Tag: mathematics

21 How to derive the CNOT matrix for a 3-qubit system where the control & target qubits are not adjacent? 2018-09-18T19:15:55.053

16 Quantum states are unit vectors... with respect to which norm? 2018-07-13T11:43:57.257

14 How to understand the Haar measure from a quantum information perspective? 2019-05-16T04:49:17.890

13 Is acting with a positive map on a state not part of a larger system allowed? 2018-05-15T07:33:05.183

13 Automatic compilation of quantum circuits 2018-08-24T18:05:02.970

11 Rigorous security proof for Wiesner's quantum money 2018-03-29T07:16:45.100

10 Graphical Calculus for Quantum Circuits 2018-07-16T00:39:56.460

10 Quantum Algorithm for God's Number 2018-08-07T06:46:53.363

10 Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem? 2019-07-30T22:54:58.067

9 How can I calculate the inner product of two quantum registers of different sizes? 2018-08-07T12:44:33.587

8 Do we have to trust the bank in "Quantum Money from Hidden Subspaces?" 2018-07-13T02:59:55.450

8 Is there an algorithm for determining if a given vector is separable or entangled? 2019-10-01T23:59:36.167

8 How do I prove that the Hadamard satisfies $H\equiv e^{i\pi H/2}$? 2019-10-22T21:42:34.990

8 Can arbitrary matrices be decomposed using the Pauli basis? 2019-11-09T12:43:20.377

8 How to check if a quantum circuit can be constructed for a given matrix representation? 2021-02-02T20:10:28.237

7 What does it mean for a density matrix to "act on a Hilbert space $\mathcal{H}"$? 2018-06-20T11:30:53.763

7 How do you represent the output of a quantum gate in terms of its basis vectors? 2018-07-29T00:53:45.717

7 Is there a general method to implement a 'greater than' quantum circuit? 2018-10-05T11:03:34.360

7 What role do Hecke operators and ideal classes perform in “Quantum Money from Modular Forms?” 2019-03-08T03:40:30.527

7 Why is the probability vector of a uniformly random state $\sum_i\alpha_i|i\rangle$ uniformly random only if $\alpha_i\in\mathbb C$? 2019-11-09T15:22:30.170

7 Why does representation theory often arise in the context of quantum algorithms for the hidden subgroup problem? 2019-11-23T18:36:43.253

7 What is the probability $\Pr(||U-I||_{op}<\varepsilon)$ of a Haar-random unitary being close to the identity? 2020-08-12T19:51:12.293

7 what matrix operations have better known time complexity on a quantum computer? 2021-02-04T10:48:09.883

6 What kind of mathematics is common in quantum computing? 2018-07-15T06:15:47.523

6 When would I consider using an outer product of quantum states, to describe aspects of a quantum algorithm? 2018-10-02T16:34:45.597

6 In Bell nonlocality, why does $P(ab|xy)\neq P(a|x)P(b|y)$ mean the variables are not statistically independent? 2018-11-14T06:44:34.750

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 Problem with the mathematical formulation of "qubitization" 2018-12-11T12:58:02.273

6 General parametrisation of an arbitrary $2\times 2$ unitary matrix? 2019-01-14T08:32:50.917

6 How to translate matrix back into Dirac notation? 2019-01-22T22:53:54.743

6 Hidden shift problem as a benchmarking function 2019-04-04T04:36:47.230

6 Encoding bosonic degrees of freedom 2019-04-23T16:27:16.803

6 Prove that $\|p^{\otimes n} - q^{\otimes n}\| \leq n \|p-q\|$ for density operators $p,q$ 2019-10-27T19:00:37.650

6 Changing qubits coefficients to trigonometric functions in Grover Algorithm 2020-02-24T18:57:04.223

6 Is it right to think of superposition as just angle? 2020-05-08T15:04:48.437

6 What are boost and shift operators and why are they called so? 2020-06-08T13:10:53.070

6 Is the Haar measure invariant under conjugation? 2020-09-06T00:18:31.727

6 Bob applies a projector - what happens to eigenvalues of Alice's reduced state? 2020-10-20T02:17:47.967

5 Generating algebra from commutation 2018-06-19T10:58:31.203

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

5 What are the standard eigenvalues in $\mathbb{C^2}\otimes\mathbb{C^2}$? 2018-06-29T14:15:00.067

5 Can we process infinite matrices with a quantum computer? 2018-08-17T15:32:26.547

5 Definition of locality in Bell experiments 2018-11-15T07:05:23.733

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 Ways in which $\frac{1}{\sqrt 2} (|00\rangle + |11\rangle)$ can be expressed as $\frac{1}{\sqrt 2} (|uu\rangle + |vv\rangle)$ 2018-12-21T12:46:17.597

5 Is the set of classical-quantum states convex? 2018-12-27T22:13:23.120

5 Extending a square matrix to a unitary matrix 2019-01-10T10:26:05.743

5 What are the constraints on a matrix that allow it to be "extended" into a unitary? 2019-01-10T12:22:28.853

5 Quantum proof for the group non-membership problem 2019-01-23T12:24:28.613

5 How is Grover's operator represented as a rotation matrix? 2019-01-28T15:26:20.137

5 How to understand the operators for watermarking schemes? 2019-03-19T16:54:52.957

5 Quantum teleportation of a state, from one of two bases 2019-03-27T01:47:09.047

5 How to show a density matrix is in a pure/mixed state? 2019-04-22T05:29:18.183

5 What is the HOG test and how would it help proving quantum supremacy? 2019-05-23T00:13:09.367

5 Understanding a quantum algorithm to estimate inner products 2019-06-05T00:30:29.103

5 Clarification of a procedure to compute the product of the exponential of two matrices 2019-06-06T02:50:20.413

5 What is the motivation for Weyl matrices in quantum information theory? 2019-06-14T06:14:19.340

5 Equivalent determinant condition for Peres-Horodecki criteria 2019-06-15T05:45:04.067

5 Motivation for the definition of k-distillability 2019-06-18T13:44:28.427

5 Finding a global phase that transform the Hadamard gate to an element of $SU(2)$ and propose an evoultion operator which implents the operation 2019-07-18T23:17:31.373

5 How to check if a two-qubit gate is entangling? 2019-10-19T21:22:40.797

5 Why are $d^2$ dimensions required to describe a density matrix? 2019-12-06T15:06:15.037

5 Do states with the same purity always have the same rank? 2019-12-10T22:44:50.530

5 Why does quantum computing generally use Heisenberg's Matrix Mechanics instead of Schrödinger's Wave Mechanics? 2019-12-23T02:57:51.917

5 Diagrammatic Quantum Reasoning: Proving the loop equation using yanking equations 2019-12-29T11:23:24.360

5 Is Connes' Embedding Problem akin the word problem for finitely presented groups? 2020-02-07T21:33:44.053

5 In Dirac notation, why do we have $\langle cf|g\rangle = c^*\langle f\vert g\rangle$? 2020-02-08T21:58:29.420

5 Represent a pure state in terms of 2 antipodal points on the Bloch sphere 2020-04-06T19:10:06.370

5 How is the ground state of a Hamiltonian defined? 2020-04-13T22:18:23.327

5 Prove that for one-qubit unitaries $\text{Tr}|U-V|=2\max_\psi\|(U-V)|\psi\rangle\|$ 2020-05-04T00:25:25.527

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 Derivation of the identity $\sum_j p_j \langle \psi_j|M|\psi_j \rangle = \sum_j p_j \operatorname{tr}\left(|\psi_j \rangle \langle \psi_j|M\right)$ 2021-01-28T15:51:52.357

5 Why is the transpose of a density matrix positive and trace preserving? 2021-02-08T19:50:58.767

4 What can I deduce about $f(x)$ if $f$ is balanced or constant? 2018-04-22T15:26:58.737

4 Projection operator on Time evolution Operator 2018-06-30T22:51:32.637

4 Simple proof that $(U \otimes V)(|x\rangle \otimes |y\rangle) = U|x\rangle \otimes V|y\rangle$? 2018-10-21T18:54:45.687

4 Determining whether $P(ab|xy)$ factorizes in Bell experiments 2018-11-21T19:35:37.000

4 Can vectorization lead to mixed states? 2018-12-02T20:26:33.073

4 Why does $x\sqrt{1-x^2}$ enhance the ability to approximate analytical functions in quantum circuit learning? 2019-02-08T14:36:24.967

4 For 2x2 and 2x3 systems, is the partial transpose the only positive but not CP operation? 2019-02-18T13:15:38.507

4 Differentiate between local and global unitaries 2019-03-01T07:03:38.450

4 Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere 2019-03-02T23:39:45.080

4 How does $x^{\frac{r}{2}} \equiv -1 \pmod {p_i^{a_i}}$ follow from "if all these powers of $2$ agree"? 2019-03-04T14:38:25.600

4 POVM three-qubit circuit for symmetric quantum states 2019-03-04T15:09:16.007

4 How to measure superposition coefficients to determine state? 2019-03-13T22:12:39.377

4 Meaning of "diagonal to the computational basis" 2019-03-20T02:13:07.107

4 Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states? 2019-04-06T16:40:35.753

4 Burnside Decomposition in Kuperberg's Hidden Shift 2019-04-15T13:33:24.393

4 Structural Physical Approximation of Partial Transpose 2019-05-21T09:45:51.753

4 How are arbitrary $2\times 2$ matrices decomposed in the Pauli basis? 2019-07-28T15:12:03.840

4 Extensions of product states 2019-09-11T21:23:06.540

4 How to show whether two states are indistinguishable or not by measuring in a different basis? 2019-09-21T22:01:49.353

4 History of anyon theory, braidings and tensor categories 2019-10-09T13:19:27.167

4 How to split a 2-local unitary operator through singular value decomposition? 2019-10-15T11:13:06.000

4 Proving $\langle j_2|\langle j_1| U(|0\rangle\!\langle0|\otimes\rho)U^\dagger|j_2\rangle|j_1\rangle =\operatorname{Tr}(M_j\rho)$ 2019-10-17T14:32:06.973

4 Matrix Index and multiplication rules for Hermitian Pauli group products 2019-10-20T11:58:22.907

4 Prove that the state $\sum_{S\in P_n}(-)^{\tau(S)}|S\rangle$ is invariant up to a phase when changing the basis 2019-11-28T05:29:26.923

4 How's quantum noise and fault-tolerance related to symplectic geometry and geometric quantization? 2019-12-04T13:52:05.150

4 Proof that most Hamiltonian evolutions are not efficiently approximable by quantum circuits 2019-12-22T09:48:19.233