation exp(−iα(σ z ⊗ σ z )) with angle α, which can be obtained from native gates on current hardware , and dress it with four general one-qubit unitaries, only two of which are independent if we want a circuit that is space inversion symmetric around every bond 
The resulting gate has 7 real parameters φ i   For the non-unitary part, which is essential because D has to cancel the non-unitary accumulated noise to obtain the noiseless unitary circuit, we use a general onequbit measurement followed by conditional preparation channel M( , with V a general one-qubit unitary and each κ i a 3-dimensional vector, resulting in a real 9-dimensional ζ i  
This yields the two-qubit correlated measurement M( With these parts we construct the parameterization with coefficients η i ∈ R that satisfy η 0 + η 1 = 1 because G i is trace preserving  Note that here the tensor product symbol corresponds to combining two one-qubit channels to make a two-qubit channel, whereas in most of the paper it is used to link the column and row indices of a density matrix 
We construct the denoiser from the noisy channels Gi = N G i   With this parameterization one denoiser channel has 17 independent real parameters, such that a denoiser of depth M , i e  consisting of M brickwall layers, has 34M real parameters (we use one unique channel per half brickwall layer)  For reference, a general channel has 544M parameters 
To determine the mitigated expectation values we use the full expression where |ρ 0 is the initial state and |1 is the vectorized identity operator on the full Hilbert space  To evaluate this on a quantum processor, we use the stochastic interpretation of (1) to resample   In particular, from each channel (1) we get a unitary with probability p 0 = |η 0 |/γ and a measurement followed by conditional preparation with probability p 1 = |η 1 |/γ 
Here γ = |η 0 | + |η 1 | is the sampling overhead, which characterizes the magnitude of the sign problem from negative η i   For quasiprobability distributions, i e  with γ > 1, every denoiser sample has an extra sign sgn(η) = N G g=1 sgn(η g ), 2  The normalized distance between the denoised Trotter supercircuit D C and the noiseless Trotter supercircuit C (top panels), at evolution times t = 0 5, 1,    , 5, and the twopoint z-spin correlator C zz i=L/2,j=L/2 (t) of a spin on the middle site at times 0 and t (bottom panels), for the infinite temperature initial state 
We consider denoisers with depths M = 1, 2, 4, 6, 8 and second-order Trotter circuits with depths Mtrot = 16, 32, 64  In the top panels we use a Heisenberg chain with L = 8, and in the bottom panels with L = 14, both with periodic boundary conditions  All gates are affected by two-qubit depolarizing noise with p = 0 01



ground_truth: Four.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What size chains were used in the benchmarking?

Read the following text and answer briefly.

Context 2: 
The non-denoised results are labelled with M = 0, and the noiseless values with p = 0  where sgn(η g ) is the sign of the sampled coefficient of the gth channel  γ = 1 means that all signs are positive  Observables Ô p=0 for the noiseless circuit are then approximated by resampling the observables from the denoiser ensemble
where γ = N G g=1 γ g is the overall sampling overhead, with γ g the overhead of the gth gate  Clearly, a large γ implies a large variance of Ô p=0 for a given number of samples, with accurate estimation requiring the cancellation of large signed terms  The number of samples required to resolve this cancellation of signs is bounded by Hoeffding's inequality, which states that a sufficient number of samples to estimate Ô p=0 with error δ at probability 1 − ω is bounded by (2γ 2 /δ 2 ) ln(2/ω)  
Since γ scales exponentially in γ g , it is clear that a denoiser with large M and γ 1 will require many samples  We observed that decompositions with γ > 1 are crucial for an accurate denoiser  Restricting to γ = 1 leads to large infidelity and no improvement upon increasing the number of terms in or the depth M of the denoiser 
Simply put, probabilistic error cancellation of gate noise introduces a sign problem and it is crucial to find optimal parameterizations (1) which minimize γ to make the approach scalable  This issue arises in all high performance error mitigation schemes , because the inverse of a physical noise channel is unphysical and cannot be represented as a positive sum over CPTP maps 
This is clearly visible in the spectra of the denoiser, which lies outside the unit circle (cf  Fig  )  This makes the tunability of the number of gates in each denoiser sample a crucial ingredient, which allows control over the sign problem, because we can freely choose the η i in   For the parametrization (1) of denoiser channels, we try to find a set of parameters for error mitigation by minimizing the normalized Frobenius distance between the noiseless and denoised supercircuits
which bounds the distance of output density matrices and becomes zero for perfect denoising  We carry out the minimization of on a classical processor, using gradient descent with the differential programming algorithm from   Instead of explicitly calculating the accumulated global noise channel and subsequently inverting it, we approximate the noiseless supercircuit C with the denoised supercircuit D C, effectively yielding a circuit representation D of the inverse noise channel 
Results  -To benchmark the denoiser we apply it to the second-order Trotter circuits of the spin-1/2 Heisenberg chain with periodic boundary conditions (PBC) where is the Pauli algebra acting on the local Hilbert space of site i  A second-order Trotter circuit for evolution time t with depth M trot consists of M trot − 1 half brickwall layers with time step t/M trot and two layers with half time step  
We consider circuits that are affected by uniform depolarizing noise with probability p for simplicity, but our approach can be used for any non-Clifford noise  The two-qubit noise channel is which acts on neighboring qubits i and i + 1 and is applied to each Trotter and denoiser gate, and p = 0 01 unless stated otherwise 
We study circuits with depths M trot = 16, 32, 64 for evolution times t = 0 5, 1,    , 5, and denoisers D with depths M = 1, 2, 4, 6, 8  In the top panels of Fig  we show (4) for a chain of size L = 8 as a function of time t  Here it can be seen that even for M trot = 32 a denoiser with M = 1 already improves by roughly an order of magnitude at all considered t 
Depending on M trot and t, further increasing M lowers , with the biggest improvements occurring for high precision Trotter circuits with large depth M trot = 64 and short time t = 0 5, where the Trotter gates are closer to the identity than in the other cases  At the other extreme, for M trot = 16 the improvements are relatively small upon increasing M > 2  In all cases the denoiser works better at early times than at late times, again indicating that it is easier to denoise Trotter gates that are relatively close to the identity 
To probe the accuracy of the denoiser on quantities that do not enter the optimization, as a first test we consider the two-point correlator between spins at different times where we have chosen the infinite temperature initial state, and C(t) is the Trotter supercircuit for time t  In the bottom panels of Fig  we show C zz i=L/2,j=L/2 (t) for the supercircuits from the upper panels, now for a L = 14 chain 
Here we see that at M trot = 16 we can retrieve the noiseless values already with M = 1, but that increasing M trot makes this more difficult  At M trot = 64 we see larger deviations, and improvement upon increasing M is less stable, but nonetheless we are able to mitigate errors to a large extent  As a further test, we compute the out-of-time-ordered correlator (OTOC) ]
In Fig  we show the results for i = L/2, for a Trotter circuit with depth M trot = 32 and a denoiser with depth M = 2  Here we see that a denoiser with M M trot is able to recover the light-cone of correlations, which are otherwise buried by the noise  In the Supplementary Material we consider how the denoiser performs at different noise levels p, and how the denoised supercircuits perform under stacking 
There we also calculate domain wall magnetization dynamics, and show the distribution of the optimized denoiser parameters and the sampling overhead associated to the denoiser as a whole  In Fig  we show the eigenvalues of the noisy supercircuits for a noisy second-order Trotter supercircuit with M trot = 16 at t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised supercircuit (right) 
The eigenvalues λ of a unitary supercircuit lie on the unit circle, and in the presence of dissipation they are pushed to the center  We see that the spectrum of the denoiser lies outside the unit circle, making it an unphysical channel which cures the effect of the noise on the circuit, such that the spectrum of the denoised circuit is pushed back to the unit circle 
The noiseless eigenvalues are shown as blue bars, making it clear that the denoiser is able to recover the noiseless eigenvalues from the noisy circuit  In the Supplementary Material we show the spectra for a p = 0 036 denoiser, where we observe a clustering of eigenvalues reminiscent of Refs    There we also investigate the channel entropy of the various supercircuits  
Conclusion  -We have introduced a probabilistic error cancellation scheme, where a classically determined denoiser mitigates the accumulated noise of a (generally non-Clifford) local noise channel  The required number of mitigation gates, i e  the dimensionality of the corresponding quasiprobability distribution, is tunable and the parameterization of the corresponding channels provides control over the sign problem that is inherent to probabilistic error cancellation 
We have shown that a denoiser with one layer can already significantly mitigate errors for second-order Trotter circuits with up to 64 layers  This effectiveness of low-depth compressed circuits for denoising, in contrast with the noiseless time evolution operator compression from , can be understood from the non-unitarity of the denoiser channels 
In particu-lar, measurements can have non-local effects, since the measurement of a single qubit can reduce some highly entangled state (e g  a GHZ state) to a product state, whereas in unitary circuits the spreading of correlations forms a light-cone  To optimize a denoiser with convenience at L > 8, the optimization can be formulated in terms of matrix product operators or channels , which is convenient because the circuit calculations leading to the normalized distance and its gradient are easily formulated in terms of tensor contractions and singular value decompositions  
This provides one route to a practical denoiser, which is relevant because the targeted noiseless circuit and the accompanying noisy variant in (4) need to be simulated classically, confining the optimization procedure to limited system sizes with an exact treatment or limited entanglement with tensor networks 
Nonetheless, we can use e g  matrix product operators to calculate (4) for some relatively small t, such that the noiseless and denoised supercircuits in (4) have relatively small entanglement, and then stack the final denoised supercircuit on a quantum processor to generate classically intractable states 
Analogously, we can optimize the channels exactly at some classically tractable size and then execute them on a quantum processor with larger size  Both approaches are limited by the light-cone of many-body correlations, as visualized in Fig  , because finite-size effects appear when the light-cone width becomes comparable with system size 
1  The normalized distance (left) and z spin correlator C zz i=L/2,j=L/2 (right), for a second-order Trotter supercircuit of depth Mtrot = 16 for time t = 1, affected by various twoqubit depolarizing errors p  We compare the values obtained with and without a denoiser, i e  M > 0 and M = 0, to the noiseless values (p = 0) 
The denoiser is affected by the same noise as the Trotter circuit  We consider denoisers with depths M = 1, 2, 4, 6, 8, and we use a L = 8 Heisenberg chain with PBC for the normalized distance, while for the correlator we use L = 14  * david luitz@uni-bonn de to observe that even for larger noise strength p, the local observable C zz improves significantly even with denoisers of depth M = 1 
For large noise strengths, we generally see that the optimization of the denoiser becomes difficult, leading to nonmonotonic behavior as a function of p, presumably because we do not find the global optimum of the denoiser  It is interesting to analyze the spectra of the supercircuits considered in this work 
As mentioned in the main text, the spectrum of the ideal, unitary supercircuit C lies on the unit circle  The comparison to this case is therefore instructive  In the main text, we showed an example of the spectra in Fig  for moderate noise strength  Here, we show additional data for stronger noise p = 0 036 in Fig  for a denoiser with M = 4 layers, optimized to mitigate errors for a second-order Trotter supercircuit with M trot = 16 layers at time t = 1 
The eigenvalues λ of the noisy supercircuit C are clustered close to zero, far away from the unit circle (except for λ = 1), showing that the circuit is strongly affected by the noise  To mitigate the impact of the noise, the denoiser consequently has to renormalize the spectrum strongly  If it accurately represents the inverse of the global noise channel, its spectrum has to lie far outside the unit circle, which is the case 
Interestingly, we observe a clustering of eigenvalues which is reminiscent to the spectra found in   By comparison to these works, we suspect that this is due to the local nature of the denoiser, and warrants further investigation  The right panel of Fig  shows the result of the denoiser, pushing the eigenvalues back to the unit circle, nearly with the exact same distribution along the circle as the noiseless eigenvalues (blue bars) 
Due to the strong noise, this is not achieved perfectly, and it is clear that this cannot work in principle if the global noise channel has a zero eigenvalue  The complexity of an operator can be quantified by its operator entanglement entropy   Here we calculate the half-chain channel entanglement entropy S of the noiseless C, noisy C, denoiser D, and denoised D C supercircuits 
We define S as the entanglement entropy of the state that is related to a supercircuit C via the Choi-Jamio lkowski isomorphism, i e  ψ C = χ C /N , where the process matrix χ ab,cd C = C ac,bd is simply a reshaped supercircuit and N ensures normalization  Then we have S = −Tr [ψ C ln ψ C ]  This entropy measure is a particular instance of the "exchange entropy", which characterizes the information exchange between a quantum system and its environment  
In Fig  we plot the various S for a second-order Trotter circuit with M trot = 16 at t = 2, for a denoiser with M = 4, both affected by two-qubit depolarizing noise with p ∈ [10 −3 , 10 −1 ]  The Trotter circuit is for a Heisenberg model with L = 6 and PBC  We see that at large p, the noise destroys entanglement in the noisy supercircuit, and that the denoiser S increases to correct for this, such that the denoised supercircuit recovers the noiseless S 
Here we investigate how denoised supercircuits perform upon repeated application  We optimize the denoiser for a Trotter supercircuit for a fixed evolution time t  Then, to reach later times, we stack the denoised supercircuit n times to approximate the evolution up to time nt: In Fig  we stack a denoised t = 1 supercircuit up to n = 20 times and calculate the correlation function, defined in the main text, for the middle site 
We consider Trotter depths M trot = 8, 16, 32, 64 and denoiser depths M = 1, 2, 4, 6, 8, for a L = 14 Heisenberg chain with p = 0 01 depolarizing two-qubit noise  The noisy results correspond to M = 0 and the noiseless results to p = 0  In Fig  we calculate the OTOC, defined in the main text, with stacked time evolution for a denoised t = 2 supercircuit with M trot = 32 and M = 2, stacked up to ten times 
We see that the stacked supercircuit performs very well, and the additional precision obtained by using deep denoisers (M = 8) pays off for long evolution times, where we see convergence to the exact result (black dashed lines in Fig  ) as a function of M   FIG    The two-point z-spin correlator C zz i=L/2,j=L/2 (t) of a spin on the middle site at times 0 and t, for the infinite temperature initial state, for denoised second-order Trotter supercircuits that are optimized at evolution time t = 1 and then stacked up to twenty times 
We use Trotter depths Mtrot = 8, 16, 32, 64 and denoiser depths M = 1, 2, 4, 6, 8  The calculations were performed for a periodic Heisenberg model with L = 14 and PBC, affected by two-qubit depolarizing noise with strength p = 0 01, which also affects the denoiser  The non-denoised results are labelled with M = 0, and the noiseless results with p = 0 
The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively  The costliest and most noise-susceptible operation is the two-qubit ZZ rotation with angle α, which is the foundation of the unitary piece in our channel parameterization, defined in the main text 
For completeness, we here present the α angles of the optimized denoisers  The results are shown in Fig  , which contains histograms for the channel count N G versus α  The histograms are stacked, with the lightest color corresponding to the angles of the denoiser at t = 0 5 and the darkest at t = 5  The top four panels are for a denoiser with M = 2 and the bottom four with M = 8 
We consider M trot = 8, 16, 32, 64  We see that in both cases the distribution widens upon increasing M trot , indicating that the unitary channels start deviating more from the identity  Moreover, while the M = 2 denoisers in all cases except M trot = 64 have ZZ contributions close to the identity, this is clearly not the case for M = 8 
For simplicity, we did not focus on obtaining denoisers with the smallest sampling overhead γ, which is required to minimize the sign problem and hence ease the sampling of mitigated quantities  Instead, we let the optimization freely choose the η i in the denoiser parameterization, as defined in the main text 
In Fig  we show the sampling overhead of the denoisers from Fig  of the main text  We see that for M = 1 and M = 2 the sampling overhead is relatively small and uniform across the different t, whereas for M > 2 the optimization sometimes yields a denoiser with large γ and other times with small γ  This could be related to the difference in α distributions from Fig   
The large fluctuations of γ appears to stem from the difficulty in finding optimal deep denoisers, and our optimization procedure likely only finds a local minimum in these cases  Here C(t) is the Trotter supercircuit for time t  In Fig  we show Z dw for the circuits from Fig 



ground_truth: L = 8 and L = 14.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What did the court in In re Ferguson conclude about the transformation prong of the Bilski test?

Read the following text and answer briefly.

Context 3: Xpp-pdf support utility
Xpp-pdf support utility
PATENT, TRADEMARK
& COPYRIGHT !
Reproduced with permission from BNA’s Patent,Trademark 11/20/09, 11/20/2009  Copyright ஽ 2009 by The Bu-reau of National Affairs, Inc  (800-372-1033) http://www bna com As the patent community anticipates a decision by the U S  Supreme Court on subject matter patentability, recent rulings by the Federal Circuit and the Board of Patent Appeals and Interferences suggest strategies for preparing method patent applications that will sur- vive the Federal Circuit’s ‘‘machine-or-transformation’’ test 
The Changing Landscape of Method Claims in the Wake of In re Bilski:What We Can Learn from Recent Decisions of Federal Courts and the Board ofPatent Appeals rulings on software-based and other business methodpatent applications 
On review before the high court is the en banc ruling ‘‘Pure’’ business methods are out  Algorithms by the U S  Court of Appeals for the Federal Circuit1 are out  Machines and data transformations that, in order to be eligible for patent protection, an in- ventive method must either be tied to a machine or re- While the patent community waits for the Supreme cite a transformation of an article 2 This ‘‘machine-or- Court’s decision in Bilski v  Kappos, No  08-964 (U S 
transformation’’ test replaced the Freeman-Walter- argued Nov  9, 2009) (79 PTCJ 33, 11/13/09), patent ap- Abele3 test and the ‘‘useful, concrete and tangible plicants seeking to write patentable claims are stuckwith trying to conform to the lower courts’ most recent 1 In re Bilski, 545 F 3d 943, 88 USPQ2d 1385 (Fed  Cir 
2008) (en banc) (77 PTCJ 4, 11/7/08) 
2 ‘‘The machine-or-transformation test is a two-branched Adriana Suringa Luedke and Bridget M  Hay- inquiry; an applicant may show that a process claim satisfies den are lawyers at Dorsey & Whitney, Min- § 101 either by showing that his claim is tied to a particular neapolis  Luedke can be reached at machine, or by showing that his claim transforms an article ’’ leudke adriana@dorsey com  Hayden can be reached at hayden bridget@dorsey com  3 In re Freeman, 573 F 2d 1237, 197 USPQ 464 (C C P A 
1978); In re Walter, 618 F 2d 758, 205 USPQ 397 (C C P A 
COPYRIGHT ஽ 2009 BY THE BUREAU OF NATIONAL AFFAIRS, INC 
result’’ inquiry advocated in State Street,4 each of gregating, and selling real estate property and claims which had been applied by the Federal Circuit and its reciting a method of performing tax-deferred real estate predecessor court in various cases, and both of which property exchanges were not statutory under Section 101  Since no machine was recited, the only issue be- In this article, we examine the 2008 decision of the fore the court was whether the claims met the ‘‘trans- Federal Circuit, federal district court decisions, and de- formation’’ prong of the Bilski test 13 The court held cisions of Patent and Trademark Office’s Board of that the claims ‘‘involve[d] only the transformation or Patent Appeals and Interferences  Based upon the out- manipulation of legal obligations and relationships’’ comes in these cases, we offer guidance as to what is that did not qualify under Bilski 14 patent-eligible under 35 U S C  § 101, strategies for pre- Concerning the recitation of the ‘‘creation of deed- senting methods in patent applications and claiming shares’’ in some of the claims, the court found that the these methods, and possible ‘‘fixes’’ for applications deedshares themselves were not physical objects, but drafted pre-Bilski that must now withstand scrutiny un- only represented intangible legal ownership interests in der the new machine-or-transformation test 
property 15 Therefore, the creation of deedshares wasnot sufficient to establish patent eligibility under Bil- A number of recent federal court and board decisions have applied the patent eligibility test set forth in Bilski, implemented step to an otherwise obvious method was not sufficient to avoid invalidity of the claim  In KingPharmeuticals Inc  v  Eon Labs Inc ,17 the district court held invalid claims to a method of increasing the oral Several cases have addressed (and rejected) claims bioavailability of metaxalone because the claims were obvious over the prior art asserted by the accused in- In In re Ferguson,6 the Federal Circuit reviewed the board’s rejection of claims directed to a method of mar- Two dependent claims added a step of informing the keting a product and a ‘‘paradigm’’ for marketing soft- patient of certain results, which the patentee argued ware as nonstatutory subject matter under Section was not obvious  The court rejected this argument, con- 101 7 The appellate court affirmed the board’s rejection, cluding that ‘‘[b]ecause the food effect is an inherent concluding that the method claims were neither tied to property of the prior art and, therefore, unpatentable, a particular machine or apparatus nor did they trans- then informing a patient of that inherent property is form a particular article into a different state or thing 8 The court defined a machine broadly as ‘‘a concrete The court also commented that the added step of in- thing, consisting of parts, or of certain devices or com- forming the patient did not meet the patent eligibility binations of devices,’’ which did not include the ‘‘shared standard set forth in Bilski because the step did not re- marketing force’’ to which the method claims were quire use of a machine or transform the metaxalone into a different state or thing 19 Notably, this conclusion The claims directed to a ‘‘paradigm’’ were non- runs counter to the Supreme Court’s instruction that statutory because the claims did not fall within any of claims are to be examined ‘‘as a whole’’ and not dis- the four statutory categories (machines, manufactures, sected into old and new elements and that are evaluated compositions of matter and processes)  Concerning the two closest possible categories, the court concluded Recent board decisions have been consistent with the that the claimed paradigm was not a process, because holdings of the federal courts  For example, in Ex parte no act or series of acts was required, and was not a Roberts,21 the board found ineligible under Section 101 manufacture, because it was not a tangible article re- a ‘‘method of creating a real estate investment instru- sulting from a process of manufacture 10 Concerning ment adapted for performing tax-deferred exchanges’’ the recitation of a ‘‘marketing company’’ in the para- because the claim did not satisfy either the machine or digm claims, the court concluded that the patent appli- cants did ‘‘no more than provide an abstract idea—a Similarly, in Ex parte Haworth,23 a method for ‘‘at- business model for an intangible marketing com- tempting to collect payments from customers having delinquent accounts concurrently with a partner that In Fort Properties Inc  v  American Master Lease owns the delinquent accounts’’ was found to be patent LLC,12 the California district court held that claims re- ineligible because the claim wording was ‘‘broad in that citing a series of transactions involving acquiring, ag- 1980); In re Abele, 684 F 2d 902, 214 USPQ 682 (C C P A 
4 State Street Bank & Trust Co  v  Signature Financial 16 See Ex parte Roberts , 2009-004444 at 4-5 (B P A I  June Group, 149 F 3d 1368, 1370, 47 USPQ2d 1596 (Fed  Cir  1998) 19, 2009) (holding a ‘‘method of creating a real estate invest- ment instrument adapted for performing tax-deferred ex- changes’’ patent ineligible as not passing the machine-or- 7 The court accepted the board’s definition of ‘‘paradigm’’ 17 593 F  Supp 2d 501 (E D N Y  2009) 
to mean ‘‘a pattern, example or model ’’ Id  at 1362 
20 See Diamond v  Diehr, 450 U S  175, 188 (1981) 
21 No  2009-004444 (B P A I  June 19, 2009) 
12 2009 WL 249205, *5 (C D  Cal  Jan  22, 2009) 
23 No  2009-000350 (B P A I  July 30, 2009) 
it refers generally to extending an offer, receiving an machine  Accordingly, the process claims       are not acceptance, and paying a commission’’ and did not in- voke, recite or limit the method of implementation us-ing any particular machine or apparatus 24 The court also evaluated similar claims that recited the use of a ‘‘comparator’’ to perform the recited pixel- B  Software Claims Not Expressly Tied to a ‘Particular by-pixel comparison and held that this recitation also did not mandate a machine 29 While the court acknowl-edged that software was offered as one ‘‘option,’’ the Other cases have addressed software methods where court concluded that the claimed function of the com- the claim language was either not expressly tied to com- parator could also be performed in one’s mind or on pa- puter hardware components or the ties to computer per such that a machine was not required  The court components were somewhat ambiguous  In several further noted that, even though the ‘‘comparator’’ was cases, courts have rejected the recitation of generic defined as a ‘‘device,’’ ‘‘the use of the term ‘device’ is computer components as sufficient to satisfy the ‘‘ma- not synonymous with machine ’’30 As a result, none of chine’’ prong of the Bilski test  A number of these deci- the claims at issue met the ‘‘machine’’ prong of the Bil- sions also addressed the ‘‘transformation’’ prong of the Concerning the ‘‘transformation’’ prong, the court re- In Research Corporation Technology Inc  v  Mi- lied in particular upon the Abele decision in expanding crosoft Corp ,25 the district court considered the patent the requirements of this test by requiring that the eligibility of method claims in six patents directed to claimed transformation process be both ‘‘(1) limited to methods of halftoning of gray scale images by using a transformation of specific data, and 2) limited to a vi- pixel-by-pixel comparison of the image against a blue sual depiction representing specific objects or sub- noise mask  Relying on the Federal Circuit’s Bilski stances ’’31 It then concluded that a number of the analysis as well as a decision of its predecessor court, patent claims did not meet the second prong of this ex- In re Abele,26 the judge concluded that a number of the panded test because the claims did not ‘‘require any vi- sual depiction or subsequent display’’ even though the transformation test set forth in Bilski 27 claimed method did transform specific image data 32 Concerning the ‘‘machine’’ prong, the district court The district court also found other claims patent- found that the pixel-by-pixel comparison recited in the eligible under Section 101 because these claims recited claims did not require the use of a machine, but could the use of the comparison data ‘‘to produce a halftoned ‘‘dictate[d] a transformation of specific data, and [were] be done on a sheet of paper using a pen  The com- further limited to a visual depiction which represents parison uses formulas and numbers to generate a bi- specific objects ’’33 Thus, the patent eligibility of the nary value to determine the placement of a dot at a claims turned on whether the claims recited the use of location  Formulas and numbers not tied to a particu- the transformed data to generate a display 
lar machine cannot be patented, under the machine In DealerTrack Inc  v  Huber,34 the district court prong, even with a field-of-use limitation because granted a summary judgment of invalidity under § 101 they represent fundamental principles, and to do so of patent claims directed to ‘‘a computer aided method’’ would preempt the entire field  The patent claims      
of managing a credit application reciting the following do not mandate the use of a machine to achieve their algorithmic and algebraic ends  Simply because adigital apparatus such as a computer, calculator, or [A] receiving credit application data from a remote the like could assist with this comparison does not render it patent eligible material  RCT’s argument [B] selectively forwarding the credit application data that a pixel by its nature is electronic and therefore to remote funding source terminal devices; necessitates a machine is a post solution argumentand the Court rejects it  The claim construction specifies that the comparison is of a value to a mask 29 The term ‘‘comparator’’ was construed by the court to be (or set of values) to determine whether the dot is a ‘‘device (or collection of operations, as in software) that com- turned on at a specific location  This process does pares an input number (called the operand) to a number pre- not require a particular machine  The Bilski test is stored in the comparator (called the threshold) and produces clear: the process claims must be tied to a particular as output a binary value (such as ‘‘0,’’ zero) if the input is alge-braically less than the threshold [the result of comparing anoperand against a fixed threshold and setting an operand less 24 Id  at 9-10  See also, e g , Ex parte Farnes, 2009-002770 than the threshold to one value and an operand greater than (B P A I  June 2, 2009) (rejecting a method claim for develop- or equal to the threshold to another value], and produces the ing a solution to a customer experience issue including steps opposite binary value (such as ‘‘1,’’ one) if the input is algebra- of: ‘‘identifying a target customer,’’ ‘‘defining a current cus- ically greater than or equal to the threshold ’’ Id  at *17 (em- tomer experience,’’ ‘‘summarizing values and benefits’’ to pro- vide to the customer, and ‘‘identifying metrics for measuring success’’); Ex parte Salinkas, 2009-002768 (B P A I  May 18, 31 Id  at *9  Notably, Bilski concluded that the Abele visual 2009) (finding patent ineligible a method of launching a depiction was ‘‘sufficient’’ to establish transformation (545 knowledge network involving ‘‘selecting an executive spon- F 3d at 963), while the Research Corporation court went fur- sor,’’ ‘‘forming a core team of experts,’’ and ‘‘providing pre- ther by making visual depiction ‘‘required’’ to establish trans- 25 2009 WL 2413623 (D  Ariz  July 28, 2009) (78 PTCJ 432, 26 684 F 2d 902, 214 USPQ 682 (C C P A  1982) 
34 2009 WL 2020761 (C D  Cal  July 7, 2009) (78 PTCJ 341, PATENT, TRADEMARK & COPYRIGHT JOURNAL [C] forwarding funding decision data from at least tation of ‘over the Internet’ suffices to tie a process one of the remote funding source terminal de- claim to a particular machine’’ and concluded that it vices to the remote application entry and display The internet continues to exist despite the addition [D] wherein the selectively forwarding the credit ap- or subtraction of any particular piece of hardware  It may be supposed that the internet itself, rather than [E] sending at least a portion of a credit application any underlying computer or set of computers, is the to more than one of said remote funding sources ‘‘machine’’ to which plaintiff refers  Yet the internet is an abstraction  If every computer user in the world [F] sending at least a portion of a credit application unplugged from the internet, the internet would to more than one of said remote funding sources cease to exist, although every molecule of every ma- sequentially until a finding [sic ] source returns a chine remained in place  One can touch a computer or a network cable, but one cannot touch ‘‘the inter- [G] sending       a credit application       after a prede- Additionally, the court found that the recitation of the [H] sending the credit application from a first remote internet in this case merely constituted ‘‘insignificant funding source to a second remote funding extra-solution activity’’ and therefore did not qualify as a ‘‘particular machine’’ under Bilski 41 ‘‘[T]ossing in In concluding that the claim did not satisfy the Bilski references to internet commerce’’ was not sufficient to machine-or-transformation test, the court held that the render ‘‘a mental process for collecting data and weigh- claimed central processor, remote application and dis- ing values’’ patent-eligible 42 Additionally, ‘‘limiting’’ play device, and remote funding source terminal device the claim to use over the Internet was not a meaningful could be ‘‘any device’’ and did not constitute a ‘‘’par- limitation, such that the claims ‘‘broadly preempt the ticular machine’ within the meaning of Bilski ’’35 The fundamental mental process of fraud detection using court relied upon several board decisions to support its associations between credit cards ’’43 premise that ‘‘claims reciting the use of general purpose processors or computers do not satisfy the test ’’36 claim,44 notwithstanding the Federal Circuit’s holding In Cybersource Corp  v  Retail Decisions Inc ,37 the in In re Beauregard,45 the district court concluded that district court held claims for ‘‘a method for verifying the ‘‘there is at present no legal doctrine creating a special validity of a credit card transaction over the Internet’’ ‘‘Beauregard claim’’ that would exempt the claim from and ‘‘a computer readable medium containing program the analysis of Bilski ’’ Moreover, ‘‘[s]imply appending instructions for detecting fraud in a credit card transac- ‘A computer readable media including program instruc- tion       over the Internet’’ invalid under § 101 based tions’ to an otherwise non-statutory process claim is in- upon the court’s interpretation of Bilski 
sufficient to make it statutory ’’46 Consequently, this Concerning the method claim, the court considered claim also failed the Bilski test 
both the ‘‘transformation’’ and ‘‘machine’’ prongs of the In at least one instance, the U S  International Trade Bilski test  In concluding that there was no transforma- Commission has interpreted the ‘‘machine’’ prong of tion, the court focused on the intangibility of the ma- Bilski less stringently than did the district courts in the nipulated data  According to the court, transformation cases discussed above  In In the Matter of Certain Video is limited to transformation of a physical article or sub- Game Machines and Related Three-Dimensional Point- stance  Accordingly, the method claim did not qualify ing Devices,47 the accused infringer filed a motion for because the data representing credit cards did not rep- summary judgment alleging that the asserted claims resent tangible articles but instead an intangible series impermissibly sought to patent a mathematical algo- of rights and obligations existing between the account rithm  According to the movant, the recitations of a ‘‘3D pointing device,’’ ‘‘handheld device,’’ or ‘‘free space Concerning whether the claimed method was tied to pointing device’’ were not sufficient to tie the claims to a particular machine, the court assessed whether ‘‘reci- a particular machine, but served ‘‘only to limit the field-of-use of the claimed mathematical algorithm and [did] not otherwise impart patentability on the claimed math- Id  at *3  The court relied upon the holdings in Ex parte Gutta, No  2008-3000 at 5-6 (B P A I  Jan  15, 2009) (stating In denying the motion for summary judgment, the ‘‘[t]he recitation in the preamble of ‘[a] computerized method ITC first noted that, ‘‘[w]hile the ultimate determination performed by a data processor’ adds nothing more than a gen- of whether the asserted claims are patentable under eral purpose computer that is associated with the steps of the § 101 is a question of law, the Federal Circuit has ac- process in an unspecified manner ’’); Ex parte Nawathe, No 
2007-3360, 2009 WL 327520, *4 (B P A I  Feb  9, 2009) (finding‘‘the computerized recitation purports to a general purpose processor [], as opposed to a particular computer specifically programmed for executing the steps of the claimed method ’’); and Ex parte Cornea-Hasegan, No  2008-4742 at 9-10 (B P A I 
Jan  13, 2009) (indicating the appellant does not dispute ‘‘the recitation of a processor does not limit the process steps to any 44 Claims having this format are called ‘‘Beauregard’’ specific machine or apparatus ’’)  The court also cited Cyber- claims and were found to not be barred by the traditional source Corp  v  Retail Decisions Inc , (discussed below), in sup- printed matter rule in In re Beauregard, 53 F 3d 1583, 1584, 35 port of its interpretation of the required ‘‘particular machine ’’ 37 620 F  Supp  2d 1068, 92 USPQ2d 1011 (N D  Cal  2009) 47 2009 WL 1070801 (U S I T C  2009) 
knowledged that ‘there may be cases in which the legal given a dataset of feature vectors associated with the question as to patentable subject matter may turn on subsidiary factual issues’ ’’ (citation omitted)  In con- for each binary partition under consideration, rank- struing the claims, the tribunal found that there was a ing features using two-category feature ranking; and genuine dispute as to whether the claimed ‘‘devices’’represented a ‘‘particular machine’’ under the Bilski while the predetermined number of features has not test and whether the claimed ‘‘two-dimensional rota- yet been selected: picking a binary partition p; tional transform’’ was merely a mathematical calcula- selecting a feature based on the ranking for binary tion or instead meant ‘‘changing the mathematical rep- resentation of a two-dimensional quantity from oneframe of reference to a differently-oriented frame of ref- adding the selected feature to an output list if not al- erence’’ as asserted by the patentee  Additionally, the ready present in the output list and removing the se- dispute over the meaning of the claimed ‘‘two- lected feature from further consideration for the bi- dimensional rotational transform’’ also raised a dis- puted issue as to whether this element recited a trans- Notably, while the independent claim failed the formation that would qualify under the ‘‘transforma- machine-or-transformation test, its dependent claim tion’’ prong of Bilski  Given these disputed issues, the was eligible because it recited, ‘‘further comprising us- ITC concluded that it was inappropriate to grant sum- ing the selected features in training a classifier for clas- mary judgment as to the patent eligibility of the claims 
sifying data into categories ’’ In view of the specifica- A similar conclusion was reached in Versata Soft- tion, the board indicated that the ‘‘classifier’’ was a par- ware Inc  v  Sun Microsystems Inc ,48 in which the dis- ticular machine ‘‘in that it performs a particular data trict court denied the defendant’s motion for summary classification function that is beyond mere general pur- judgment of invalidity under Section 101 based upon pose computing ’’53 The board also concluded that the the Bilski court’s refusal ‘‘to adopt a broad exclusion claim ‘‘transforms a particular article into a different over software or any other such category of subject state or thing, namely by transforming an untrained matter beyond the exclusion of claims drawn to funda- classifier into a trained classifier ’’54 In Ex parte Casati,55 the board reversed the examin- Less stringent ‘‘machine’’ prong analyses are also er’s Section 101 rejection of a method claim reciting: found at the board level  For example, in Ex parteSchrader,50 the board held patent-eligible under Bilski A method of analyzing data and making predictions, reading process execution data from logs for a busi- A method for obtaining feedback from consumers re- ceiving an advertisement from an ad provided by anad provider through an interactive channel, the collecting the process execution data and storing the process execution data in a memory defining a ware-house; creating a feedback panel including at least one feed-back response concerning said advertisement; and analyzing the process execution data; generatingprediction models in response to the analyzing; and providing said feedback panel to said consumers, using the prediction models to predict an occurrence said feedback panel being activated by a consumer to of an exception in the business process 
provide said feedback response concerning said ad-vertisement to said ad provider through said interac- In this case, giving consideration to the specification, which ‘‘unequivocally describes the data warehouse aspart of the overall system apparatus, and subsequent Here, the board found ‘‘interactive channel’’ to be descriptions describe the memory/warehouse device in part of an ‘‘overall patent eligible system of appara- terms of machine executable functions,’’ the board con- tuses’’ when viewed in the context of the specification, cluded that ‘‘one of ordinary skill in the art would un- which included ‘‘the Internet and World Wide Web, In- derstand that the claimed storing of process execution teractive Television, and self service devices, such as In- data in a memory defining a warehouse constitutes formation Kiosks and Automated Teller Machines ’’51 patent-eligible subject matter under § 101 because the In another recent decision, Ex parte Forman,52 the memory/warehouse element ties the claims to a particu- board found a ‘‘computer-implemented feature selec- tion method’’ including a ‘‘classifier’’ eligible under Other recent board decisions have reached the oppo- Section 101 because it satisfied both the machine and transformation prong  Here, the ‘‘classifier’’ was recitedin a dependent claim, in which its independent claim re-cited: 53 Id  at 13 
54 Id  See also Ex parte Busche, No  2008-004750 (B P A I 
A computer-implemented feature selection method May 28, 2009) (holding a process claim and a computer pro- for selecting a predetermined number of features for gram product claim, each reciting training a machine, ‘‘are di- a set of binary partitions over a set of categories rected to machines that have such structure as may be adaptedby training ’’) 55 No  2009-005786 (B P A I  July 31, 2009) 
48 2009 WL 1084412, *1 (E D  Tex  March 31, 2009) 
56 Id  at 7  See also Ex parte Dickerson, No  2009-001172 at 49 Citing Bilski, 545 F 3d at 959 n  23 
16 (B P A I  July 9, 2009) (holding claims that ‘‘recite a comput- 50 No  2009-009098 (B P A I  Aug  31, 2009) 
erized method which includes a step of outputting information from a computer       are tied to a particular machine or appa- 52 No  2008-005348 (B P A I  Aug  17, 2009) 
PATENT, TRADEMARK & COPYRIGHT JOURNAL implemented methods ineligible under the Bilski test transformation test applied to this type of claim 63 because the claims failed to tie the method steps to any Then, applying the Bilski test, the board concluded that concrete parts, devices, or combinations of devices  For the claim did not qualify  According to the board, the example, in Ex parte Holtz,57 the board found ineligible under Section 101 a ‘‘method for comparing file tree de-scriptions’’ because the claim ‘‘obtains data (a file struc- does not transform physical subject matter and is not ture), compares data (file structures), generates a tied to a particular machine        Limiting the claims change log, and optimizes the change log without tying to computer readable media does not add any practi- these steps to any concrete parts, devices, or combina- cal limitation to the scope of the claim  Such a field- tions of devices’’ and the ‘‘file structures’’ did not repre- of-use limitation is insufficient to render an other- Similarly, in Ex parte Gutta,58 the board held ineli- gible under § 101 a ‘‘method for identifying one or moremean items for a plurality of items       having a sym- II  The Current Scope of Patent Eligibility bolic value of a symbolic attribute,’’ concluding that the These recent cases establish that some types of meth- claim ‘‘computes a variance and selects a mean item ods are clearly patent-eligible under Section 101, others without tying these steps to any concrete parts, devices, clearly are not eligible, and yet others may be depend- or combinations of devices’’ and ‘‘symbolic values are ing on how they are described and claimed 
neither physical objects nor do they represent physicalobjects ’’ First, the eligibility of system and apparatus claims is largely unaffected by the Bilski decision, with the ca- In contrast to the district court’s decision in Cyber- veat that such claims may be more closely scrutinized source Corp , discussed supra, in a recent board deci- for compliance with Diamond v  Diehr and Gottschalk sion, Ex parte Bodin,59 ‘‘a computer program product’’ v  Benson, which prohibit patenting of a claim directed was found to be patent-eligible subject matter as being to ‘‘laws of nature, natural phenomena, [or] abstract embodied in a ‘‘computer readable medium ’’ Here, the board considered whether the phrase ‘‘recorded on the Also, methods that are performed at least in part by a recording medium’’ as it is recited in the body of the machine qualify for patent eligibility under Section 101 
claims was the same as ‘‘recorded on a computer- Thus, for example, some computer-implemented and readable medium ’’ Acknowledging the differences be- software-related inventions remain patentable as long tween a statutory claim to a data structure stored on a as they are properly described and claimed as being computer readable medium compared to a nonstatutory performed by a computer or computer components 
claim to a data structure that referred to ideas reflected The tie to a machine, however, cannot merely be im- in nonstatutory processes, the board stated: ‘‘[w]hen plicit based upon the description and context of the ap- functional descriptive material is recorded on some plication or general language in the preamble of the computer-readable medium, it becomes structurally claim  Instead, the use of a machine to perform one or and functionally interrelated to the medium and will be more of the claimed functions must be expressly de- statutory in most cases since use of technology permits scribed in the body of the claim so as to be a meaning- the function of the descriptive material to be real- ful limitation on the claim  If a method claim can be read in such a way that all functions can be performed Similarly, in Ex parte Azuma,61 a claim to a ‘‘com- by a human, it will likely not pass the machine prong of puter program product       comprising: a computer us- able medium’’ was found to be directed to statutory The ‘‘Interim Examination Instructions for Evaluat- subject matter under § 101 because the language ‘‘com- ing Subject Matter Eligibility Under 35 U S C  § 101’’ re- puter usable medium’’ referred to tangible storage me- cently issued by the Patent and Trademark Office con- dia, such as a server, floppy drive, main memory and firm that the recitation of a general purpose computer hard disk as disclosed by appellant’s specification, and is sufficient to satisfy Section 101 where the general did not ‘‘implicate the use of a carrier wave ’’ purpose computer is ‘‘programmed to perform the pro- In an older decision, Ex parte Cornea-Hasegan,62 cess steps,       in effect, becom[ing] a special purpose however, the Board seemingly came to the opposite conclusion, holding that a claim reciting ‘‘a computer Concerning data transformation, there seems to be readable media including program instructions which agreement of the Federal Circuit and at least one dis- when executed by a processor cause the processor to trict court that a method that is both limited to transfor- perform’’ a series of steps was not patent-eligible under mation of specific data and limited to a visual depiction Bilski  The board first determined that ‘‘analysis of a representing specific objects or substances qualifies un- ‘manufacture’ claim and a ‘process’ claim is the sameunder 63 Id  at 11 
57 No  2008-004440 at 12-13 (B P A I  Aug  24, 2009) 
65 Diamond v  Diehr, 450 U S  175, 185, 205 USPQ 488 58 No  2008-004366 at 10-11 (B P A I  Aug  10, 2009) 
(1980); Gottschalk v  Benson, 409 U S  63, 67, 175 USPQ 673 59 No  2009-002913 (B P A I  Aug  5, 2009) 
60 Id  at 10 (comparing In re Lowry, 32 F 3d 1579, 1583-84, 66 ‘‘Interim Examination Instructions for Evaluating Sub- 32 USPQ2d 1031 (Fed  Cir  1994) to In re Warmerdam, 33 F 3d ject Matter Eligibility Under 35 U S C  § 101,’’ U S  Patent and 1354, 1361-62, 31 USPQ2d 1754 (Fed  Cir  1994)) 
Trademark Office, Aug  24, 2009, at 6 (78 PTCJ 530, 8/28/09) 
61 No  2009-003902 at 10 (B P A I  Sept  14, 2009) 
The authors’ recent experiences with examiners suggest that 62 No  2008-004742 (B P A I  Jan  13, 2009) 
the examiners are following these instructions 
der Section 101 67 Thus, claims analogous to those in In Concerning claims directed to computer program re Abele68 in which ‘‘data clearly represented physical products, one district court has held that appending ‘‘A and tangible objects, namely the structure of bones, or- computer readable media including program instruc- gans, and other body tissues [so as to recite] the trans- tions’’ to an otherwise non-statutory process claim is in- formation of that raw data into a particular visual depic- sufficient to make it statutory 72 The board has also tion of a physical object on a display’’ are patent- held ineligible claims to ‘‘a computer readable me- dia ’’73 The board has, however, also upheld the eligibil-ity of ‘‘a computer program product’’ as being embod- ied in a computer readable medium 74 Given these in- Bilski has had a significant impact in eliminating consistent decisions, the patent eligibility of claims in patent protection for inventions that are performed en- tirely by humans or can be interpreted as such if read Concerning claims directed to generalized computer broadly  This includes claims that describe processes processing functions, several Board decisions suggest for creating or manipulating legal and financial docu- that, absent a tie to a concrete real-world application, ments and relationships  In this area in particular, many such claims are likely to be deemed an ‘‘algorithm’’ un- pending applications filed prior to Bilski are no longer der Benson and therefore held to be non-statutory  75 patent-eligible, and many issued patents are no longer Any recitation of a specific field of use for the claimed valid  This retroactive impact of the Bilski decision is process or use of the outcome of such processes are troubling, given the investment in these patents and ap- also more likely to be found ‘‘field-of-use’’ or ‘‘post- plications, which have now been rendered essentially solution activity’’ limitations insufficient to render the worthless despite the suggestion in the Federal Circuit’s claim patent-eligible  Thus, the more tied a claimed pro- earlier State Street decision, now overruled, that such cess is to tangible results or particular applications (not claims qualified for patent protection 
just fields of use), the more likely it is to qualify under Inventions that do not fit within the four statutory categories are also not patent-eligible  The Federal Cir-cuit and the board have rejected claims directed to ‘‘a III  Presenting and Claiming Methods in Patent signal,’’ ‘‘a paradigm,’’ ‘‘a user interface’’ and ‘‘a corr-elator’’ on the basis that these items did not qualify as a ‘‘machine, manufacture, composition of matter or pro- Several strategies for describing and claiming meth- cess’’ under § 101  70 There is also an increasing focus ods or processes in patent applications may avoid or on the tangibility of the claimed invention in that, to minimize potential Section 101 problems 
qualify as a ‘‘machine’’ or ‘‘manufacture’’ under Section First, the description provided in a patent application should include well-defined steps or functions associ-ated with method or process  For example, when the claims include ‘‘initiating’’ method steps, a description Remaining areas of uncertainty concerning the scope of well-defined physical steps or functions for initiating of Section 101 include (1) what qualifies under Bilski as should be provided, and a concrete item, machine, de- a ‘‘transformation of an article or data,’’ (2) whether vice, or component that is responsible for the initiating claims to computer programs (Beauregard claims) function should be identified  For claiming ‘‘identify- qualify, and (3) whether internal computer processing ing’’ method steps, provide specific parameters for functionality not tied to a specific application or tan- making the identification, such as according to a speci- fied measurement 76 Where data is involved, the source Concerning data transformation, other than Abele- and type of data should be specified 
style claims discussed above, what qualifies as a data or Also, drawings should be provided that depict the article transformation remains unclear  Claims that concrete item, device, component or combination have been held not to meet the transformation prong in- thereof, and each method or process step or function clude claims directed to the creation or manipulation of should be linked expressly to at least one item, device data representing an intangible series of rights and ob- or component in the drawings that performs the step or ligations (e g , credit card data) and claims directed to function  Broadening language indicating that other the transformation or manipulation of legal obligations components may also be used to perform the function and relationships  Beyond these specific examples, it is may also be included to avoid an unduly narrow inter- difficult to predict what will or will not qualify as a data or article transformation under Bilski 
The claims should affirmatively claim the device, ma- chine or component performing each step or function 
67 In re Bilski, 545 F 3d at 963; Research Corporation Tech- For computer or software-related inventions, the de- nologies, 2009 WL 2413623 at *9 
scription should specify that the software functionality 68 The claimed process involved graphically displaying vari- ances of data from average values wherein the data was X-rayattenuation data produced in a two dimensional field by a com- 72 Cybersource Corp , 620 F  Supp  2d at 1080 
puted tomography scanner  See In re Bilski, 545 F 3d at 962- 73 Cornea-Hasegan, No  2008-004742 
74 Ex parte Bodin, No  2009-002913 (B P A I  Aug  5, 2009) 
69 In re Bilski, 545 F 3d at 963 
75 E g , Ex parte Greene, No  2008-004073 (B P A I  Apr  24, 70 In re Nuijten 500 F 3d 1346, 1357, 84 USPQ2d 1495 (Fed 
2009); Daughtrey, No  2008-000202; Ex parte Arning, No 
Cir  2007) (74 PTCJ 631, 9/28/07) (signal); In re Ferguson, 558 2008-003008 (B P A I  Mar  30, 2009); Cybersource Corp , 620 F 3d 1359, 1366, 90 USPQ2d 1035 (Fed  Cir  2009) (77 PTCJ F  Supp 2d at 1080 (concerning claim 2) 
489, 3/13/09) (paradigm); Ex parte Daughtrey, No  2008- 76 See Brief of American Bar Association as Amicus Curiae 000202 (B P A I  Apr  8, 2009) (user interface); Ex parte Laba- Supporting Respondent, Bilski v  Kappos, No  08-964, ABA die, No  2008-004310 (B P A I  May 6, 2009) (correlator) 
Amicus Br  at 12-13 (U S  amicus brief filed Oct  2, 2009) (78 71 E g , Nuijten, 500 F 3d at 1356-7 
PATENT, TRADEMARK & COPYRIGHT JOURNAL is performed by a computer or computer components 
patent or published application, the option of importing Specificity as to the type of computer component per- subject matter into the specification is limited to ‘‘non- forming each function may be helpful in establishing essential’’ subject matter  In other words, the specifica- eligibility under the Bilski test 
tion can only be amended to disclose a machine for per-forming process steps as long as one skilled in the art IV  Fixing Pre-Bilski Applications to Meet the New would recognize from the original disclosure that the process is implemented by a machine  The key in mak- For patent applications filed prior to the Bilski deci- ing this type of amendment is avoiding (or overcoming) sion, it can be challenging to meet the new require- a rejection under 35 U S C  § 112, para  1, for lack of ments for patent eligibility, particularly when no ma- chine or transformations were expressly described in If incorporation by reference is not an option, a patent applicant may submit evidence, such as a decla- In some cases, there may be sufficient explicit de- ration by the inventor or a duly qualified technical ex- scription of a machine, e g , a computer, such that the pert, demonstrating that one skilled in the art would un- machine can be added into the body of the claims  For derstand the disclosed method to be one performed by example, patent applications for computer-related in- a machine  Unlike attorney argument, which can be dis- ventions sometimes contain a generic description of regarded, such evidence must be considered by the ex- computers that are used to perform the claimed method, and such a generic description may be suffi- One other option is to reformat the claims  Since Bil- cient to impart patent eligibility to the claims when the ski ostensibly does not apply to system and apparatus general-purpose computer is programmed to become a claims, in some instances it may be possible for an ap- plicant to convert his method claims into system claims For patent applications lacking in an explicit descrip- to avoid application of the Bilski test  This strategy, tion of any machine, however, the application may in- however, is unlikely to succeed where the patent speci- corporate by reference patents or publications that can fication does not describe such a system for implement- be used to bolster the specification and provide support ing the method and therefore does not provide the req- for the requisite claim amendments  When an applica- uisite disclosure of the claimed invention under Section tion incorporates by reference a U S  patent or pub- lished U S  patent application, any description from the incorporated references, whether or not the subject The future of the Bilski machine-or-transformation matter is ‘‘essential’’ to support the claims, may be im- test now rests with the Supreme Court  Regardless of ported into the specification  This option may enable the outcome of the appeal, however, it is clear that the importation of the requisite description of a machine, scope of statutory subject matter under Section 101 has which can then also be recited in the claims 77 When been narrowed  The Supreme Court now has a chance the document incorporated by reference is not a U S 
to clarify what has been excluded; it may even reject ormodify the Bilski machine-or-transformation test  How 77 Manual of Patent Examining Procedure, Eighth Ed , Rev 
this will affect the development and protection of cur- 7/2008, at § 608 01(P); see also 37 C F R  § 1 57 
rent and future technologies remains to be seen 
Source: http://www dorsey com/files/upload/luedke_bna_patent_journal_nov09 pdf
(resolução 404 2012 retificação 19062012)
RESOLUÇÃO Nº 404 , DE 12 DE JUNHO DE 2012 Dispõe sobre padronização dos procedimentos administrativos na lavratura de Auto de Infração, na expedição de notificação de autuação e de notificação de penalidade de multa e de advertência, por infração de responsabilidade de proprietário e de condutor de veículo e da identificação de condutor infrator, e dá outras providências 
Cheloidi e cicatrici ipertrofiche in dermatologia
a cura del dr  Antonio Del Sorbo - Specialista in Dermatologia e Venereologia antoniodelsorbo@libero it I Cheloidi di Alibert A volte una ferita anche apparentemente banale, guarisce lasciando una cicatrice voluminosa, rossastra e soprattutto antiestetica  I cheloidi sono cicatrici abnormi che possono far seguito a intervento chirurgico (es: tiroide, mammella, etc) e questo u



ground_truth: It required the transformation to be limited to specific data and a visual depiction representing specific objects or substances.