Tag: nielsen-and-chuang

17 Connection between stabilizer generators and parity check matrices in the Steane code 2018-10-03T22:19:33.770

12 What is the difference between "code space", "code word" and "stabilizer code"? 2018-04-17T18:44:52.797

12 Simulate hamiltonian evolution 2019-02-14T10:01:57.727

8 Nielsen and Chuang's proof for 'approximating arbitrary unitary gates is generically hard' 2019-05-12T07:39:06.533

7 Quantum channel representation of projective measurement 2019-06-13T00:57:22.930

7 Derive phase damping quantum operation 2019-07-27T14:21:40.190

7 Why is Deutsch's gate universal? 2020-03-17T19:30:48.713

7 What's the 'physical consistency' in the partial trace scenario? 2021-01-23T23:45:06.900

6 How can we be sure that for every $A$, $A^\dagger A$ has a positive square root? 2018-12-02T11:28:41.900

6 Partial trace over a product of matrices - one factor is in tensor product form 2018-12-25T08:15:27.197

6 Phase estimation algorithm: probability bound of obtaining $m$ 2019-03-25T18:29:36.593

6 Error syndromes and recovery procedure in bit flip code 2019-06-07T21:39:40.613

5 Nielsen & Chuang Exercise 2.1 - "Linear dependence: example" 2018-06-20T23:08:14.950

5 Intuitive role of the polar decomposition in proof of Uhlmann's theorem for fidelity 2018-11-09T10:55:09.557

5 Confusion on the definition of the phase-damping channel 2018-11-26T11:40:24.430

5 Construction of ${R_n(\theta)}$ using only the Hadamard and ${\pi/8}$ gates 2018-12-04T15:26:31.950

5 How does $\mathcal E(\rho)=\mathrm{Tr}_{env}[U(\rho\otimes\rho_{env})U^\dagger]$ turn into $P_0\rho P_0+P_1\rho P_1$? 2018-12-17T06:28:36.610

5 Proof of the optimality of Grover's algorithm 2019-03-27T17:02:42.607

5 Find the quantum operation corresponding to a given unitary evolution and projective measurement 2019-07-13T22:19:53.150

5 Given $n-k$ stabiliser generators, how can we find an additional $k$ commuting generators? 2019-08-29T13:04:55.050

5 Nielsen & Chuang Exercise Question on CSS code 2019-11-11T16:14:40.357

5 Nielsen and Chuang, Exercise 6.5: How to simulate oracle for n+1 qubits using one oracle gate for n qubits and one extra qubit? 2019-12-25T05:10:07.270

5 Uncomputation in quantum implementation of a classical algorithm 2020-01-04T15:39:05.720

5 Question Regarding Quantum Period-Finding Fourier Transform Approximation 2020-05-05T01:52:19.353

5 Procedures and intuition for designing simple quantum circuits? 2020-06-12T15:48:38.343

5 Is there any 'official' list of errata for Nielsen & Chuang? 2020-09-01T13:53:33.640

5 Nielsen&Chuang 5-qubit quantum error-correction encoding gate 2020-10-20T08:40:31.943

5 In Nielsen and Chuang, how can $\frac{1}{2(e-1)}$ result from $\frac12\int_{e-1}^{2^{t-1}-1}dl\frac{1}{l^2}$? 2020-11-29T13:13:01.290

5 What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$? 2021-01-17T23:14:06.043

4 How to find the operator sum representation of the depolarizing channel? 2018-12-16T20:35:45.460

4 Are three POVM measurements on a single qubit physically realizable? 2019-11-17T00:10:18.633

4 How is the partial trace related to the operator sum representation? 2019-11-25T13:25:14.487

4 What kind of errors does the master equation in the Lindblad form describe, continuous errors or discrete errors? 2020-01-10T07:33:03.800

4 Constructing a circuit for $C^1(U)$ for rotation operators with TWO single qubit gates and CNOT gate 2020-01-22T23:02:54.447

4 How does $U_f$ in Deutsch's Algorithm affect the state $|x\rangle$? 2020-02-16T17:28:05.050

4 Prove that there exist tripartite $|\psi\rangle$ which cannot be written as $|\psi\rangle=\sum_i\lambda_i|i_A\rangle|i_B\rangle|i_C\rangle$ 2020-02-25T11:41:34.587

4 What does it look like to split an EPR pair? 2020-04-08T15:22:15.233

4 Is the quantum state fidelity defined as $F(\rho, \sigma)=\text{tr}\sqrt{\rho^{1/2}\sigma\rho^{1/2}}$ or its square? 2020-04-13T15:30:02.260

4 Deutsch's algorithm in Qiskit 2020-05-04T16:10:31.040

4 Correct Formulation of N&C Exercise 4.11 and other textbooks misquoting 2020-05-19T14:59:37.843

4 Complexity of controlled operations in a two-level unitary operation 2020-12-10T22:27:08.673

3 Nielsen & Chuang Exercise 2.2 - “Matrix representations: example” 2018-06-21T13:16:32.857

3 Nielsen & Chuang Exercise 2.3 - “Matrix representation for operator products” 2018-06-26T09:16:44.673

3 Nielsen & Chuang Exercise 2.5 - Inner products of complex vectors 2018-06-28T20:43:47.690

3 Phase shifter acting on double rail states 2019-01-02T17:26:56.797

3 What do you specify when you physically apply a unitary? 2019-01-13T12:50:38.063

3 Why isn't the circuit performing a measurement in the Bell basis? 2019-03-03T10:11:27.533

3 N&C quantum circuit for Grover's algorithm 2019-03-26T08:56:59.427

3 In what sense do repeated applications of Grover's operator rotate the state closer to the target? 2019-03-27T19:08:51.400

3 Quantum addressing scheme 2019-04-04T14:48:39.820

3 Proof of joint entropy theorem 2019-05-06T16:26:44.240

3 Exercise 10.34 of Nielsen and Chuang : $-I$ not element of stabilizer group iff $g_j^2=I$ and $g_j \neq I$ where $g_j$ generators 2019-08-28T11:36:31.913

3 Time Evolution Operator of Rabi Oscillations 2019-09-22T17:11:00.827

3 Premise of the proof of the No-Cloning Theorem 2019-11-15T22:39:25.447

3 Problem 2.2 in Nielsen & Chuang - Properties of the Schmidt number 2020-01-17T21:07:51.877

3 Viewing two-qubit measurement as a projective measurement 2020-03-04T05:38:51.057

3 Nielsen and Chuang ex 2.73 2020-04-17T18:42:32.873

3 How to perform Quantum Process Tomography for three qubit gates? 2020-04-20T16:27:50.297

3 Do any two distinct pure states form a basis? 2020-04-23T00:59:39.520

3 Showing measurement of a Hermitian Unitary operator gives final states as eigenvectors 2020-04-28T17:52:12.377

3 Problem with building quantum circuit for Hamiltonian operation 2020-05-05T05:49:01.113

3 Deriving $\left( A | v \rangle \right)^\dagger = \langle v | A^\dagger$ without using $A^\dagger=\left(A^* \right)^T$ 2020-08-23T00:15:45.970

3 Nielsen & Chuang Exercise 2.55: Prove that $\exp \left[ -\frac{iH(t_2 - t_1)}{\hbar} \right]$ is unitary 2020-09-03T18:14:06.033

3 Show that for any measurement operator $M_m$ there exists unitary $U_m$ such that $M_m=U_m\sqrt{E_m}$ with $E_m$ POVM 2020-09-25T02:25:30.420

3 Nielsen & Chuang Exercise 6.13: Standard deviation of classical counting algorithm 2020-11-21T19:54:40.933

3 Application of QFT to Order-finding 2021-01-12T12:51:25.223

3 What's the difference between $p(i|m)$ and $p(m|i)$ in measurement? 2021-01-18T21:32:01.877

3 How do we find the stabilizer generators for the three-qubit bit-flip code spanned by $|000\rangle$ and $|111\rangle$? 2021-02-03T15:12:48.910

2 Nielsen & Chuang Exercise 2.4 - “Matrix representation for identity” 2018-06-27T12:40:32.250

2 FANOUT with Toffoli Gate 2019-01-02T04:31:17.803

2 Nielsen & Chuang Exercise 2.2 - Matrix representations in different input and output basis 2019-02-07T12:36:00.657

2 If CNOTs and single qubit gates are universal then why do we need to prove that controlled U operations can be composed by them as well? 2019-02-17T16:10:22.100

2 Clarification needed for the N&C proof that BQP ⊆ PSPACE 2019-03-03T17:01:37.310

2 Eigenstate of unitary operator used for Order-Finding 2019-04-20T14:22:37.140

2 Method to find $r$ in the case when $r'$ returned by the continued fractions procedure is a factor of $r$ 2019-05-09T08:52:11.303

2 Proving the inequality $|\mathrm{tr}(AU)|\le \mathrm{tr}|A|$ in Uhlmann's theorem 2019-05-13T19:48:26.997

2 Angular Error associated with Quantum Search Algorithm 2019-06-28T11:44:34.347

2 Hamiltonian for Single-photon, Single-atom QED Cavity 2019-07-03T18:30:05.630

2 Amplitude Damping of a Harmonic Oscillator 2019-07-21T16:54:03.077

2 Can someone show the linear algebra calculations for X, H, and CNOT gates? 2019-09-12T22:30:49.043

2 Nielsen and Chuang, Exercise 6.12: How to simulate the specific Hamiltonian in the search algorithm by the Oracle gates? 2019-12-18T15:06:26.033

2 Conditional version of the triangle inequality for Von Neumann entropy 2020-02-05T05:04:52.377

2 Understanding Steps in Deutsch's Algorithm 2020-02-12T02:28:48.953

2 Understanding the outer products in density matrices 2020-02-21T19:32:46.210

2 Why is Hilbert space considered especially large? 2020-03-27T10:56:09.650

2 Question Regarding Simulating Hamiltonian With Quantum Circuit 2020-04-26T05:15:34.430

2 Identity for linear codes and their duals: why do we have $\sum_y (-1)^{x\cdot y}=|C|\delta_{x\in C^\perp}$? 2020-04-28T17:36:02.800

2 How to implement the exponential of an outer product? 2020-05-08T17:49:28.357

2 Nielsen & Chuang Theorem 2.6 Proof 2020-08-26T14:12:44.430

2 Does composition of two single qubit rotations yield a single rotation around a unit vector? 2020-10-04T20:45:09.713

2 von Neumann entropy in a limiting case 2020-10-24T16:29:52.203

2 CSS Code and Fault-tolerant Problem in Nielsen and Isaac Chuang‘s book 2020-11-28T01:17:28.317

2 In Uhlmann's theorem, should the polar decomposition be written as $A=|A|V$ or $A=V|A|$? 2020-11-28T13:34:26.287

2 EPR Experiment: What does it mean for Alice to measure $\vec{v} \cdot \vec{\sigma}$ on her qubit? 2020-12-27T18:59:36.860

2 Output of Quantum Phase Estimation Algorithm 2021-01-15T01:48:16.357

2 What are Sideband Pulses 2021-01-22T23:20:53.447

2 In Bell's inequalities, what is the meaning of assuming that the physical properties $P_Q,P_R,P_S,P_T$ have definite values? 2021-02-10T10:23:17.503

2 How would I compute a density matrix of a 2 qubit mixed state? 2021-02-22T23:42:17.180

2 How would I compute a density matrix of a complex qubit mixed state? 2021-02-23T01:34:46.513