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description= 30 interview questions for quantum computing roles at IBM, Google, IonQ, and more. Covers fundamentals, algorithms, error correction, and Qiskit coding.;
author= QuantumComputingCourses.com;
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Text of the page (random words):
ate ansatz ψ θ and measures the expectation value of the hamiltonian which is decomposed into a sum of pauli operators that can each be measured directly a classical optimiser gradient descent cobyla spsa then updates the parameters θ to reduce the energy estimate the classical optimiser is necessary because finding the optimal circuit parameters is itself an optimisation problem with a complex landscape quantum hardware cannot intrinsically search this space it can only evaluate a single objective value at one set of parameters per circuit execution the hybrid approach offloads the optimisation loop to classical computers keeping quantum circuits shallow enough to run on nisq hardware q17 what is the difference between bqp and np can quantum computers solve np complete problems bqp bounded error quantum polynomial time is the class of decision problems solvable by a quantum computer in polynomial time with error probability at most 1 3 np is the class of problems whose solutions can be verified in polynomial time classically and np complete problems are the hardest problems in np whether p np is the most famous open question in computer science it is widely believed that bqp does not contain all of np while bqp contains some problems outside p like integer factoring which is in bqp but believed to be outside p np complete problems like 3 sat or the travelling salesman problem are not known to be in bqp grover s algorithm gives a quadratic speedup for brute force search but an np complete problem with n 2ⁿ states would still require o 2 n 2 quantum steps still exponential the relationship is p bqp pspace and np is believed to partially overlap with bqp but not be contained in it quantum computers are likely not a silver bullet for np hardness the complexity theoretic evidence suggests the exponential wall is not entirely removed by quantum computation q18 what is quantum simulation and why is it considered one of the most promising near term applications quantum simulation means using a controllable quantum device to mimic the behaviour of another less controllable quantum system the core insight attributed to feynman is that simulating quantum systems classically is generically exponentially hard the state of n interacting particles requires 2ⁿ complex amplitudes a quantum computer with n qubits can naturally represent and evolve this state applications span quantum chemistry computing molecular ground state energies to predict reaction rates and drug behaviour condensed matter physics understanding high temperature superconductors topological materials and materials science designing new battery cathodes or catalysts quantum simulation is considered near term promising because the required circuits are shallower than for full fault tolerant algorithms like shor s molecules of pharmaceutical relevance involve 50 to 200 electrons a scale where even trotterised hamiltonian simulation may become tractable on early fault tolerant machines both vqe and qpe target this application companies like quantinuum ibm and google already demonstrate quantum chemistry simulations on small molecules and the trajectory suggests this will be one of the first areas where quantum computers deliver genuine value 03 error correction and hardware 7 questions open one to read the full answer q19 what is a logical qubit and how does it differ from a physical qubit a physical qubit is an actual hardware qubit a superconducting transmon a trapped ion a spin in silicon etc subject to real noise decoherence and gate errors a logical qubit is an error protected quantum bit encoded across many physical qubits using a quantum error correcting code the logical qubit behaves as a reliable long lived qubit even as individual physical qubits experience errors the encoding works because quantum error correction can detect and fix errors without measuring and thus collapsing the logical state instead it measures stabilisers multi qubit observables that commute with the logical operators but anticommute with error operators to identify where errors occurred without learning the logical information the overhead is significant current estimates suggest 1000 to 10000 physical qubits per logical qubit for codes like the surface code at practically useful error rates depending on the physical error rate a useful fault tolerant algorithm like shor s algorithm on a 2048 bit key requires roughly 4000 logical qubits implying millions of physical qubits this is why the gap between today s noisy hardware and practically useful quantum computation remains large q20 explain the surface code at a high level the surface code is the leading quantum error correcting code for superconducting and similar qubit architectures physical qubits are arranged on a 2d square lattice with data qubits at the vertices and ancilla measurement qubits between them the code encodes one logical qubit across d x d data qubits where d is the code distance the key feature is locality all stabiliser measurements which detect errors involve only nearest neighbour qubits this is crucial for hardware implementation because long range interactions are hard to engineer reliably the stabilisers are products of pauli x and z operators on 2x2 plaquettes by measuring these regularly any single qubit error manifests as a pair of defects violated stabilisers that can be matched and corrected classically using algorithms like minimum weight perfect matching the surface code s threshold error rate below which increasing d reduces logical error rates is approximately 1 which is achievable with current hardware the tradeoff is high physical qubit overhead a distance d code needs roughly 2d² physical qubits for one logical qubit google s 2024 below threshold experiment on its willow processor published in nature was a landmark demonstration of the surface code working as theory predicts q21 what is the quantum error correction threshold theorem the threshold theorem states that if the physical error rate per gate is below a critical threshold value then arbitrarily long quantum computations can be performed with arbitrarily small logical error rate at the cost of polynomial overhead in physical resources the intuition is that error correcting codes can correct errors faster than errors accumulate provided errors are rare enough below the threshold adding more physical qubits increasing the code distance reduces the logical error rate exponentially above the threshold adding more qubits makes things worse because you introduce more errors than you correct the threshold value depends on the code the error model and the correction strategy for the surface code with depolarising noise the threshold is roughly 0 5 to 1 error per gate different codes have different thresholds concatenated codes often have lower thresholds but are more hardware intensive the theorem is foundational because it proves that scalable quantum computing is physically possible in principle it would be impossible if errors always compounded without correction in practice reaching threshold is the primary target for current quantum hardware efforts q22 what are t1 and t2 times and why do they matter t1 energy relaxation time measures how long it takes a qubit excited to 1 to spontaneously decay back to 0 it is an amplitude damping process driven by energy loss to the environment if t1 is short any qubit will probabilistically flip to 0 during a circuit t2 dephasing time or coherence time measures how long a qubit in a superposition state 0 1 2 maintains its phase before the relative phase between 0 and 1 randomises t2 is always less than or equal to 2 t1 due to the contributions of both energy relaxation and pure dephasing pure dephasing t2 is typically limited by low frequency flux noise or charge noise rather than energy loss these times set hard limits on circuit depth a rough rule of thumb is that you can execute on the order of t2 gate time gates before dephasing causes significant errors for superconducting qubits with t2 200 microseconds and gate times 50 nanoseconds that is about 4000 gate operations per qubit improving t1 and t2 is a central goal of hardware research since longer coherence times translate directly into deeper circuits and more complex algorithms q23 what is gate fidelity and how is it measured gate fidelity measures how closely a physical quantum gate implementation matches the ideal unitary operation a fidelity of 1 0 means the gate is perfect a fidelity of 0 99 means a 1 error rate per gate formally the average gate fidelity is the average overlap between the ideal output and the actual output averaged over a uniform distribution of input states the standard measurement technique is randomised benchmarking rb in rb you apply sequences of random clifford gates of increasing length followed by their inverse which should ideally return the qubit to 0 the probability of returning to 0 decays exponentially with sequence length and the decay rate directly gives the error per clifford gate this technique is robust to state preparation and measurement spam errors which would otherwise contaminate direct fidelity measurements process tomography is a more complete characterisation it reconstructs the full quantum process matrix but requires resources that grow exponentially with the number of qubits and is only practical for one or two qubits interleaved randomised benchmarking extends rb to characterise a specific gate by interleaving it with random cliffords current two qubit gate fidelities are around 99 0 to 99 9 for leading superconducting and trapped ion systems q24 name three different physical implementations of qubits and one advantage of each superconducting qubits used by ibm google are built from josephson junctions cooled to near absolute zero where certain circuits exhibit quantised energy levels that act as qubits their key advantage is fast gate times single qubit gates in tens of nanoseconds and two qubit gates around 100 500 nanoseconds and compatibility with microwave control electronics that leverage existing semiconductor industry know how they also scale more straightforwardly on a chip trapped ion qubits used by ionq quantinuum use individual atomic ions suspended in an electromagnetic trap with qubit states encoded in two internal electronic energy levels their main advantage is high gate fidelity and long coherence times two qubit gate fidelities above 99 9 have been demonstrated and ions can remain coherent for minutes to hours all to all connectivity within a trap is also easier than in superconducting architectures photonic qubits encode quantum information in the polarisation or path of individual photons their key advantage is room temperature operation and natural compatibility with fibre optic quantum communication photons do not decohere from thermal noise and can travel long distances making them ideal for quantum networking and some measurement based computing architectures q25 what is nisq and what are its limitations nisq stands for noisy intermediate scale quantum the term coined by john preskill in 2018 describes the class of quantum devices that are available now and in the near term machines with 50 to a few thousand physical qubits that are not fully error corrected they are intermediate scale because they are too large to simulate classically for all purposes but too noisy and too small to run the fault tolerant algorithms that would provide unambiguous quantum advantage the limitations are fundamental not just engineering shortcomings without error correction errors accumulate with circuit depth limiting the useful computation to shallow circuits coherence times constrain how long a circuit can run crosstalk between qubits introduces correlated errors that are hard to model or correct the number of qubits limits problem size vqe and qaoa were designed specifically for nisq devices by keeping circuits shallow but even these algorithms face the barren plateau problem gradients vanishing exponentially with system size making classical optimisation hard and there is no rigorous proof they outperform classical methods on any practical problem the consensus is that nisq devices are important for research and benchmarking but transformative practical applications will require fault tolerant hardware 04 frameworks and coding 5 questions open one to read the full answer q26 what is the difference between qiskit and pennylane when would you choose one over the other qiskit is ibm s open source quantum computing framework its primary abstraction is the quantum circuit you construct a circuit potentially transpile it to a target backend and execute it either on a simulator or ibm hardware via ibm quantum qiskit has deep integration with ibm hardware and the largest ecosystem of tutorials textbook content and community support it includes tools for circuit optimisation transpilation noise simulation and error mitigation pennylane developed by xanadu is built around the concept of differentiable quantum computing its central contribution is automatic differentiation of quantum circuits it computes gradients of quantum expectation values with respect to circuit parameters using parameter shift rules or backpropagation making it directly compatible with pytorch and jax this makes pennylane the natural choice for quantum machine learning research and variational algorithms where gradient based optimisation is used choose qiskit when your goal is circuit level control ibm hardware access or learning quantum computing fundamentals with maximum community resources choose pennylane when you are doing quantum machine learning hybrid classical quantum gradient descent or want to target multiple hardware backends it supports qiskit cirq and others as backends from one interface q27 write a simple quantum circuit that creates a bell state show code in qiskit a bell state is the maximally entangled two qubit state 00 11 2 you create it with two gates a hadamard on the first qubit creating superposition followed by a cnot with the first qubit as control and the second as target entangling them here is the qiskit implementation from qiskit import quantumcircuit from qiskit_aer import aersimulator from qiskit primitives import statevectorsampler build the circuit qc quantumcircuit 2 2 qc h 0 hadamard on qubit 0 creates 0 1 superposition qc cx 0 1 cnot qubit 1 flips when qubit 0 is 1 qc measure 0 1 0 1 print qc draw simulate and sample sim aersimulator result sim run qc shots 1024 result print result get_counts expected 00 512 11 512 never 01 or 10 the result will show only 00 and 11 outcomes in roughly equal measure never 01 or 10 that is the signature of entanglement the two qubits are correlated even though each appears random individually the hadamard gate creates the superposition and the cnot gates creates the correlation neither gate alone creates entanglement q28 what is a parameterised quantum c...
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