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I Glossary AbstractionsâDifferent models (a representation or way of thinking) about a computer system design that allow the user to focus on the critical aspects of the system components to be designed. Adiabatic quantum computerâAn idealized analog universal quantum computer that operates at 0 K (absolute zero). It is known to have the same computational power as a gate-based quantum computer. AlgorithmâA specific approach, often described in mathematical terms, used by a computer to solve a certain problem or carry out a certain task. Analog computerâA computer whose operation is based on analog signals and that does not use Boolean logic operations and does not reject noise. Analog quantum computerâA quantum computer that carries out a computation without breaking the operations down to a small set of primitive operations (gates) on qubits; there is currently no model of fault tolerance for such machines. Analog signalâA signal whose value varies smoothly between a range of real or complex numbers. Asymmetric cryptography (also public key cryptography)âA category of cryptography where the system uses public keys that are widely known and private keys that are secret to the owner; such systems are commonly used for key exchange protocols in the encryption of most of todayâs electronic communications. BasisâAny set of linearly independent vectors that span their vector space. The wave function of a qubit or system of qubits is commonly written as a linear combination of basis functions or states. For a single qubit, the most common basis is { |0 , |1 }, corresponding to the states of a classical bit. Binary representationâA series of binary digits where each digit has only two possible values, 0 or 1, used to encode data and upon which machine-level computations are performed. Certificate authorityâAn entity that issues a digital certificate to certify the ownership of a public key used in online transactions. CipherâAn approach to concealing the meaning of information by encoding it. CiphertextâThe encrypted form of a message, which appears scrambled or nonsensical. Classical attacksâAttempts by a classical computer to break or subvert encryption. Classical computerâA computerâfor example, one of the many deployed commercially todayâwhose processing of information is not based upon quantum information theory. PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-1

Coding theoryâThe science of designing encoding schemes for specific applicationsâfor example, to enable two parties to communicate over a noisy channel. CoherentâThe quality of a quantum system that enables quantum phenomena such as interference, superposition, and entanglement. Mathematically speaking, a quantum system is coherent when the complex coefficients of the contributing quantum states are clearly defined in relation to each other, and the system can be expressed in terms of a single wave function. CollapseâThe phenomenon that occurs upon measurement of a quantum system where the system reverts to a single observable state, resulting in the loss of contributions from all other states to the systemâs wave function. CollisionâIn hashing, the circumstance where two different inputs are mapped to the same output, or hash value. Complexity classâA category that is used to define and group computational tasks according to their complexity. Computational complexityâThe difficulty of carrying out a specific computational task, typically expressed as a mathematical expression that reflects how the number of steps required to complete the task varies with the size of the input to the problem. Compute depthâThe number of sequential operations required to carry out a given task. ConcatenationâThe ordered combination of two sequences in order. In the context of quantum error correction (QEC), this refers to carrying out two or more QEC protocols sequentially. Control and measurement planeâAn abstraction used to describe components of a quantum computer, which refers to the elements required to carry out operations on qubits and to measure their states. Control processor planeâAn abstraction used to describe components of a quantum computer, which includes the classical processor responsible for determining what signals and measurements are required to implement a quantum program. CryostatâA device that regulates the temperature of a physical system at very low temperatures, generally in an experimental laboratory. CryptanalysisâThe use of a computer to defeat encryption. CryptographyâThe study and practice of encoding information in order to obfuscate its content that relies upon the difficulty of solving certain mathematical problems. CryptosystemâA method of deploying a specific cryptographic algorithm to protect data and communications from being read by an unintended recipient. DecoherenceâA process where a quantum system will ultimately exchange some energy and information with the broader environment over time, which cannot be recovered once lost. This process is one source of error in qubit systems. Mathematically speaking, decoherence occurs when the relationship between the coefficients of a quantum systemâs contributing states become ill-defined. PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-2

Decryption algorithmâA set of instructions for returning an encrypted message to its unencrypted form. Such an algorithm takes as input a cipher text and its encryption key, and returns a cleartext, or readable, version of the message. Digital gatesâA transistor circuit that performs a binary operation using a number of binary single bit inputs to create a single-bit binary output. Digital quantum computersâQuantum systems where the computation is done by using a small set of primitive operations, or gates, on qubits. Digital signatureâAn important cryptographic mechanism used to verify data integrity. Dilution refrigeratorâA specialized cooling device capable of maintaining an apparatus at temperatures near absolute zero. Discrete-log problem on elliptic curvesâAn algebraic problem used as the basis of a specific cryptographic protocol where, given the output, it is computationally hard to compute the inputs. DistanceâIn an error-correcting code, the number of bit errors that would be required to convert one valid state of a computer to another. When the number of errors is less than (Dâ1)/2, one can still extract the error-free state. EncryptionâThe application of cryptography to protect information, currently widely used in computer systems and Internet communications. Encryption algorithmâA set of instructions for converting understandable data to an incomprehensible cipher, or ciphertext. In practice, the algorithm takes as input the message to be encrypted along with an encryption key and scrambles the message according to a mathematical procedure. EntanglementâThe property where two or more quantum objects in a system are correlated, or intrinsically linked, such that measurement of one changes the possible measurement outcomes for another, regardless of how far apart the two objects are. Error-corrected quantum computerâAn instance of a quantum computer that emulates an ideal, fault- tolerant computer by running a quantum error correction algorithm. Fault tolerantâResilient against errors. FidelityâThe quality of a hardware operation, sometimes quantified in terms of the probability that a particular operation will be carried out correctly. Fundamental noiseâNoise resulting from energy fluctuations arising spontaneously within any object that is above absolute zero in temperature. GateâA computational operation that takes in and puts out one or more bits (in the case of a classical computer) or qubits (in the case of a quantum computer). Gate synthesisâConstruction of a gate out of a series of simpler gates. HamiltonianâA mathematical representation of the energy environment of a physical system. In the mathematics of quantum mechanics, a Hamiltonian takes the form of a linear algebraic operator. PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-3

Sometimes, the term is used to denote the physical environment itself, rather than its mathematical representation. Host processorâAn abstraction used to describe the components of a quantum computing system, referring to the classical computer components driving the part of the system that is user controlled. Key exchangeâA step in cryptographic algorithms and protocols where keys are shared among intended recipients to enable their use in encrypting and decrypting information. Logical qubitâAn abstraction that describes a collection of physical qubits implementing quantum error correction in order to carry out a fault-tolerant qubit operation. Logic gateâIn classical computing, a collection of transistors that input and output digital signals, and that can be represented and modeled using Boolean logic (rules that combine signals that can be either false, 0, or true, 1). LosslessâNo energy is dissipated. MeasurementâObservation of a quantum system, which yields only a single classical output and collapses the systemâs wave function onto the corresponding state. MicroprocessorâAn integrated circuit that contains the elements of a central processing unit on a single chip. NoiseâUnwanted variations in a physical system that can lead to error and unwanted results. Noise immunityâThe ability to remove noise (unwanted variations) in a signal to minimize error. Noisy intermediate-scale quantum (NISQ) computerâA quantum computer that is not error-corrected, but is stable enough to effectively carry out a computation before the system loses coherence. A NISQ can be digital or analog. Nondeterministic polynomial time (NP)âA specific computational complexity class. One-way functionsâFunctions that are easy to compute in one direction while being for all intents and purposes impossible to compute in the other direction. OverheadâThe amount of work (for example, number of operations) or quantity of resources (for example, number of qubits or bits) required to carry out a computational task; âcostâ is sometimes used synonymously. Post-quantum cryptographyâThe set of methods for cryptography that are expected to be resistant to cryptanalysis by a quantum computer. PrimitiveâA fundamental computational operation. ProgramâAn abstraction that refers to the sequence of instructions and rules that a computer must perform in order to complete one or more tasks (or solve one or more tasks) using a specific approach, or algorithm. Quantum annealerâAn analog quantum computer that operates through coherent manipulation of qubits by changing the analog values of the systemâs Hamiltonian, rather than by using quantum gates. In PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-4

particular, a quantum annealer performs computations by preparing a set of qubits in some initial state and changing their energy environment until it defines the parameters of a given problem, such that the final state of the qubits corresponds, with a high probability, to the answer of the problem. In general, a quantum annealer is not necessarily universalâthere are some problems that it cannot solve. Quantum communicationâThe transport or exchange of information as encoded into a quantum system. Quantum computationâThe use of quantum mechanical phenomena such as interference, superposition, and entanglement to perform computations that are roughly analogous to (although operate quite differently from) those performed on a classical computer. Quantum computerâThe general term for a device (whether theoretical or practically realized) that carries out quantum computation. A quantum computer may be analog or gate-based, universal or not, and noisy or fault tolerant. Quantum cryptographyâA subfield of quantum communication where quantum properties are used to design communication systems that may not be eavesdropped upon by an observer. Quantum information scienceâThe study of how information is or can be encoded in a quantum system, including the associated statistics, limitations, and unique affordances of quantum mechanics. Quantum interferenceâWhen states contributing to coherent superpositions combine constructively or destructively, like waves, with coefficients adding or subtracting. Quantum sensing and metrologyâThe study and development of quantum systems whose extreme sensitivity to environmental disturbances can be exploited in order to measure important physical properties with more precision than is possible with classical technologies. Quantum systemâA collection of (typically very small) physical objects whose behavior cannot be adequately approximated by equations of classical physics. QubitâA quantum bit, the fundamental hardware component of a quantum computer, embodied by a quantum object. Analogous to a classical bit (or binary digit), a qubit can represent a state corresponding to either zero or one; unlike a classical bit, a qubit can also exist in a superposition of both states at once, with any possible relative contribution of each. In a quantum computer, qubits are generally entangled, meaning that any qubitâs state is inextricably linked to the state of the other qubits, and thus cannot be defined independently. Run timeâThe amount of time required to carry out a computational task. In practice, the actual time required for a task depends heavily on the design of a device and of its particular physical embodiment, so run time may be described in terms of the number of computational steps. Scalable, fault-tolerant, universal gate-based quantum computerâA system that operates through gate-based operations on qubits, analogous to circuit-based classical computers, and uses quantum error correction to correct any system noise (including errors introduced by imperfect control signals, or unintended coupling of qubits to each other or to the environment) that occurs during the time frame of the calculation. SHA256âA specific hash function that outputs a 256-bit hash value regardless of the input size. PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-5

Shorâs algorithmâ A quantum algorithm developed by Peter Shor in the 1990s that, if implemented on a real quantum computer, would be capable of breaking the encryption used to protect Internet communications and data. SignalâAn electromagnetic field used to convey information in an electronic circuit. Software toolsâComputer programs that help a user design and compose a new computer program. Standard cell libraryâA set of predesigned and tested logic gates. SuperpositionâA quantum phenomenon where a system is in more than one state at a time. Mathematically speaking, the wave function of a quantum system in a superposition state is expressed as the sum of the contributing states, each weighted by a complex coefficient. Surface codeâA quantum error correction code (QECC) that is less sensitive to noise than other established QECCs, but has higher overheads. Symmetric encryptionâA type of encryption where a secret key, shared by both the sender and the receiver, is used to encrypt and decrypt communications. Systematic noiseâNoise resulting from signal interactions that is always present under certain conditions and could in principle be modeled and corrected. Transport Layer Security (TLS) handshakeâThe most common key exchange protocol, used to protect Internet traffic. Unitary operationâAn algebraic operation on a vector that preserves the vector length. Universal computerâA computer that can perform any computation that could be performed by a Turing machine. Wave functionâA mathematical description of the state of a quantum system, so named to reflect their wave-like characteristics. Wave-particle dualityâThe phenomenon where a quantum object is sometimes best described in terms of wave-like properties and sometimes in terms of particle-like properties. PREPUBLICATION COPY â SUBJECT TO FURTHER EDITORIAL CORRECTION I-6