{"id":1529,"date":"2026-10-19T11:39:00","date_gmt":"2026-10-19T11:39:00","guid":{"rendered":"https:\/\/www.interviewbit.com\/varsity\/blog\/?p=1529"},"modified":"2026-10-19T11:39:04","modified_gmt":"2026-10-19T11:39:04","slug":"quantum-walk","status":"publish","type":"post","link":"https:\/\/www.interviewbit.com\/varsity\/blog\/quantum-walk\/","title":{"rendered":"Quantum Walks Explained: The Future of Search Algorithms"},"content":{"rendered":"\n<div class=\"wp-block-group vlf-insights is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"vlf-insights-title wp-block-paragraph\">Key Insights<\/p>\n\n\n\n<ul class=\"wp-block-list vlf-insights-list\">\n\n<li>Quantum walks are quantum analogues of classical random walks, using superposition and interference rather than classical transition probabilities.<\/li>\n\n\n<li>Discrete-time quantum walks use coin and shift operations, while continuous-time quantum walks evolve through a Hamiltonian.<\/li>\n\n\n<li>Quantum interference can improve search efficiency for certain problems, but the advantage depends on the algorithm and problem structure.<\/li>\n\n\n<li>Quantum-walk algorithms can solve the element-distinctness problem using <img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\"> queries, compared with a classical randomized query lower bound of <img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"\"> in the standard model.<\/li>\n\n\n<li>Quantum walks and Grover&rsquo;s algorithm offer different approaches to quantum search; neither guarantees an advantage for every search problem or practical implementation.<\/li>\n\n\n<li>Qiskit can be used to construct and inspect quantum circuits, but a simple coin-and-position circuit is only a demonstration, not a complete multi-step quantum walk.<\/li>\n\n\n<li>Noise, circuit depth and hardware connectivity can limit the performance of quantum-walk implementations on current quantum devices.<\/li>\n\n<\/ul>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum walks are the quantum mechanical analogues of classical random walks, in which a particle or &ldquo;walker&rdquo; explores a graph, lattice or network using quantum superposition and interference rather than classical transition probabilities. Unlike a classical walker, whose movement follows probabilistic rules, a quantum walker evolves through probability amplitudes that can interfere with one another. This difference enables quantum-walk algorithms to solve certain search and graph problems with fewer queries than classical approaches.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This article explores how quantum walks work, the differences between discrete-time and continuous-time models, and how quantum interference can support faster search algorithms. It also examines applications such as graph search and element distinctness, demonstrates a simple quantum circuit using Qiskit, and discusses the limitations of implementing quantum walks on current quantum hardware.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Is a Classical Random Walk, and How Is a Quantum Walk Different?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Classical and quantum random walks describe movement through possible positions, but they use different mathematical rules.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1774\" height=\"887\" src=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro.png\" alt=\"Comparison of classical random walks based on transition probabilities and quantum walks based on superposition and interference.\" class=\"wp-image-1531\" srcset=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro.png 1774w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro-300x150.png 300w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro-1024x512.png 1024w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro-768x384.png 768w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-classical-random-walks-based-on-transition-pro-1536x768.png 1536w\" sizes=\"auto, (max-width: 1774px) 100vw, 1774px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">How a Classical Random Walk Works<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine a walker moving left or right along a line. At each step, it chooses a direction according to a probability rule. On a graph, vertices represent positions and edges represent possible moves. As the walk continues, its probability distribution spreads across reachable positions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What Changes in a Quantum Walk?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In a quantum walk, the walker is represented by a quantum state. Multiple positions can have amplitudes in a superposition, and these amplitudes can interfere constructively or destructively. Measurement then produces a position according to the resulting probabilities.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The difference is not simply that a quantum walker can represent multiple positions at once. The phases and amplitudes associated with different paths also affect the final distribution. This interference is central to quantum walks in quantum computing.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Are Discrete-Time and Continuous-Time Quantum Walks?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The two main models differ in how they evolve the quantum state: discrete-time quantum walks use successive operations, while continuous-time quantum walks evolve according to a Hamiltonian.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1774\" height=\"887\" src=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and.png\" alt=\"Comparison of discrete-time coin-and-shift quantum walks and continuous-time quantum walks on a graph.\" class=\"wp-image-1532\" srcset=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and.png 1774w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and-300x150.png 300w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and-1024x512.png 1024w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and-768x384.png 768w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/comparison-of-discrete-time-coin-and-shift-quantum-walks-and-1536x768.png 1536w\" sizes=\"auto, (max-width: 1774px) 100vw, 1774px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Discrete-Time Quantum Walk: Coin + Shift<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A discrete-time quantum walk typically uses two components:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Coin operation:<\/strong> Determines a superposition of possible movement directions, often using a Hadamard gate.<\/li><li><strong>Shift operation:<\/strong> Moves the walker according to the coin state.<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For a one-dimensional line, the coin and position registers work together. Repeated coin-and-shift operations allow different paths to interfere. This model is often called a coined quantum walk because it uses an additional coin degree of freedom to control movement.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Continuous-Time Quantum Walk<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A continuous-time quantum walk does not require a separate coin operation in its standard formulation. Instead, a Hamiltonian determines how the state evolves over time. The graph&rsquo;s structure can be encoded using a matrix such as its adjacency matrix or graph Laplacian.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Unlike the discrete-time model, which applies operations in steps, the continuous-time model evolves continuously. Both approaches can be useful, depending on the graph and algorithm being studied.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">How Do Quantum Walks Enable Faster Search Algorithms?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum-walk algorithms can offer quadratic or other speed-ups for specific problems, but they do not make every search faster. Their performance depends on the problem structure, algorithm and computational model.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The Role of Quantum Interference<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">As a quantum walk evolves, different paths contribute amplitudes to the same position. Constructive interference increases an amplitude, while destructive interference reduces it. A carefully designed algorithm can use these effects to increase the probability of measuring a useful target state.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is the key idea behind quantum-walk search: the evolution is designed to exploit the structure of the search space rather than simply sample positions randomly.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">How Quantum Walks Relate to Grover&rsquo;s Search<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Grover&rsquo;s algorithm provides a quadratic speed-up for unstructured search, requiring approximately O(&radic;N) oracle queries compared with O(N) for classical exhaustive search in the standard comparison.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum-walk search algorithms instead use dynamics over a state space or graph. They can offer advantages for certain structured problems, but they do not automatically outperform Grover&rsquo;s algorithm. The graph, oracle costs and implementation requirements all matter.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Are the Applications of Quantum Walks?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum walks support research into search, graph algorithms and problems where relationships between possible states are important.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Search Algorithms<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A quantum-walk search algorithm can represent candidate states as vertices and use the walk&rsquo;s evolution to increase the probability of finding a target. These methods are related to Grover&rsquo;s search but are not identical; their advantages depend on the structure of the problem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Graph Problems and Network Analysis<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In a quantum walk on a graph, vertices represent possible positions and edges represent allowed transitions or interactions. Researchers study these models for graph traversal, connectivity-related problems and network analysis. Practical advantages depend on the graph, the algorithm and the computational resources required.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Element Distinctness<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The element distinctness problem asks whether a list of N elements contains a duplicate. A well-known quantum-walk algorithm solves this problem using O(N^(2\/3)) queries, matching a lower bound of &Omega;(N) for classical randomized algorithms in the standard query model. These are query-complexity results, not guarantees of equivalent speed-ups on physical hardware.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>How Do You Simulate a Quantum Walk Using Qiskit?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Qiskit can model a small quantum circuit using a coin qubit, a position register and gates that implement conditional movement. A simple example illustrates the basic mechanics, although it is not a complete multi-step walk.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Build a Simple Circuit for a One-Dimensional Walk<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The following two-qubit example prepares a coin superposition and conditionally flips a position qubit:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>from qiskit import QuantumCircuit\nqc = QuantumCircuit(2, 2)\ncoin = 0\nposition = 1\nqc.h(coin)                 # Create coin superposition\nqc.cx(coin, position)      # Conditional position flip\nqc.measure([0, 1], [0, 1])\nprint(qc.draw())<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate creates a superposition of coin states, while the CNOT gate conditionally flips the position qubit. Measurement returns classical samples of the final states.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is a toy example of coin-controlled movement, not a complete general-purpose quantum walk on a line. A multi-step implementation needs a suitable position encoding, repeated coin-and-shift operations and explicit boundary conditions. The<a href=\"https:\/\/qiskit.qotlabs.org\/docs\/api\/qiskit\/qiskit.circuit.QuantumCircuit\"> <\/a><a href=\"https:\/\/qiskit.qotlabs.org\/docs\/api\/qiskit\/qiskit.circuit.QuantumCircuit\">official Qiskit Quantum Circuit documentation<\/a> explains the circuit methods used here.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What Should You Observe in the Simulation?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Run the circuit repeatedly and inspect its measurement counts. The two correlated outcomes should occur with approximately equal probabilities in an ideal simulation. To explore a genuine multi-step quantum walk, extend the circuit with a correctly designed shift operation and compare how its position distribution changes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Are the Limitations of Quantum Walks on NISQ Hardware?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Theoretical speed-ups do not automatically translate into practical advantages on noisy intermediate-scale quantum (NISQ) devices. Quantum walks can require repeated gates, conditional operations and precise interference, all of which can be affected by hardware limitations.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Noise, Circuit Depth and Connectivity<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Gate errors can distort amplitudes and measurement probabilities, while deeper circuits create more opportunities for errors to accumulate. Graph-specific operations may also require many gates, and limited qubit connectivity can introduce additional routing operations.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">When Is a Quantum Walk Useful in Practice?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Evaluate whether the problem maps naturally to a graph, whether a proven algorithmic advantage exists, and whether the circuit fits the available hardware constraints. Compare its performance with a relevant classical baseline before claiming a practical benefit.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum walks offer a framework for understanding how quantum interference can support search and graph algorithms. However, these advantages depend on the problem and do not guarantee better performance on current quantum hardware. Learning to model and simulate quantum walks provides a foundation for exploring these techniques further.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To build on these concepts, the <strong><a href=\"https:\/\/www.interviewbit.com\/varsity\/iit-delhi\/quantum-computing\">Applied Quantum Computing &amp; AI programme by IIT Delhi<\/a>.<\/strong>, delivered through Varsity by InterviewBit, offers structured learning in quantum computing, algorithms and circuit design, helping learners progress from foundational concepts to more advanced applications.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">FAQs About Quantum Walks<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Is a quantum walk the same as a quantum random walk?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The terms are often used interchangeably. Quantum walk is commonly used for the broader family of quantum analogues of classical random walks.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Who introduced the concept of quantum walks?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Quantum walks developed through multiple research contributions. Discrete-time and continuous-time models emerged through distinct lines of work, so the field is not attributable to a single researcher.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Does a quantum walk require entanglement?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Not universally. Entanglement can arise in multi-qubit implementations, but whether it is required depends on the walk model and algorithm.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is a coined quantum walk?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">It is a discrete-time quantum walk that uses an additional coin degree of freedom to determine movement between positions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is a quantum walk on a graph?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">It is a walk in which graph vertices represent possible positions and edges define allowed transitions or interactions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Can quantum walks be used for network routing?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">They can be studied for graph search, connectivity and network-structure problems. Practical routing advantages depend on the algorithm and implementation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is the difference between quantum-walk search and Grover&rsquo;s algorithm?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Grover&rsquo;s algorithm addresses unstructured search, while quantum-walk algorithms can exploit the structure of a graph or state space. Neither approach is universally superior.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is the element distinctness problem in quantum computing?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">It asks whether any two entries in a list are equal. It is a prominent example of a problem for which quantum-walk techniques offer a query-complexity advantage.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Can quantum walks be simulated on a classical computer?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Small quantum walks can be simulated classically, although the resources needed to represent and evolve quantum states can increase rapidly with system size.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What should I learn before implementing quantum walks?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Build familiarity with qubits, superposition, quantum gates, measurement, basic graph theory and Python. Then progress to quantum circuits and algorithmic complexity.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Resources<\/h2>\n\n\n\n<ol class=\"wp-block-list\"><li><a href=\"https:\/\/qiskit.qotlabs.org\/docs\/api\/qiskit\/circuit\">IBM Quantum Documentation &mdash; Quantum Circuit Model<\/a><\/li><li><a href=\"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539705447311\">Ambainis &mdash; Quantum Walk Algorithm for Element Distinctness<\/a><\/li><li><a href=\"https:\/\/qiskit.qotlabs.org\/docs\/api\/qiskit\/qiskit.circuit.QuantumCircuit\">IBM Quantum Documentation &mdash; QuantumCircuit<\/a><\/li><li><a href=\"https:\/\/quantum.cloud.ibm.com\/docs\/en\/guides\/measure-qubits\">IBM Quantum Documentation &mdash; Measure Qubits<\/a><\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Key Insights Quantum walks are the quantum mechanical analogues of classical random walks, in which a particle or &ldquo;walker&rdquo; explores a graph, lattice or network using quantum superposition and interference rather than classical transition probabilities. Unlike a classical walker, whose movement follows probabilistic rules, a quantum walker evolves through probability amplitudes that can interfere with [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":1562,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1529","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantum-computing"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":8}},"acf":{"reviewed_by":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Quantum Walks Explained: Algorithms, Applications and Qiskit<\/title>\n<meta name=\"description\" content=\"Learn how quantum walks work, explore discrete-time and continuous-time models, 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