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Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing applications that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of quantum computing systems can be achieved by breaking the abstractions between these layers. We review several works along this line, including two hardware-aware compilation optimizations that break the quantum Instruction Set Architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions., Invited paper by Proceedings of IEEE special issue

Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error events were extracted using fast, mid-circuit measurements and resets of the physical qubits. Among the error decoders we considered, we introduce a perfect matching decoder that was calibrated from measurements containing up to size-4 correlated events. To compare the decoders, we used a partial post-selection scheme shown to retain ten times more data than full post-selection. We observed logical errors per round of $2.2\pm0.1\times10^{-2}$ (decoded without post-selection) and $5.1\pm0.7\times10^{-4}$ (full post-selection), which was less than the physical measurement error of $7\times10^{-3}$ and therefore surpasses a pseudo-threshold for repeated logical measurements., 16 pages, 14 figures, 5 tables, for peer-review

Leakage is a particularly damaging error that occurs when a qubit leaves the defined computational subspace. Leakage errors limit the effectiveness of quantum error correcting codes by spreading additional errors to other qubits and corrupting syndrome measurements. The effects of leakage errors on the surface code has been studied in various contexts. However, the effects of a leaked data qubit versus a leaked ancilla qubit can be quite different. Here, we study the effects of data leakage and ancilla leakage separately. We show that data leakage is much less damaging. We show that the surface code maintains its distance in the presence of leakage by either confining leakage to data qubits or eliminating aniclla qubit leakage at the critical fault location. We also introduce new techniques for handling leakage by using gates with one-sided leakage and by mixing two types of leakage reducing circuits: one to handle data leakage and one to handle ancilla leakage., Comment: comments welcome

Author(s): Pogorzelski, David; Nguyen, Uyen; McKay, Paula; Thabane, Lehana; Camara, Megan; Ramsey, Lolita; Seymour, Rachel; Goodman, J Brett; McGee, Sheketha; Fraifogl, Joanne; Hudgins, Andrea; Tanner, Stephanie L; Bhandari, Mohit; Slobogean, Gerard P; Sprague, Sheila; PREP-IT Investigators Executive Committee:; Steering Committee; Adjudication Committee; Data and Safety Monitoring Committee; Research Methodology Core; Patient Centred Outcomes Core; Orthopaedic Surgery Core; Operating Room Core; Infectious Disease Core; Military Core; McMaster University Methods Center; University of Maryland School of Medicine Administrative Center; University of Maryland School of Pharmacy, The PATIENTS Program; PREP-IT Clinical Sites: Lead Clinical Site (Aqueous-PREP and PREPARE); Aqueous-PREP and PREPARE; Aqueous-PREP; PREPARE; PREP-IT Investigators Executive Committee | Abstract: IntroductionPragmatic trials in comparative effectiveness research assess the effects of different treatment, therapeutic, or healthcare options in clinical practice. They are characterized by broad eligibility criteria and large sample sizes, which can lead to an unmanageable number of participants, increasing the risk of bias and affecting the integrity of the trial. We describe the development of a sampling strategy tool and its use in the PREPARE trial to circumvent the challenge of unmanageable work flow.MethodsGiven the broad eligibility criteria and high fracture volume at participating clinical sites in the PREPARE trial, a pragmatic sampling strategy was needed. Using data from PREPARE, descriptive statistics were used to describe the use of the sampling strategy across clinical sites. A Chi-square test was performed to explore whether use of the sampling strategy was associated with a reduction in the number of missed eligible patients.Results7 of 20 clinical sites (35%) elected to adopt a sampling strategy. There were 1539 patients excluded due to the use of the sampling strategy, which represents 30% of all excluded patients and 20% of all patients screened for participation. Use of the sampling strategy was associated with lower odds of missed eligible patients (297/4545 (6.5%) versus 341/3200 (10.7%) p l 0.001).ConclusionsImplementing a sampling strategy in the PREPARE trial has helped to limit the number of missed eligible patients. This sampling strategy represents a simple, easy to use tool for managing work flow at clinical sites and maintaining the integrity of a large trial.

Hardware efficient transpilation of quantum circuits to a quantum devices native gateset is essential for the execution of quantum algorithms on noisy quantum computers. Typical quantum devices utilize a gateset with a single two-qubit Clifford entangling gate per pair of coupled qubits, however, in some applications access to a non-Clifford two-qubit gate can result in more optimal circuit decompositions and also allows more flexibility in optimizing over noise. We demonstrate calibration of a low error non-Clifford Controlled-$\frac{\pi}{2}$ phase (CS) gate on a cloud based IBM Quantum computing using the Qiskit Pulse framework. To measure the gate error of the calibrated CS gate we perform non-Clifford CNOT-Dihedral interleaved randomized benchmarking. We are able to obtain a gate error of $5.9(7) \times 10^{-3}$ at a gate length 263 ns, which is close to the coherence limit of the associated qubits, and lower error than the backends standard calibrated CNOT gate., Comment: 9 pages, 4 figures, references are updated, QPT curve in the Fig. 2 is updated based on new analysis procedure detailed in Appendix B. Conclusions unchanged

We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values as high as 16. The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system. It quantifies the largest random circuit of equal width and depth that the computer successfully implements. Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting toolchains are expected to have higher quantum volumes. The quantum volume is a pragmatic way to measure and compare progress toward improved system-wide gate error rates for near-term quantum computation and error-correction experiments., Comment: 12 pages, 8 figures, closer to published version

In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such a layout is particularly suitable for superconducting qubit architectures to minimize frequency collisions and crosstalk. In some cases, frequency collisions can be reduced by several orders of magnitude. The heavy hexagon code is a hybrid surface/Bacon-Shor code mapped onto a (heavy) hexagonal lattice whereas the heavy square code is the surface code mapped onto a (heavy) square lattice. In both cases, the lattice includes all the ancilla qubits required for fault-tolerant error-correction. Naively, the limited qubit connectivity might be thought to limit the error-correcting capability of the code to less than its full distance. Therefore, essential to our construction is the use of flag qubits. We modify minimum weight perfect matching decoding to efficiently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity. Simulations show that high threshold values for both codes can be obtained using our decoding protocol. Further, our decoding scheme can be adapted to other topological code families., 20 pages, 21 figures, Comments welcome! V2 conforms to journal specifications

Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, which is efficient and uses a small stabilizer circuit. In some regimes, we show that the overhead can be improved by several orders of magnitude., 26 pages, 17 figures, 5 tables. Comments welcome! v2 (published version): quantumarticle documentclass and expanded discussions on the fault-tolerant schemes

Ensuring that patients adhere to prescribed medication remains an important challenge in global health. While technology has been utilized to monitor and improve adherence, solutions to date have been too costly for large-scale deployment in developing regions. This paper describes 99DOTS, a low-cost approach for tracking adherence using a combination of paper packaging and low-end mobile phones. Every day, patients reveal an unpredictable phone number behind the pills and send a free call to that number to indicate that drugs were dispensed and taken. Within five years of its inception, 99DOTS has become a standard of care for tuberculosis in India and has enrolled over 200,000 patients. We provide a holistic account of the project's evolution, including its iterative design, scaled implementation, and lessons learned along the way. We hope this account will serve as a useful case study for anyone seeking to establish and scale new low-cost technologies for a global audience.

The concept of quantum computing has inspired a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. With experimental demonstrations stretching back more than two decades, the quantum computing community has achieved a major milestone over the past few years: the ability to build systems that are stretching the limits of what can be classically simulated, and which enable cloud-based research for a wide range of scientists, thus increasing the pool of talent exploring early quantum systems. While such noisy near-term quantum computing systems fall far short of the requirements for fault-tolerant systems, they provide unique test beds for exploring the opportunities for quantum applications. Here, we highlight an IBM-specific perspective of the facets associated with these systems, including quantum software, cloud access, benchmarking quantum systems, error correction and mitigation in such systems, understanding the complexity of quantum circuits, and how early quantum applications can run on near-term quantum computers.

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that preserve them. Such states are obtained by stabilizer circuits (consisting of CNOT, Hadamard and Phase gates) and can be represented compactly on conventional computers using $O(n^2)$ bits, where $n$ is the number of qubits. As an additional application, the work by Aaronson and Gottesman suggests the use of superpositions of stabilizer states to represent arbitrary quantum states. To aid in such applications and improve our understanding of stabilizer states, we characterize and count nearest-neighbor stabilizer states, quantify the distribution of angles between pairs of stabilizer states, study succinct stabilizer superpositions and stabilizer bivectors, explore the approximation of non-stabilizer states by single stabilizer states and short linear combinations of stabilizer states, develop an improved inner-product computation for stabilizer states via synthesis of compact canonical stabilizer circuits, propose an orthogonalization procedure for stabilizer states, and evaluate several of these algorithms empirically., 38 pages, 10 figures, 2 Appendices. arXiv admin note: substantial text overlap with arXiv:1210.6646

Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental challenge. Until now, no clear definitions for fault-tolerantly preparing GKP states have been provided. Without careful consideration, a small number of faults can lead to large uncorrectable shift errors. After proposing a metric to compare approximate GKP states, we provide rigorous definitions of fault-tolerance and introduce a fault-tolerant phase estimation protocol for preparing such states. The fault-tolerant protocol uses one flag qubit and accepts only a subset of states in order to prevent measurement readout errors from causing large shift errors. We then show how the protocol can be implemented using circuit QED. In doing so, we derive analytic expressions which describe the leading order effects of the non-linear dispersive shift and Kerr non-linearity. Using these expressions, we show that to mitigate the non-linear dispersive shift and Kerr terms would require the protocol to be implemented on time scales four orders of magnitude longer than the time scales relevant to the protocol for physically motivated parameters. Despite these restrictions, we numerically show that a subset of the accepted states of the fault-tolerant phase estimation protocol maintain good error correcting capabilities even in the presence of noise., 30 pages, 9 figures. Comments welcome! v2 has been updated to conform to journal specifications. An additional appendix has been added to further clarify the noise model used in our simulations

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits., Comment: Contribution to the special issue of Quantum Science & Technology on "What would you do with 1000 qubits"

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the $X$- or the $Z$-basis. Given the connectivity of the lattice, we perform full characterization of the static $Z$-interactions within the set of five qubits, as well as dynamical $Z$-interactions brought along by single- and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove non-ideal $Z$ errors., Comment: 8 pages, 4 figures

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework., 5 pages, 1 eps figure, ((11,48,3)) code removed, encoding circuits added, typos corrected in codewords and elsewhere

Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more accurate and complete theory with new and more powerful possibilities for information processing. The goal of both classical and quantum information theory is to quantify the optimal rates of interconversion of different resources. These rates are usually characterized in terms of entropies. However, nonadditivity of many entropic formulas often makes finding answers to information theoretic questions intractable. In a few auspicious cases, such as the classical capacity of a classical channel, the capacity region of a multiple access channel and the entanglement assisted capacity of a quantum channel, additivity allows a full characterization of optimal rates. Here we present a new mathematical property of entropic formulas, uniform additivity, that is both easily evaluated and rich enough to capture all known quantum additive formulas. We give a complete characterization of uniformly additive functions using the linear programming approach to entropy inequalities. In addition to all known quantum formulas, we find a new and intriguing additive quantity: the completely coherent information. We also uncover a remarkable coincidence---the classical and quantum uniformly additive functions are identical; the tractable answers in classical and quantum information theory are formally equivalent. Our techniques pave the way for a deeper understanding of the tractability of information theory, from classical multi-user problems like broadcast channels to the evaluation of quantum channel capacities., Comment: 13 pages with 4 figures + 25 page appendix

The resonator-induced phase (RIP) gate is a multi-qubit entangling gate that allows a high degree of flexibility in qubit frequencies, making it attractive for quantum operations in large-scale architectures. We experimentally realize the RIP gate with four superconducting qubits in a three-dimensional (3D) circuit-quantum electrodynamics architecture, demonstrating high-fidelity controlled-Z (CZ) gates between all possible pairs of qubits from two different 4-qubit devices in pair subspaces. These qubits are arranged within a wide range of frequency detunings, up to as large as 1.8 GHz. We further show a dynamical multi-qubit refocusing scheme in order to isolate out 2-qubit interactions, and combine them to generate a four-qubit Greenberger-Horne-Zeilinger state., Comment: 5 pages, 4 figures in main text with 9 pages 4 figures in the supplemental material

Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for manipulating those circuits and, as such, have been limited to subgroups of the Clifford group. However, universal quantum computers require additional, non-Clifford gates to approximate arbitrary unitary transformations. We define a scalable randomized benchmarking procedure over $n$-qubit unitary matrices that correspond to protected non-Clifford gates for a class of stabilizer codes. We present efficient methods for representing and composing group elements, sampling them uniformly, and synthesizing corresponding $\mathrm{poly}(n)$-sized circuits. The procedure provides experimental access to two independent parameters that together characterize the average gate fidelity of a group element., 5+4 pages, 1 figure

Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the absence of noise, quantum and classical parity learning are easy and almost equally powerful, both information-theoretically and computationally. We show that in the presence of noise this story changes dramatically. Indeed, the classical learning problem is believed to be intractable, while the quantum version remains efficient. Depolarizing the qubits at the oracle's output at any constant nonzero rate does not increase the computational (or query) complexity of quantum learning more than logarithmically. However, the problem of learning from corresponding classical examples is the learning parity with noise problem, for which the best known algorithms have superpolynomial complexity. This creates the possibility of observing a quantum advantage with a few hundred noisy qubits. The presence of noise is essential for creating this quantum-classical separation.

The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code., The physical realization of a quantum computer requires built-in error-correcting codes that compensate the disruption of quantum information arising from noise. Here, the authors demonstrate a quantum error detection scheme for arbitrary single-qubit errors on a four superconducting qubit lattice.

The resonator-induced phase gate is a multi-qubit controlled-phase gate for fixed-frequency superconducting qubits. Through off-resonant driving of a bus resonator, statically coupled qubits acquire a state-dependent phase. However, photon loss leads to dephasing during the gate, and any residual entanglement between the resonator and qubits after the gate leads to decoherence. Here we consider how to shape the drive pulse to minimize these unwanted effects. First, we review how the gate's entangling and dephasing rates depend on the system parameters and validate closed-form solutions against direct numerical solution of a master equation. Next, we propose spline pulse shapes that reduce residual qubit-bus entanglement, are robust to imprecise knowledge of the resonator shift, and can be shortened by using higher-degree polynomials. Finally, we present a procedure that optimizes over the subspace of pulses that leave the resonator unpopulated. This finds shaped drive pulses that further reduce the gate duration. Assuming realistic parameters, we exhibit shaped pulses that have the potential to realize ~212 ns spline pulse gates and ~120 ns optimized gates with ~6e-4 average gate infidelity. These examples do not represent fundamental limits of the gate and in principle even shorter gates may be achievable., 13 pages, 10 figures

An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent estimates of the threshold are near some experimentally achieved gate fidelities. However, the landscape of threshold estimates includes pseudothresholds, threshold estimates based on a subset of components and a low level of the recursion. In this paper, we observe that pseudothresholds are a generic phenomenon in fault-tolerant computation. We define pseudothresholds and present classical and quantum fault-tolerant circuits exhibiting pseudothresholds that differ by a factor of $4$ from fault-tolerance thresholds for typical relationships between component failure rates. We develop tools for visualizing how reliability is influenced by recursive simulation in order to determine the asymptotic threshold. Finally, we conjecture that refinements of these methods may establish upper bounds on the fault-tolerance threshold for particular codes and noise models.

Compilers and computer-aided design tools are essential for fine-grained control of nanoscale quantum-mechanical systems. A proposed four-phase design flow assists with computations by transforming a quantum algorithm from a high-level language program into precisely scheduled physical actions.

Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the accuracy threshold and can increase overhead and experimental complexity, and these costs have not been thoroughly understood. Our work explores a variety of techniques for leakage-resilient, fault-tolerant error correction in the context of topological codes. Our contributions are threefold. First, we develop a leakage model that differs in critical details from earlier models. Second, we use Monte-Carlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform three-outcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulation results show that simple circuits with one extra CNOT per qubit and no additional ancillas reduce the accuracy threshold by less than a factor of 4 when leakage and depolarizing noise rates are comparable. This becomes a factor of 2 when the decoder uses 3-outcome measurements. Finally, when the physical error rate is less than 2 x 10^-4, placing LRUs after every gate may achieve the lowest logical error rates of all of the circuits we considered. We expect the closely related planar and rotated codes to exhibit the same accuracy thresholds and that the ideas may generalize naturally to other topological codes., 20 pages, 12 figures

In this paper, we analyze the performance of randomized benchmarking protocols on gate sets under a variety of realistic error models that include systematic rotations, amplitude damping, leakage to higher levels, and 1/f noise. We find that, in almost all cases, benchmarking provides better than a factor-of-two estimate of average error rate, suggesting that randomized benchmarking protocols are a valuable tool for verification and validation of quantum operations. In addition, we derive new models for fidelity decay curves under certain types of non-Markovian noise models such as 1/f and leakage errors. We also show that, provided the standard error of the fidelity measurements is small, only a small number of trials are required for high confidence estimation of gate errors., 13 pages, 11 figures

We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors, and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is `activated' on the otherwise unperturbed qubit subspace via a microwave drive. We implement this microwave-activated conditional-phase gate with a fidelity from quantum process tomography of 87%., 5 figures

Quantum error correction (QEC) is an essential step towards realising scalable quantum computers. Theoretically, it is possible to achieve arbitrarily long protection of quantum information from corruption due to decoherence or imperfect controls, so long as the error rate is below a threshold value. The two-dimensional surface code (SC) is a fault-tolerant error correction protocol} that has garnered considerable attention for actual physical implementations, due to relatively high error thresholds ~1%, and restriction to planar lattices with nearest-neighbour interactions. Here we show a necessary element for SC error correction: high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. The experiment is performed on a sub-section of the SC lattice with three superconducting transmon qubits, in which two independent outer code qubits are joined to a central syndrome qubit via two linking bus resonators. With all-microwave high-fidelity single- and two-qubit nearest-neighbour entangling gates, we demonstrate entanglement distributed across the entire sub-section by generating a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with fidelity ~94%. Then, via high-fidelity measurement of the syndrome qubit, we deterministically entangle the otherwise un-coupled outer code qubits, in either an even or odd parity Bell state, conditioned on the syndrome state. Finally, to fully characterize this parity readout, we develop a new measurement tomography protocol to obtain a fidelity metric (90% and 91%). Our results reveal a straightforward path for expanding superconducting circuits towards larger networks for the SC and eventually a primitive logical qubit implementation., Comment: 9 pages, 4 main figures, 3 extended data figures

We discuss how the presence of gauge sub-systems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not require entangled ancillary states and it can be implemented with nearest-neighbor two-qubit measurements. By using these methods, we prove a lower bound on the quantum accuracy threshold, 1.94 \times 10^{-4} for adversarial stochastic noise, that improves previous lower bounds by nearly an order of magnitude., 4 pages, 2 figures. v3: small revisions, appendix moved to chapter 5 in quant-ph/0703230

Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be {\em universal}; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic operations exists for these codes. This result strongly supports the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal fault-tolerant computation on additive codes., Comment: 12 pages; reference added to 0707.4000; minor revisions v3

The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. \textbf{A71}, 062323]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence ($LU\Leftrightarrow LC$) to include all stabilizer states represented by graphs with neither cycles of length 3 nor 4. To compare our result with Van den Nest et al.'s, we show that any stabilizer state of distance $\delta=2$ is beyond their criterion. We then further prove that $LU\Leftrightarrow LC$ holds for a more general class of stabilizer states of $\delta=2$. We also explicitly construct graphs representing $\delta>2$ stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with $2^m-1$ ($m\geq 4$) vertices using quantum error correcting codes which have non-Clifford transversal gates., Comment: Revised version according to referee's comments. To appear in Physical Review A

The assumption of maximum parallelism support for the successful realization of scalable quantum computers has led to homogeneous, ``sea-of-qubits'' architectures. The resulting architectures overcome the primary challenges of reliability and scalability at the cost of physically unacceptable system area. We find that by exploiting the natural serialization at both the application and the physical microarchitecture level of a quantum computer, we can reduce the area requirement while improving performance. In particular we present a scalable quantum architecture design that employs specialization of the system into memory and computational regions, each individually optimized to match hardware support to the available parallelism. Through careful application and system analysis, we find that our new architecture can yield up to a factor of thirteen savings in area due to specialization. In addition, by providing a memory hierarchy design for quantum computers, we can increase time performance by a factor of eight. This result brings us closer to the realization of a quantum processor that can solve meaningful problems., 12 pages, 8 figures, To appear in the International Symposium on Computer Architecture (ISCA-33), Boston, MA, 2006

Recent experimental advances have demonstrated technologies capable of supporting scalable quantum computation. A critical next step is how to put those technologies together into a scalable, fault-tolerant system that is also feasible. We propose a Quantum Logic Array (QLA) microarchitecture that forms the foundation of such a system. The QLA focuses on the communication resources necessary to efficiently support fault-tolerant computations. We leverage the extensive groundwork in quantum error correction theory and provide analysis that shows that our system is both asymptotically and empirically fault tolerant. Specifically, we use the QLA to implement a hierarchical, array-based design and a logarithmic expense quantum-teleportation communication protocol. Our goal is to overcome the primary scalability challenges of reliability, communication, and quantum resource distribution that plague current proposals for large-scale quantum computing., 13 pages, 9 figures, 2 tables. To appear in the 2005 International Symposium on Microarchitecture (MICRO-38)

The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we prove three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find there does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank (arXiv:cs/0610159)., Comment: 11 pages, 1 figure